Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80. But 76 goes up to 80. There are many ways to round. This is the most common method: • Decide which is the last digit to keep • Leave it the same if the next digit is less than 5 (this is called rounding down) • Increase it by 1 if the next digit is 5 or more (this is called rounding up)

Rounding Numbers

Rounding numbers means adjusting the digits of a number in such a way that it gives an approximate value. This value is an easier representation of the given number. For example, the population of a town could be easily expressed as 700,000 rather than 698,869. Rounding numbers makes calculations simpler, resulting in a figure that is easy to remember. However, rounding of numbers is done only for those numbers where the exact value does not hold that much importance.

Let us learn more about rounding numbers, to get a better idea of how to round off a number to the nearest ten, hundred, thousand, and so on.

What is Rounding Numbers?

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Let us understand the concept of rounding through an example. Susan covered a distance of 2.05 miles, which she noted as approximately 2 miles. How did she estimate the approximate value of the distance she covered? Why didn't she record her distance as 3 miles? Noting an approximate and simpler value for a given number helps to make the analysis and calculations easier while using that number. Here, Susan noted an easier value to keep a record of the distance travelled by her.

Numbers can be rounded to different digits, like, they can be rounded to the nearest ten, hundred, thousand, and so on. For example, 541 rounded to the nearest hundred is 500 because 541 is much closer to 500 than 600. While rounding a number, we need to know the answer to the question,' What are we rounding the number to?' Suppose we need to round the number 7456. When 7456 is rounded to the nearest ten, it becomes 7460, but when 7456 is rounded to the nearest thousand, then it becomes 7000. A few examples like these are given below.

Rounding Numbers to the Nearest Ten

Rounding numbers to the nearest ten means we need to check the digit to the right of the tens place, that is the ones place. For example, when we round the number 7486 to the nearest ten, it becomes 7490.

Rounding Numbers to the Nearest Hundred

Rounding numbers to the nearest hundred means we need to check the digit to the right of the hundreds place, that is, the tens place. For example, when 7456 is rounded to the nearest hundred, it becomes 7500.

Round-Up and Round-Down

While rounding is a generic term, we usually use the terms, 'round up' or 'round down' to specify if the number has increased or decreased after rounding. When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

Rules for Rounding Numbers

How do we decide which value is more appropriate between different approximated values of a number? Should we choose a number greater than the given number or go with the smaller one?

  • We first need to know what our rounding digit is. This digit is the one that will ultimately be affected.
  • After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit.
  • If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.
  • If the digit to the right is 5 or more than 5, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.

a.) If the bill at a furniture store comes to $3257, what is the rounded value of the amount to the nearest ten?

b.) If the bill comes to $3284, what would be the rounded value of this amount to the nearest ten?

Rounding Numbers to the nearest ten

a.) $3257 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 5. Now, let us check the number to the right, which is 7 in this case. Since 7 is more than 5, we will replace 5 with 6, and all the digits to the right will become 0. So, $3257 is rounded to $3260.

b .) Here, $3284 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 8. Now, let us check the number to the right, which is 4 in this case. Since 4 is less than 5, 8 will remain unchanged and the remaining digits to the right will change to 0. So, $3284 is rounded to $3280.

How to Round Off Whole Numbers?

Whole numbers are rounded off by following the same rules mentioned above. Let us apply the rules with the help of an example.

Example: Round 7234 to the nearest hundred.

  • Step 1: Mark the place value up to which the number needs to be rounded. Here, 7234 needs to be rounded to the nearest hundred. So, we mark 2 which is in the hundreds place.
  • Step 2: Observe and underline the digit to the right of 2, that is the tens place. Here, it is 3, so we will mark it as: 7 2 3 4
  • Step 3: Compare the underlined digit with 5.
  • Step 4: If it is less than 5, all the digits towards its right including it will be replaced by 0 while the digit in the hundreds place (2) will remain unchanged. Therefore, 7234 will be rounded to 7200.

Note: If the number to the right of 2 was 5 or greater than 5, then all the digits to the right of 2 would become 0, and 2 would be increased by 1 changing it to 3. For example, if the given number was 7268, then it would be rounded up to 7300 (to the nearest hundred).

How to Round Off Fractions?

Fractions are numerical values that represent a part of a whole. They are written in the form of (p/q), where q is not equal to zero. A simple rule to round fractions to the nearest whole number is to compare proper fractions to 1/2. In case if it is an improper fraction, we need to change it to a mixed fraction and then compare the fractional part with 1/2. We round up the fraction if it is equal to or greater than 1/2, and we round down if it is less than 1/2. Let us understand rounding off fractions to the nearest whole number using the following example.

Example: Round the given fractions to the nearest whole number:

b.) \(6 \dfrac{2}{5}\)

a.) We can round off a proper fraction to the nearest whole number by following the simple rule of comparing it with 1/2. Since 3/4 is greater than 1/2, it will be rounded off to 1.

b.) \(6 \dfrac{2}{5}\) is a mixed fraction. Here, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 6 aside, we will check if 2/5 is greater than or less than 1/2. Since 2/5 is less than 1/2, we will round the given mixed fraction to 6.

c.) 21/5 is an improper fraction, so we will convert it to a mixed fraction. This will make it \(4 \dfrac{1}{5}\). Now, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 4 aside, we will check if 1/5 is greater than or less than 1/2. Since 1/5 is less than 1/2, we will round the given fraction to 4.

How to Round Off Decimal Numbers?

A decimal number is a combination of a whole number part and a fractional part separated by a decimal point. Rounding decimal numbers works in the same way as we round whole numbers although we need to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal point as well as the digits given after the decimal point. Observe the decimal place value chart to understand this better.

Decimal Place Value Chart

We usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. However, sometimes we even need to round a decimal to the nearest whole number. In this case, we check the tenths digit. If it is equal to or more than 5, then the given number is rounded up, and if the tenths digit is less than 5 then the given number is rounded down.

Example 1: Round 5.62 to the nearest whole number.

Solution: Since we need to round this decimal to the nearest whole number, we will check the tenths digit. In this case, the tenths digit is 6, which is more than 5. So, the number will be rounded to 6. In other words, 5.62 ≈ 6

In the other cases, where we need to round decimals to the nearest tenths, hundredths, or thousandths, we need to remember the simple rule of marking the number up to which we are rounding and checking the number to its right. For example, when we round decimal numbers to the nearest hundredths, we need to check the thousandths place. Similarly, if we need to round decimal numbers to the nearest tenths, we need to check the hundredths place. If the number to be checked is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. Let us understand this with an example.

Example 2: Round 0.439 to the nearest hundredths.

Solution: In this case, the digit to the right of the hundredths place, that is, the thousandths place is 9, which is more than 5. So, we will add 1 to the digit in the hundredths place, that is, 3 + 1 = 4, and write 0 in the digits to the right. So, 0.439 will be rounded to 0.44

Note: It should be noted that when we round a decimal number to the nearest hundredth, the round decimal fraction is said to be correct to two places of decimal. In other words, if we are asked to round off a number to two decimal places, it means we need to round it to the nearest hundredths. Similarly, when we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths .

Tips on Rounding Numbers:

The following tips are helpful in solving questions related to rounding numbers.

  • While rounding numbers, we always need to check the digit to the right of the rounding number. If it is less than 5, the rounding number remains the same and the following digits are changed to 0. If the digit to the right is equal to or more than 5, we increase the rounding digit by 1 and the following numbers are changed to 0.
  • When we round decimal numbers, we usually come across terms like round to the nearest tenths, hundredths, thousandths, and so on.
  • When we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths, similarly, when we are asked to round off a number up to two decimal places, it means we need to round it to the nearest hundredths.
  • When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

Related Topics

Check out the following links related to rounding numbers.

  • What are Numbers?
  • Number Line

Rounding Numbers Examples

Example 1: Round 321 to the nearest hundred, using the rules for rounding numbers.

While rounding numbers to the nearest hundred, we check the digit in the tens place. In this case, it is 2, which is less than 5. Therefore, this digit and all the digits to its right will change to 0 and the digit in the hundreds place will remain the same. Therefore, 321 is rounded to 300. This can be expressed as 321 ≈ 300.

Example 2: Using the rules of rounding numbers, round \(6 \dfrac{1}{5}\) to the nearest whole number.

A mixed fraction is made up of a whole number part and a fractional part. When we round off mixed fractions to a whole number, we compare the fractional part with 1/2. In this case, 6 is the whole number part and 1/5 is the fractional part. Now, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 6 aside, we will check if 1/5 is greater than or less than 1/2. Since 1/5 is less than 1/2, we will round the given fraction to 6. Therefore \(6 \dfrac{1}{5}\) ≈ 6

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Practice Questions

Faqs on rounding numbers, what is rounding numbers in math.

Rounding a number means converting a number to a simpler value such that its value remains close to what it was. Rounding numbers makes calculation simpler and converts figures to an approximate value which is easier to remember. For example, if the population of a town is 692,769, it can be rounded to 700,000, and it would be easier to remember an approximate figure of 700,000 rather than the real figure.

What are the Rules for Rounding Off Decimal Numbers?

There are some basic rules that need to be followed for rounding decimal numbers. They are similar to rounding the other numbers, however, we need to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal point as well as the digits given after the decimal point. In other words, we usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. Sometimes, we even round the decimal to the nearest whole number. In all these cases, we use the following rules.

For example, if we need to round 0.476 to the nearest tenths, it means we will check the digit to its right, which is the hundredths digit. In this case, it is 7 which is more than 5. Therefore, 0.476 will be rounded up to 0.5 to the nearest tenths.

What is 62 Rounded to the Nearest ten?

When 62 is rounded to the nearest 10, we need to check the digit in ones place. Here, it is 2, which is less than 5. So, 6 will remain the same, and 2 will change to 0. Therefore, 62 rounded to the nearest ten will be 60.

Where do we Use Rounding of Numbers in Real Life?

In real life, we usually round numbers whenever the exact value is not so important. For example, if we want to know the approximate amount that we spent in a grocery store, or the amount while estimating a budget, or while expressing larger figures like the population of a town. We estimate the amount to simpler numbers so that calculation becomes easier. For example, if we know that our monthly expenditure would be around $590, we can easily round the number to $600 which is a figure that is easier to remember.

How to Round Numbers to the Nearest Tenth?

If we need to round decimal numbers to the nearest tenth, we need to check the digit to the right of the digit on the tenths place, which is the hundredths place. If the number in the hundredths place is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. For example, to round 56.73 to the nearest tenth, we will check the digit in the hundredths place, which is 3 in this case. Since 3 is less than 5, 7 will remain the same and the following digits will become 0. So, 56.73 rounded to the nearest tenths will become 56.7

What is the Purpose of Rounding Numbers?

Rounding numbers means adjusting the digits of a number such that it gives an estimated result. Rounding a number gives an approximate value which is a simpler and a shorter representation of the given number. For example, if the population of a town is 498,821, it would be easier if it is expressed as 500,000. This helps in making calculations easier with a figure that is easy to remember and note. However, rounding of numbers is done in those cases where the exact value does not hold that much importance.

What is Rounding Numbers to the Nearest Ten?

When we round numbers to the nearest ten, we first mark the digit in the tens place. Then, we observe the 'ones' place, which lies to the right of the tens column. According to the rules, if the digit in the ones place is 5 or more than 5, we add 1 to the digit in the tens place, that is, we increase the tens place by 1 and write 0 in all the digits to the right. However, If the digit in the ones place is less than 5, we write 0 in the ones place and in all the places to its right, and the digit in the tens place remains the same. For example, if we need to round 389 to the nearest ten, we will check the digit in ones place. In this case, it is 9 which is more than 5. So, 8 will change to 9, and 389 will be rounded to 390.

How to Round Numbers to the Nearest 100?

In order to round numbers to the nearest hundred, we need to check the digit to its right, which is the tens place. For example, if we need to round 3270 to the nearest 100, we will check the tens place. In this case, it is 7, which means the digit in the hundreds place will be increased by 1, that is, 2 will become 3 and the remaining digits to its right will become zero. Therefore, 3270 will be rounded up to 3300.

How to Round Numbers to the Nearest Thousand?

When we round numbers to the nearest thousand, we check the digit in the hundreds place. If the digit in the hundreds place is 5 or more than 5, we increase the thousands place by 1 and write 0 in all the digits to the right. In case, if the digit in the hundreds place is less than 5, we write 0 in the hundreds place and in all the places to its right, while the digit in the thousands place remains as it is. For example, let us round 76431 to the nearest thousand. We will first check the digit in the hundreds place. In this case, it is 4, which is less than 5. So, 6 will remain as it is and all the digits to the right will become 0. Therefore, 76431 will be rounded to 76000.

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What Is Rounding in Math: Rounding Numbers Explained for Teachers, Parents and Kids

Sophie bartlett.

Here you can find out about rounding numbers, why it is used, and how you can help children understand it. Rounding digits requires a solid understanding of place value. Students will need to be aware of the number of decimal places or significant figures a value has to go from that original number to a rounded number.

What is rounding in math?

Rounding to the nearest 10, rounding to the nearest 100 , rounding to the nearest integer or whole number , rounding to the nearest tenth, when do children learn about rounding numbers in elementary school, how does rounding numbers relate to other areas of math, rounding in math in real life, 3 worked examples for rounding in math, 5 rounding in math practice questions and answers, rounding numbers check for understanding.

Use this quiz to check grades 3-5 students' understanding of rounding numbers

Rounding numbers makes them ‘easier’ to use or understand while also keeping the number close to its original value. Instead of using exact numbers, simpler values can be used.

For example, 189.2 could be rounded to 189, 190 or 200, depending on the degree of accuracy required. In context, $19.99 could be rounded to $20; 56 minutes could be rounded to an hour.

Students first officially encounter this in 3rd grade. In order to round to the nearest 10, children must first understand what multiples of ten are (numbers in the ten times table, or numbers divisible by 10, e.g. 30, 250, 3430 etc.).

They must then be able to identify which multiples of 10 a given number is between, e.g. 218 is between 210 and 220 (a number line is often used for this, as seen below).

rounding maths 1

Finally, children should then identify the nearest multiple of 10 – in this case, 220. Children should round numbers up If they lie halfway between two multiples (and therefore end in a 5).

In this case, the number will always round up to the multiple of 10 above it.

Students first officially encounter this in 3rd grade. In order to round to the nearest 100, children must first understand what multiples of 100 are (numbers in the 100 times table, or numbers divisible by 100, e.g. 500, 2500, 34300 etc.).

They must then be able to identify which multiples of 100 a given number is between, e.g. 218 is between 200 and 300 (a number line is often used for this).

Finally, children should then identify the nearest multiple of 100 – in this case, 200. If a number lies halfway between (and therefore ends in 50), the number will always round up to the multiple of 100 above it.

Students following Common Core State Standards first officially encounter this in 5th grade. Children must be able to identify which whole numbers, also termed ‘integers’, are either side of a decimal number.

For example, 6.2 is between 6 and 7; 14.92 is between 14 and 15 (again, a number line is a useful tool in helping to visualize this).

They should then work out which of these integers is closer to the decimal number using the numbers to the right of the decimal point.

As before, if the decimal number is exactly halfway between two integers (such as 3.5), it will always round up to the integer above it (in this case, 4).

Students first officially encounter this in 5th grade. In a similar fashion to the methods previously explained, children should be able to identify the tenths either side of a decimal number.

For example, 4.62 is between 4.6 and 4.7; 5.213 is between 5.2 and 5.3.

Sometimes these decimal numbers could be written with a 0 in the hundredths place and/or thousandths place value to make it easier to work out the surrounding tenths: in the first example above, 4.62 has 62 hundredths and is therefore between 60 hundredths (4.60, or 4.6) and 70 hundredths (4.70, or 4.7).

Finally, children should then work out which of these tenths is closer to the decimal number. As the nearest hundredth of 4.62 is 60, the nearest tenth is will be 6.

Once again, if the decimal number is exactly halfway between two tenths (such as 2.75), it will always round up to the tenth above it (in this case, 2.8).

Schools following Common Core:

In 3rd grade children are taught to:

  • Round any number to the nearest 10 or 100.
  • Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3

This progresses to 4th grade , where students are expected to:

  • Use place value understanding to round whole numbers to any place.
  • Assess the reasonableness of answers using mental computation and estimation strategies including rounding

And finally to 5th grade:

  • Use place value understanding to round decimals to any place. 

Other schools:

Depending on the state curriculum or standards a school is using, rounding may be taught in different grade levels. If your child is in a district that follows the Texas Essential Knowledge and Skills, rounding to the 10s and 100s begins in 3rd grade, rounding to the nearest hundred thousand is taught in 4th grade, and rounding decimals to the nearest tenth and hundredth is introduced in 5th grade.

rounding numbers bofu slide min

Rounding is used to estimate and check answers to problems.

For example, when multiplying decimals (such as 0.7 x 0.8), students may misinterpret the magnitude of the answer (in this case, perhaps 5.6).

Rounding the decimals and then multiplying (0.7 and 0.8 both round to 1, and 1 x 1 = 1) helps to check the accuracy of the answer (5.6 is much larger than 1, so the multiplication could be recalculated to achieve 0.56, which is much closer to 1).

Rounding is useful in real life.  For example, rounding remainders appropriate to the context: 

  • Rounding up: A mini bus holds 12 people and you need to transport 161 people. 161 ÷ 12 = 13.4, but you can’t have 0.4 of a mini bus, so you would need to round up to work out that 14 mini buses would be needed.
  • Rounding down: An egg carton holds 12 eggs and you have 161 eggs to package. 161 ÷ 12 = 13.4, but you can’t have 0.4 of an egg carton and they all must be fully filled, so you would need to round down to work out that 13 egg cartons would be needed.

In the first example, 13.4 wouldn’t conventionally be rounded up, but in the context of the problem, it was required to be.

Here’s a fun real-life activity parents could get their children to do during their next trip to the grocery store: tell your child you have $15 to spend on fruit and vegetables and they need to determine how many items you could purchase by rounding up their prices to the nearest whole dollar. Find out how accurate their estimates were when you check out!

1) Round 218 to the nearest multiple of 10.

rounding maths 2

Answer: 220

2) Round 42.4 to the nearest whole number.

rounding maths 3

3) Round 1.15 to the nearest tenth.

rounding maths 4

Answer: 1.2 (any number that is halfway between always rounds up)

Once children are confident with the concept through using a number line, they may be able to round by just looking at two digits:

  • When rounding to the nearest 10, you only need to look at the tens place (to identify if it will change or not) and the ones place (to identify if it will round the tens digit up or down) – e.g. in 3,2 68 , the 8 rounds the 6 ‘up’ to a 7, becoming 3,2 7 0
  • When rounding to the nearest 100, you only need to look at the hundreds digit (to identify if it will change or not) and the tens digit (to identify if it will round the hundreds digit up or down) – e.g. in 742, 12 5, the 2 rounds the 1 ‘down’ to stay as 1, becoming 742, 1 00
  • When rounding to the nearest 1000, you only need to look at the digits in the thousands and hundreds place – e.g. in 4 2 , 5 17, the 5 rounds the 2 ‘up’ to a 3, becoming 4 3 ,000

… and so on.

Q: Circle the number which is closer to 1000 and explain how you know: 996, 1006

Answer: 996 is closer to 1000 as it is only 4 away, whereas 1006 is 6 away.

Q: Round 73,482 to the nearest: a) 10,000   b) 1,000   c) 100

Answer: a) 70,000   b) 73,000 c)   73,500

Q: Round 3,593,174 to the nearest million.

Answer: 4,000,000

Q: John thinks of a whole number. He multiplies it by 4. He rounds his answer to the nearest 10. The result is 50. Write all the possible numbers that John could have started with.

Answer: 12 or 13 (Any number from 45 – 54 would be rounded to 50 when being rounded to the nearest 10. There are only two multiples of 4 within that range: 48 and 52. Dividing those by 4 gives you 12 and 13)

Q: Round each of these numbers to the nearest 100: a) 20,906   b) 2,090.6   c) 209.06

Answer: a) 20,900   b) 2,100   c) 200

See relevant section above: rounding to the nearest 10, 100, whole number, tenth or worked examples for rounding in math

0.5 should be rounded up to the next whole number

In order to round to the nearest 1000, children must first understand what multiples of 1000 are (numbers in the 1000 times table, or numbers divisible by 1000, e.g. 5000, 25000, 343000 etc.). They must then be able to identify which multiples of 1000 a given number is between, e.g. 2185 is between 2000 and 3000 (a number line is often used for this). Finally, children should then identify the nearest multiple of 1000 – in this case, 2000. If a number lies halfway between (and therefore ends in 500), the number will always round up to the multiple of 1000 above it.

Wondering about how to explain other key math vocabulary to children? Check out our Math Dictionary For Kids and our What is Math Mastery? blog.

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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

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Simple Rules for Rounding Numbers Correctly

Easy Steps to Help You Round Numbers Quickly and Correctly

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Rounding numbers is important when you want to preserve significant figures in calculations and to record long numbers. In everyday life, rounding is useful for calculating a tip or dividing the bill among diners when eating at a restaurant, or when you're estimating the amount of cash you'll need for a trip to the grocery store.

Rules for Rounding Whole Numbers

When rounding numbers, you must first understand the term "rounding digit." When working with whole numbers and rounding to the closest 10, the ​ rounding digit is the second number from the right—or the 10's place. When rounding to the nearest hundred, the third place from the right is the rounding digit—or the 100's place.

First, determine what your rounding digit is and then look to the digit at the right side.

  • If the digit is 0, 1, 2, 3, or 4, do not change the rounding digit. All digits that are on the righthand side of the requested rounding digit become 0.
  • If the digit is 5, 6, 7, 8, or 9, the rounding digit rounds up by one number. All digits that are on the righthand side of the requested rounding digit will become 0.

Rounding Rules for Decimal Numbers

Determine what your rounding digit is and look to the right side of it.

  • If that digit is 4, 3, 2, or 1, simply drop all digits to the right of it.
  • If that digit is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of it.

Some teachers prefer another method, sometimes referred to as the "Banker's Rule," which provides more accuracy. When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e., round off to the nearest even digit). Following this rule, 2.315 and 2.325 both round to 2.32—instead of 2.325 rounding up to 2.33—when rounded off to the nearest 100th. The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.

Examples of How to Round Numbers

765.3682 becomes:

  • 1,000 when rounding to the nearest 1,000
  • 800 when rounding to the nearest 100
  • 770 when rounding to the nearest 10
  • 765 when rounding to the nearest one (1)
  • 765.4 when rounding to the nearest 10th
  • 765.37 when rounding to the nearest 100th
  • 765.368 when rounding to the nearest (1,000th)

Rounding comes in handy when you are about to leave a tip at a restaurant. Let's say your bill is $48.95. One rule of thumb is to round to $50 and leave a 15 percent tip. To quickly figure out the tip, say that $5 is 10 percent , and to reach 15 percent you need to add half of that, which is $2.50, bringing the tip to $7.50. If you want to round up again, leave $8—if the service was good, that is.

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round or nearly round .

of, relating to, or used for making something round .

turning, curving, or circling around.

pertaining to the mathematical process of rounding: a rounding error.

the act or process of making something round.

Mathematics .

the process of replacing a number by another number of approximately the same value but having fewer digits: To the nearest dollar, the rounding of $27.68 yields $28.

a similar process that specifies one of various rules. Generally, the number is first truncated to one or two digits more than is desired; then the last one or two digits are adjusted in a specified way in order to reflect the magnitude of the original number. In rounding the final digits, 0–4 are simply dropped, 6–9 are dropped after the preceding digit is increased by 1, and 5 is handled in various ways depending on the surrounding digits and the particular convention being followed. : Compare truncate (def. 2) .

Origin of rounding

Words nearby rounding.

  • roundheaded
  • round herring
  • rounding error
  • round kumquat
  • Round Lake Beach

Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2024

How to use rounding in a sentence

In her findings, 63 percent of temperature samples were biased by this double- rounding .

Scrapping the quail research might score some easy political points, but it was a rounding error on these agencies’ budgets.

Still, Microsoft sees a lot, so any difference with actual numbers is likely a rounding error.

At Trilogy, the work of leaders includes investing in employees’ growth and continuing the “ rounding ” that has long kept executives close to what’s happening at the front lines.

If we don’t do something to offset the damage to our retirement system, today’s problems could end up looking like a rounding error compared to what the future holds.

Democrats were working hard to pass a budget in a divided government, and Yee was charged in part with rounding up the votes.

And what could be more honorable than rounding up your besties to pay homage to a hallowed pop deity?

The White House has been rounding up senators to vouch for her.

rounding out the Big Three, GM was also up 15 percent year over year.

By August we were rounding up any young man we found, whether we were looking for him or not.

On rounding a point a few minutes after, he was again arrested by a scene which, while it charmed, amazed him.

In rounding Point Bradley, there is a rocky shelf that runs off the point for perhaps one hundred yards.

rounding a corner, Black Hood sighted a taxi cab cruising along.

Below it is the café and restaurant de la Rotonde, a very well-built looking place, with its rounding façade on the corner.

The men were now rounding up their charges into an open meadow half a mile distant, preparatory to an early start in the morning.

British Dictionary definitions for rounding

/ ( ˈraʊndɪŋ ) /

computing a process in which a number is approximated as the closest number that can be expressed using the number of bits or digits available

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

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Mathematics LibreTexts

1.1.2: Rounding Whole Numbers

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Learning Objectives

  • Learn the rules for rounding.
  • Round whole numbers to specific place values, including tens, hundreds, and thousands.

Introduction

In some situations, you don’t need an exact answer. In these cases, rounding the number to a specific place value is possible. For example, if you travelled 973 miles, you might want to round the distance to 1,000 miles, which is easier to think about. Rounding also comes in handy to see if a calculation is reasonable.

Rounding Whole Numbers

These are the rules for rounding whole numbers :

First, identify the digit with the place value to which you are rounding. You might circle or highlight the digit so you can focus on it better.

Then, determine the possible numbers that you would obtain by rounding. These possible numbers are close to the number that you’re rounding to, but have zeros in the digits to the right.

If you are rounding 186 to the nearest ten, then 180 and 190 are the two possible numbers to round to, as 186 is between 180 and 190. But how do you know whether to round to 180 and 190?

Usually, round a number to the number that is closest to the original number.

When a number is halfway between the two possible numbers, round up to the greater number.

Since 186 is between 180 and 190, and 186 is closer to 190, you round up to 190.

You can use a number line to help you round numbers.

A camera is dropped out of a boat, and sinks to the bottom of a pond that is 37 feet deep. Round 37 to the nearest ten.

Screen Shot 2021-04-06 at 12.16.13 PM.png

The digit you’re rounding to is the tens digit, 3.

37 is between 30 and 40.

37 is only 3 away from 40, but it’s 7 away from 30. So, 37 is closer to 40.

To the nearest ten, 37 rounds to 40.

Round 33 to the nearest ten.

Screen Shot 2021-04-06 at 12.22.04 PM.png

33 rounds to 30 because 33 is closer to 30.

To the nearest ten, 33 rounds to 30.

You can determine where to round without using a number line by looking at the digit to the right of the one you’re rounding to. If that digit is less than 5, round down. If it’s 5 or greater, round up. In the example above, you can see without a number line that 33 is rounded to 30 because the ones digit, 3, is less than 5.

Round 77 to the nearest ten.

77 rounds to 80 because the ones digit, 7, is 5 or greater.

77 rounded to the nearest ten is 80.

There are 576 jellybeans in a jar. Round this number to the nearest ten.

576 rounds to 580 because the ones digit, 6, is 5 or greater.

576 rounded to the nearest ten is 580.

In the previous examples, you rounded to the tens place. The rounded numbers had a 0 in the ones place. If you round to the nearest hundred, the rounded number will have zeros in the tens and ones places. The rounded number will resemble 100, 500, or 1, 200.

A runner ran 1,539 meters, but describes the distance he ran with a rounded number. Round 1,539 to the nearest hundred.

1,539 rounds to 1,500 because the next digit is less than 5.

1,539 rounded to the nearest hundred is 1,500.

If you round to the nearest thousand, the rounded number will have zeros in the hundreds, tens, and ones places. The rounded number will resemble 1,000 , 2,000 , or 14,000.

A plane’s altitude increased by 2,721 feet. Round this number to the nearest thousand.

2,721 rounds to 3,000 because the next digit, 7, is 5 or greater.

2,721 rounded to the nearest thousand is 3,000.

Now that you know how to round to the nearest ten, hundred, and thousand, try rounding to the nearest ten thousand.

Round 326,749 to the nearest ten thousand.

326,749 rounds to 330,000 because the next digit, 6, is 5 or greater.

326,749 rounded to the nearest ten thousand is 330,000.

A record number of 23,386 people voted in a city election. Round this number to the nearest hundred.

  • Incorrect. The two possible numbers are 23,300 and 23,400, but 23,386 is closer to 23,400. The tens digit, 8, is 5 or greater, so you should round up. The correct answer is 23,400.
  • Correct. The two possible numbers are 23,300 and 23,400, and 23,386 is closer to 23,400. The tens digit, 8, is 5 or greater, so you should round up.
  • Incorrect. This number is rounded to the nearest thousand, not the nearest hundred. The correct answer is 23,400.
  • Incorrect. This number is rounded to the nearest ten, not the nearest hundred. The correct answer is 23,400.

In situations when you don’t need an exact answer, you can round numbers. When you round numbers, you are always rounding to a particular place value, such as the nearest thousand or the nearest ten. Whether you round up or round down usually depends on which number is closest to your original number. When a number is halfway between the two possible numbers, round up to the larger number.

Rounding Numbers

  • If the number is 0-4 ----> round down
  • If the number is 5-9 ----> round up
  • You need to know what place value you are rounding to.

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What is Rounding?

Rounding simply refers to making a number simpler while keeping its value nearest to what it was. The outcome however will be less exact, but much easier to use. Example: 92 rounded to the nearest ten are 90 since 92 is closer to 90 than to 100. When rounding a number, you first need to see: what are you rounding it to? We can round the numbers to the nearest ten, the nearest hundred, the nearest thousand, and so on.

Rounding Decimals

Let us see how we perform rounding decimals.

Say we want to round the number 728.363. Typically based upon which place value we'll round to, the final outcome will differ. Rounding 728.363:

Rounding to the nearest hundred, we get 700.

Rounding to the nearest ten, we get 730.

Rounding to the nearest one, we get 728.

Rounding to the nearest tenth, we get 728.4.

Tips for Rounding Decimals

In order to avoid confusion or make errors while solving rounding numbers or rounding long decimals, just consider only the number in the place you are rounding to and also the number that follows it. For example, to round 4.273891401 to the nearest hundredth (100 th ), just look at the number from the left in the hundredths place—7—and the number that follows it—2. Then you can easily round it to 4.27.

How to do Rounding of Fractions?

Rounding fractions works just in a similar manner as rounding whole numbers. The only difference is that rather than rounding to 10s (tens), (100s) hundreds, thousands (1000s), and so on, we just round to 10 th (tenths), 100 th (hundredths), 1000 th (thousandths), and so on. Let’s consider some examples to get a knowhow of the concept better:

6.7199 rounded to the nearest tenth (10 th ) is 6.7.

2.0731 rounded to the nearest hundredth (100 th ) is 2.07.

4.8693 rounded to the nearest thousandth (1000 th ) is 4.869.

How to do Rounding and Sums?

Rounding can certainly make sums easy. For instance, at a merchant shop you might choose articles with the following prices:

If you wanted to know how much they would cost, you could add up the prices using a calculator, or try to just add them in your head. Or you could simply estimate by rounding off to the nearest rupees, like this:

By rounding off, we could easily find out that we would require about Rs. 6.00 to pay for the items purchased. If you see, this is quite close to the exact number of Rs. 5.8.

Rounding a Number to The Nearest Ten

Round to the Nearest Ten: 799.

Determine the tens digit: the 1 st 9 in 799.

Determine the next smallest place value: the 2 nd 9 in 799.

Is that digit ≥ five? Thus, round up.

The tens digit increases by one. Because 9+1=10, you would require to carry the 1 and add it to the digit in the 100s place. Each digit then after becomes a zero.

799 rounded to the nearest ten is 800.

Rounding a Number to The Nearest Hundred

Let’s take a digit 4350.

Round to the Nearest Hundred: 4350

Determine the hundreds digit: the 3 in 4350

Determine the next smallest place value: the 5 in 4350

Is that digit ≥ five? : Yes, therefore round up.

Increase the hundreds digit by one, so 3 becomes 4. Every digit after becomes a zero.

4350 rounded to the nearest hundred is 4450.

Did You Know?

A few statisticians prefer to round 5 to the nearest even number.

As a result of rounding 5 to the nearest even number, about half of the time five (5) will be rounded up, and about half of the time, it will be rounded down.

In this way, 38.5 rounded to the nearest even number would be 38—it would be rounded down. And, 38.5 rounded to the nearest even number would be 39—it would be rounded up.

In order to learn how to round a number to its nearest multiple, you can check the online round to nearest multiple calculators. The calculator is a useful tool to round to multiples of whole numbers or decimals.

How to Prepare Notes on Rounding Numbers?

All students must go through Rounding

This page has explained everything in detail

Students can read up the matter here and then highlight all the important areas

They can follow the sequence that’s here and then understand whatever has been explained

They must not copy everything from the page but write them down in their own words

They can use drawings and other forms of illustrations to better understand the topic

They can then revise from the same before a test

Does Vedantu have any Material on Rounding Numbers?

Yes, Vedantu has ample study material on Rounding numbers. All students can read from Rounding and understand the topics better. They can go through this page as it has all the information that they need. This material can be accessed in the form of a PDF offline even when students do not have access to the internet.

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FAQs on Rounding Numbers

1. What is meant by a round number?

A round number is mathematically described as an integer that is the product of a reasonable number of relatively small factors in comparison to its neighboring numbers, such as 56 = 2 × 2 × 2 × 7. A round number is informally regarded as an integer that ends with one or more "0"s in a provided base. That being said, a rounded number has approximately the same value as the number you begin with, but it is less accurate.

2. What is an example of a round number?

Take for example the number 431. In this case, 431 rounded to the nearest hundred are 400. Since 431 is closer in value to 400 than to 500. When rounding off to the nearest dollar, $2.78 becomes $3.00, because $2.78 is closer to $3.00 than to $2.00.

3. How to round numbers?

Below is standard rules for rounding a number:

If the number you want to round is followed by 5, 6, 7, 8, or 9, round up the number like 47 rounded to the nearest ten is 50.

If the next smallest place value is ≥ to five (5, 6, 7, 8, or 9), you raise the value of the digit you're rounding to by (+1).

Any left out digits before the decimal point becomes zeros, and after one’s are dropped.

If the number you want to round is followed by 0, 1, 2, 3, or 4, round down the number like 43 rounded to the nearest ten is 40.

4. How can students perform rounding decimals?

Students can perform rounding decimals once they read up this page on Vedantu- Rounding.

This page has valid information on the topic and can be used by all students to study the topic. Once they have gone through this page, they will understand how such topics need to be dealt with. Rounding decimals is an easy chapter if they are understood properly by the students. This page will guide them in the right manner.

5. How can fractions be rounded?

The rounding of fractions is similar to the rounding of whole numbers. There is a slight difference in the approach used. IT gets clearer if the students read Rounding on Vedantu. This page has a lot of information that is relevant for the students of math to know about. Unless these basics are clear, they will not be able to solve the other sums that are based on these. The exact manner has been explained in the chapter so that the students understand how fractions are rounded and avoid making errors in the tests. They can even revise from this page before they appear for a test on the topic as this page has covered nearly everything.

6. How can a number be rounded to the nearest ten?

All the explanations have been provided on Vedantu if the students check out Rounding. This page has been created by expert Math teachers who know the topic inside out and so, only the most relevant bits have been included here. All the explanations provided here are valid and any student who is struggling with the fundamentals of Rounding Numbers can read from here. This page is the ideal guidebook for all students of Math.

7. How can a student know about the kinds of sums that might come for a math test on Rounding Numbers?

Students who have math tests on Rounding Numbers can read from Rounding  on Vedantu’s platform.  This page has genuine input on the topic and is quite easy to understand. The explanations are to the point and in simple terms. Any student grappling with certain concepts of Rounding Numbers can read this page and understand the topic better. It is quite informative and strategic before a test on the same. The material provided is free of cost for all students, teachers and parents.

8. Are there any hacks or tips for rounding decimals?

There are quite a few hacks that the students can employ so as to make the rounding of numbers easier.  Some of which have been mentioned in Rounding on Vedantu’s online tutoring platform. This page has everything that the math student needs to understand about Rounding numbers. It is quite useful and also quite simple to understand. Knowing the tricks about Rounding Numbers will assist the students in doing well in their exams. They will be able to tackle all questions related to the topic that comes their way. A strategic approach in a subject like Math can do wonders.

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Table of Contents

Last modified on August 3rd, 2023

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Rounding whole numbers.

The standard way we approximate a number when given a collection of any object, by mentally considering the collection as in groups of tens, hundreds, or thousands, is rounding numbers. Rounding whole numbers is a way by which we make numbers look good. It is a handy way to estimate the numbers in the rounded form instead of expressing them in the exact form.

Numbers that look nice in our minds end with a zero, such as 10, 30, or 200.

Thus, rounding numbers usually means we will try to put zero(s) at the end.

We can round any number to its nearest ten, hundred, thousand, or ten-thousand.

Rounded numbers are the approximate values; they will never give exact answers.

rounding math definition

Round 62 to the nearest ten

  • 6 is the digit in 10th place, 2 is the unit digit
  • 2 < 5, so add nothing to 6.
  • Replace 2 with 0
  • The rounded off result of 62 to the nearest ten is 60

Round 67 to the nearest ten

  • 6 is the digit in 10th place, 7 is the unit digit
  • 7 > 5, so add 1 to 6.
  • Replace 7 with 0
  • The rounded off result of 67 to the nearest ten is 70

How to Round Whole Numbers

Steps to round whole numbers:

  • Locate the position (10, 100, or 1000) of the digit to be rounded off.
  • Locate the digit to the exact right of the digit we will round off.
  • Rounding Down: If the digit is less than 5, replace it and all the digits to its right with zeros. Leave the round-off digit as it is.
  • Rounding Up: If digit is 5 or larger, replace it with zeros and all the digits to its right. Increase the round-off digit by 1.

Let us see how to round the numbers to the nearest tens, hundreds, and thousands.

Rounding Whole Numbers to the Nearest Ten

When rounding a whole number to its nearest ten, we need to locate the last digit at the unit place.

Case 1 – The last digit is 1, 2, 3, or 4, then replace it with 0 (zero), and keep the digit in the 10th place unchanged.

Case 2 – The last digit is 5 or larger, then replace it with 0 (zero), and add 1 to the digit in the 10th place.

Rounding 241 – Here the digit in the 10th place is 4, the digit in the unit place is 1 which is <5.

So we change 1 to 0 and keep 4 unchanged. Thus, the rounded-off result is 240.

Now, Rounding 346 – Here the digit in the 10th place is 4, the digit in the unit place is 6 which is >5.

So we change 6 to 0 and add 1 to 4. Thus, the rounded-off result is 350.

Rounding Whole Numbers to the Nearest Hundred

When rounding a whole number to its nearest hundred, we need to locate the last 2 digits.

Case 1 – The last 2 digits is 49 or less, then replace the last 2 digits with 0s (zeroes), and keep the digit in the 100th place unchanged.

Case 2 – The last 2 digits are 50 or larger, then replace the last 2 digits with 0s (zeroes), and add 1 to the digit in the 100th place.

Rounding 817 – Here the 2 digits after 8 is 17 which is <50.

So we replace 17 with 00 and keep 8 unchanged. Thus, the rounded-off result is 800.

Rounding 689 – Here the 2 digits after 6 is 89 which is >50.

So we replace 89 with 00 and add 1 to 6. Thus, the rounded-off result is 700.

Rounding Whole Numbers to the Nearest Thousand

When rounding a whole number to its nearest thousand, we need to locate the last 3 digits.

Case 1 – The last 3 digits is 499 or less, then replace the last 3 digits with 0s (zeroes), and keep the digit in the 1000th place unchanged.

Case 2 – The last 3 digits are 500 or larger, then replace the last 3 digits with 0s (zeroes), and add 1 to the digit in the 1000th place.

Rounding 39,450 – Here the 3 digits after 9 is 450 which is <500.

So we replace 450 with 000 and keep 9 unchanged. Thus, the rounded-off result is 39,000.

Rounding 61,728 – Here the 3 digits after 1 is 728 which is >500.

So we replace 728 with 000 and add 1 to 1. Thus, the rounded-off result is 62,000.

Solved Examples

Round 564 to the nearest ten.

As we know, 4<5 So, the rounded off result of 564 = 560

Round 929 to the nearest ten.

As we know, 9>5 So, the rounded off result of 929 = 930

Round 2,901 to the nearest hundred.

As we know, 01<50 So, the rounded off result of 2,901 = 2,900

Round 9,456 to the nearest hundred.

As we know, 56>50 So, the rounded off result of 9,456 = 9,500

Round 49,287 to the nearest thousand.

As we know, 287<500 So, the rounded off result of 49,287 = 49,000

Round 84,788 to the nearest thousand.

As we know, 788>500 So, the rounded off result of 84,788 = 85,000

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Rounding To The Nearest Tens – Definition, Examples, FAQs

What is rounding, purpose of rounding, applications of rounding, solved examples on rounding to the nearest tens, practice problems on rounding to the nearest tens, frequently asked questions on rounding to the nearest tens.

Rounding refers to converting a particular number to an easy number. The rounded number is not exact but an estimate of the given number. 

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Usually, we round numbers for:

  • Making calculations easy.
  • Making the numbers easy to understand and remember.

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Estimation: We use rounding to guess the most appropriate answer. Rounding is the process of estimation.

For example, Oolzoo wants to buy ice-creams worth $\$97$. He can estimate the amount to the nearest tens and give $\$100$ to the storekeeper, who will return $\$3$ to him.

Estimation helps us calculate easily.

Step-by-Step Process to Round to the Nearest Tens

We can follow the given steps for rounding whole numbers to the nearest tens:

Step 1: We look at the number we want to round.

Step 2: To round off numbers to the nearest tens, we mark the digits in the ones column and tens column.

Step 3: (i) If the digit in the ones column is between 0 and 4 (i.e., if the digit is less than 5), we replace this digit with 0. This is called rounding down.

        (ii) If the digit in the ones column is between 5 and 9 (i.e., if the digit is greater than 4 but less than 10), we replace this digit with 0 and increase the digit in the tens column by 1. This is called rounding up.

Note: If the given number has any digit to the right of the ones column, we remove them.   

The number we get after rounding up or rounding down and removing any digit on the right of the ones column is our answer.

Example 1: Round 523 to the nearest ten.

Step 1: We must round the number 523 to the nearest ten.

Step 2: To round to the nearest tens, we mark the digits in the ones and tens column. In this number, we see that the digit 3 is in the ones column and the digit 2 is in the tens column.

Step 3: Since the digit in the ones column (i.e., 3) is between 0 and 4, we replace this digit with 0. This means we replace 3 with 0.

As no digit exists on the right of the ones column, we don’t have to remove anything.

So, the number we get after rounding 523 to the nearest ten is 520.  

Example 2: Round 147.32 to the nearest tens.

Step 1: We have to round the number 147.32 to the nearest ten.

Step 2: To round to the nearest tens, we mark the digits in the ones and tens column.In this number, we see that the digit 7 is in the ones column and the digit 4 is in the tens column.

Step 3: Since the digit in the ones column (i.e., 7) is between 5 and 9, we replace this digit with 0. This means we replace 7 with 0. We then increase the digit in the tens column by 1. This means increasing 4 by 1 and getting 5 in the tens column.  

Note: In 147.32, there are two digits on the right of the ones column (i.e., 3 and 2). We remove them.

So, after rounding 147.32 to the nearest ten, the number we get is 150.   

Example 3: Eddie is 169 cm tall. Write his height to the nearest tens.

Measuring height

Step 1: We have to round the number 169 to the nearest ten.

Step 2: To round to the nearest tens, we mark the digits in the ones and tens column.In this number, we see that the digit 9 is in the ones column and the digit 6 is in the tens column.

Step 3: Since the digit in the ones column (i.e., 9) is between 5 and 9, we replace this digit with 0. This means we replace 9 with 0. We then increase the digit in the tens column by 1. This means we increase 6 by 1 and get 7 in the tens column.  

(As no digit exists on the right of the ones column, we don’t have to remove anything.)

So, after rounding 169 to the nearest ten, the number we get is 170.   

Exception: 

Example 4: Round the number 195.278 to the nearest tens.

Step 1: We have to round the number 195.278 to the nearest ten.

Step 2: To round to the nearest tens, we mark the digits in the ones and tens column.In this number, we see that digit 5 is in the ones column and digit 9 is in the tens column.

Step 3: Since the digit in the ones column (i.e., 5) is between 5 and 9, we replace this digit with 0. This means we replace 5 with 0. We then increase the digit in the tens column by 1. This means we increase 9 by 1 and get 10. We keep the 0 in the tens column and carry 1 to the hundreds column. Here, we already have 1 in the hundreds column. We add the carry 1 to this 1 and get 2.

Note: In 195.278, there are three digits on the right of the ones column (i.e., 2, 7, and 8). We remove them.

So, after rounding 195.278 to the nearest ten, the number we get is 200. Since we have moved up the number to the nearest ten, we call it rounding up.

Example 5: A park measures 249.9 miles in length. How long is the park to the nearest 10, in miles?

Measuring length of park

Step 1: We have to round the number 249.9 to the nearest ten.

Step 2: To round to the nearest tens, we mark the digits in the ones and tens column.In this number, we see that digit 9 is in the ones column and digit 4 is in the tens column.

Step 3: Since the digit in the ones column (i.e., 9) is between 5 and 9, we replace this digit with 0. This means we replace 9 with 0. We then increase the digit in the tens column by 1. This means we increase 4 by 1 and get 5 in the tens column.  

Note: In 249.9, there is a digit on the right of the ones column (i.e., 9). We remove it.

So, after rounding 249.9 to the nearest ten, the number we get is 250.   

Note : Since we have moved up the number to the nearest ten, we call it rounding up.

Example 1: Round 105 to the nearest tens.

Solution : To round to the nearest tens, we mark the digits in the ones and tens column. In the number 105, we have 5 in the ones column and 0 in the tens column. Since the digit in the ones column (i.e., 5) is between 5 and 9, we replace this digit with 0. We then increase the digit in the tens column by 1. This means we increase 0 by 1 and get 1 in the tens column.  

So, after rounding 105 to the nearest tens, the number we get is 110.   

Example 2: Round 860 to the nearest tens.

Solution : To round to the nearest tens, we mark the digits in the ones and tens column.In the number 860, we have 0 in the ones column and 6 in the tens column. Since the digit in the ones column (i.e., 0) is between 0 and 4, we replace this digit with 0. But here, 0 already exists in the ones column. So, no change occurs in the ones column. This means we get the same number, 860, after following the steps of rounding off.

So, 860 rounded to the nearest tens remains the same, i.e., 860.   

Example 3: The average height of students in a college is 69.5 inches. Write the height rounded to the nearest tens.

Solution : To round to the nearest tens, we mark the digits in the ones and tens column. In the number 69.5, we have 9 in the ones column and 6 in the tens column. Since the digit in the ones column (i.e., 9) is between 5 and 9, we replace this digit with 0. We then increase the digit in the tens column by 1. This means we increase 6 by 1 and get 7 in the tens column.  

Now we remove the digit on the right of the ones column (i.e., 5).

So, the average height of 69.5 inches rounded to the nearest tens is 70 inches.

Rounding To The Nearest Tens - Definition With Examples

Attend this quiz & Test your knowledge.

The price of a book is $743. What is the price of the book rounded to the nearest tens?

Round 3596 to the nearest tens., james drove 347.8 miles to reach his father’s house. round off the distance to the nearest tens..

Can a number remain the same even after rounding to the nearest tens?

Yes. Any number with 0 in the ones column will remain the same even after rounding to the nearest tens.

Is it necessary to learn place value for rounding off numbers?

Yes. While rounding off, you will have to deal with digits in the hundreds column, tens column, ones column, etc. Knowing about place value will help you do so.

What is rounded up and rounded down?

When we round off a number, if the rounded-off value is greater than the original value, we say it is rounded up. If the rounded-off value is less than the original value, it is said to be rounded down.

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Rounding Decimals – Definition with Examples

Created: December 20, 2023

Last updated: January 7, 2024

Welcome to another exciting topic on Brighterly , where we make learning math fun and engaging for children. Today, we’re diving into the world of rounding decimals. This is a fundamental concept in mathematics that helps simplify complex numbers for easier understanding and calculation.

Rounding decimals involves reducing the number of digits in a decimal while trying to keep its value close to the original. It’s like approximating, but with a rule that tells us how to do it systematically. This process is particularly useful in real-life scenarios where precision isn’t as important as simplicity. For example, if you’re estimating the cost of groceries, calculating the distance of a road trip, or determining the average score in a game, rounding decimals can make the task much easier.

At Brighterly, we believe in the power of examples. So, let’s consider the number 3.14159. If we round it to the nearest whole number, we get 3. If we round it to the nearest tenth, we get 3.1. And if we round it to the nearest hundredth, we get 3.14. As you can see, each rounding step makes the number simpler, yet it remains close to the original value.

Rounding Decimals

Rounding decimals is a fundamental concept in mathematics that helps simplify complex numbers for easier understanding and calculation. It involves reducing the number of digits in a decimal while trying to keep its value close to the original. This process is particularly useful in real-life scenarios where precision isn’t as important as simplicity. For example, if you’re estimating the cost of groceries or calculating the distance of a road trip, rounding decimals can make the task much easier.

Rounding to the Nearest Whole

When rounding to the nearest whole number, we look at the digit in the tenths place. If it’s 5 or more, we round up the whole number part, and if it’s less than 5, we keep the whole number part as it is. For example, rounding 3.7 to the nearest whole number gives us 4, while rounding 3.4 gives us 3. This method is often used in financial calculations where cents are not considered.

Rounding to the Nearest Tenths

Rounding to the nearest tenths involves looking at the digit in the hundredths place. If this digit is 5 or more, we round up the number in the tenths place. If it’s less than 5, we keep the number in the tenths place as it is. For instance, rounding 3.74 to the nearest tenth gives us 3.7, while rounding 3.75 gives us 3.8. This method is often used in scientific calculations where a higher degree of precision is required.

Rounding to the Nearest Hundredths

When rounding to the nearest hundredths, we look at the digit in the thousandths place. If this digit is 5 or more, we round up the number in the hundredths place. If it’s less than 5, we keep the number in the hundredths place as it is. For example, rounding 3.745 to the nearest hundredth gives us 3.75, while rounding 3.744 gives us 3.74. This method is often used in engineering and physics where a high degree of accuracy is needed.

What is Rounding Decimals Calculator?

A Rounding Decimals Calculator is a digital tool that automatically rounds decimal numbers to the nearest whole number, tenth, hundredth, or any other specified place value. It’s a handy tool for students, teachers, engineers, and anyone who frequently works with decimal numbers. These calculators are widely available online and can be used for free.

Rounding Decimals Worksheet PDF

Rounding Decimals Worksheet

Rounding Decimals Worksheet Answer Key PDF

Rounding Decimals Worksheet Answer Key

You can find the answers and more practice questions in our Rounding Decimals Practice Worksheets on Brighterly .

How to Round off a Decimal Number?

To round off a decimal number, you need to identify the digit at the place value you’re rounding to. Look at the digit to the right of it. If this digit is 5 or more, round up the number you’re considering. If it’s less than 5, keep the number as it is. Discard all the digits to the right of the place value you’re rounding to.

Solved Examples on Rounding Decimal

Let’s look at some solved examples on rounding decimal:

Round 3.14159 to the nearest whole number. The digit in the tenths place is 1, which is less than 5, so we keep the whole number part as it is. The answer is 3.

Round 3.14159 to the nearest tenth. The digit in the hundredths place is 4, which is less than 5, so we keep the number in the tenths place as it is. The answer is 3.1.

Round 3.14159 to the nearest hundredth. The digit in the thousandths place is 5, which is 5 or more, so we round up the number in the hundredths place. The answer is 3.14.

These examples should give you a clear understanding of how to round decimal numbers.

Practice Problems on Rounding Decimal

Here are some practice problems on rounding decimal for you to try:

  • Round 4.56789 to the nearest whole number.
  • Round 4.56789 to the nearest tenth.
  • Round 4.56789 to the nearest hundredth.

Remember, practice is key to mastering any concept in mathematics.

Rounding Decimals Worksheets With Answers

Rounding Decimals Worksheets With Answers

Rounding Decimals Worksheet With Answers

Rounding Decimals Worksheet With Answers

Rounding decimals, as we’ve learned, is a crucial skill not only in mathematics but also in everyday life. It’s a tool that helps us simplify complex numbers, making them easier to understand and work with. At Brighterly, we believe that understanding this concept is a stepping stone to mastering more complex mathematical concepts.

Whether you’re rounding to the nearest whole number, tenth, or hundredth, the process remains the same. The key is to look at the digit to the right of the place value you’re rounding to, and decide whether to round up or keep the number as it is.

But remember, the beauty of mathematics lies in its application. So, the next time you’re faced with a complex decimal number, don’t shy away. Use your rounding skills to simplify it. And as always, keep practicing, because practice makes perfect!

Frequently Asked Questions on Rounding Decimal

What is rounding decimals.

Rounding decimals is a mathematical process where we simplify a decimal number to a specified place value. It involves looking at the digit to the right of the place value we’re rounding to and deciding whether to round up or keep the number as it is.

How do you round to the nearest whole number?

To round to the nearest whole number, we look at the digit in the tenths place. If this digit is 5 or more, we round up the whole number part. If it’s less than 5, we keep the whole number part as it is.

How do you round to the nearest tenth?

When rounding to the nearest tenth, we look at the digit in the hundredths place. If this digit is 5 or more, we round up the number in the tenths place. If it’s less than 5, we keep the number in the tenths place as it is.

How do you round to the nearest hundredth?

To round to the nearest hundredth, we look at the digit in the thousandths place. If this digit is 5 or more, we round up the number in the hundredths place. If it’s less than 5, we keep the number in the hundredths place as it is.

What is a rounding decimals calculator?

A rounding decimals calculator is a digital tool that helps simplify the process of rounding decimals. You input a decimal number and specify the place value to which you want to round. The calculator then provides the rounded number, saving you time and ensuring accuracy.

This article was created using information from the following sources:

  • Calculator Soup – Rounding Numbers Calculator
  • BBC Bitesize – Rounding Decimals
  • Math Drills – Rounding Decimals

I am a seasoned math tutor with over seven years of experience in the field. Holding a Master’s Degree in Education, I take great joy in nurturing young math enthusiasts, regardless of their age, grade, and skill level. Beyond teaching, I am passionate about spending time with my family, reading, and watching movies. My background also includes knowledge in child psychology, which aids in delivering personalized and effective teaching strategies.

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Definition of round

 (Entry 1 of 6)

Definition of round  (Entry 2 of 6)

Definition of round  (Entry 3 of 6)

Definition of round  (Entry 4 of 6)

transitive verb

intransitive verb

Definition of round  (Entry 5 of 6)

Definition of round  (Entry 6 of 6)

  • agglomerate

Preposition

Examples of round in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'round.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Middle English round, rounde "spherical, circular, rounded," borrowed from Anglo-French reund, rund, rount, going back to Vulgar Latin *retundus, altered (by presumed vowel dissimilation) from Latin rotundus — more at rotund

Middle English, "in a circle," derivative of round, rounde round entry 1

Middle English rond, round, rounde "spherical body or form, circle," in part derivative of round, rounde round entry 1 , in part borrowed from Anglo-French rund, rond (in en rund "round about") and runde (in a la runde "round about"), both nominal derivatives of reund, rund round entry 1

Middle English rounden "to form a ball, be circular, cut (hair) close around the head," in part derivative of round round entry 1 , in part borrowed from Anglo-French runder "to revolve" and Old French rondir "to make round," derivatives of rund, rond round entry 1

derivative of round entry 2

alteration of Middle English rounen , from Old English rūnian ; akin to Old English rūn mystery — more at rune

14th century, in the meaning defined at sense 1a(1)

14th century, in the meaning defined above

14th century, in the meaning defined at sense 1a

14th century, in the meaning defined at transitive sense 1a

1573, in the meaning defined at sense 1

15th century, in the meaning defined at sense 1

Phrases Containing round

  • (all) round the year
  • all - round
  • all year round
  • change round
  • crowd around / round
  • enough / plenty to go round
  • get one's head round
  • get round to (something)
  • merry - go - round
  • rally round
  • round dance
  • round number
  • round of applause
  • round - robin
  • round - shouldered
  • round table
  • round the twist
  • round the bend
  • round the clock
  • round - trip ticket
  • steamship round
  • show (someone) round
  • see around / round
  • run about / round with
  • work round to
  • whip - round
  • what goes round comes round
  • turn round and (do something)
  • theater - in - the - round
  • year - round
  • a clip round the ear
  • round angle
  • a square peg in a round hole
  • paper round
  • bottom round
  • round steak
  • round window
  • sniff around / round
  • the other way round
  • in the round

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“Round.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/round. Accessed 21 Feb. 2024.

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Rounding the Mean – Definition, Applications, and Examples

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Rounding the Mean Definition Applications and Examples 1

In this article, we will delve into the reasons for rounding the mean , the different rounding methods available, and the potential implications of rounding on data analysis and decision-making processes . 

Rounding the mean refers to the process of adjusting the calculated average of a set of numbers to a specified degree of precision . The mean , or average , is obtained by summing all the values in a dataset and dividing by the number of data points .

However, the mean often results in a decimal value that may not be practical or necessary , depending on the context. Rounding the mean involves reducing the number of decimal places or digits after the decimal point to a more suitable level, typically to simplify the value or align it with the desired level of precision .

This adjustment facilitates easier interpretation , communication , and comparison of the mean within a given context or application. Rounding the mean i s a common practice in various fields, including statistics , finance, research, and everyday data analysis .

Exercise 

Consider the following data set of exam scores : 78, 83, 89, 92, 95 . Round the mean to the nearest whole number .

To find the mean, sum all the scores and divide by the number of scores:

Mean = (78 + 83 + 89 + 92 + 95) / 5

Mean = 437 / 5

Mean = 87.4

Rounding the mean to the nearest whole number, we get: Rounded Mean = 87

Suppose we have the following dataset of rainfall measurements (in millimeters) for five cities: 12.5, 13.2, 11.8, 10.6, 14.1 . Round the mean to one decimal place .

To find the mean, sum all the measurements and divide by the number of measurements:

Mean = (12.5 + 13.2 + 11.8 + 10.6 + 14.1) / 5

Mean  = 62.2 / 5

Mean  = 12.44

Rounding the mean to one decimal place, we get: Rounded Mean = 12.4

Consider a dataset of temperatures (in degrees Celsius) recorded throughout a week: 22.3, 21.6, 24.1, 20.9, 23.5, 24.9. Round the mean to the nearest whole number .

To find the mean, sum all the temperatures and divide by the number of temperatures:

Mean = (22.3 + 21.6 + 24.1 + 20.9 + 23.5 + 24.9) / 6

Mean  = 137.3 / 6

Mean  = 22.88

Rounding the mean to the nearest whole number, we get: Rounded Mean = 23

Suppose we have a dataset representing the ages of a group of individuals : 32, 28, 35, 40, 37, 30 . Round the mean to the nearest multiple of 5 .

To find the mean, sum all the ages and divide by the number of ages:

Mean = (32 + 28 + 35 + 40 + 37 + 30) / 6

Mean  = 202 / 6

Mean  = 33.67

Rounding the mean to the nearest multiple of 5, we get: Rounded Mean = 35

Consider a dataset of product prices (in dollars): $12.99, $9.99, $14.99, $8.49, $11.99. Round the mean to two decimal places .

To find the mean, sum all the prices and divide by the number of prices:

Mean = ($12.99 + $9.99 + $14.99 + $8.49 + $11.99) / 5

Mean  = $58.45 / 5

Mean  = $11.69

Rounding the mean to two decimal places, we get: Rounded Mean = $11.69

Applications 

Rounding the mean finds applications in various fields where data analysis and s tatistical calculations are performed. Here are some examples of its applications in different domains:

Rounding the mean is commonly employed in financial calculations , such as computing average returns on investments or determining mean values of financial indicators. It helps simplify monetary values and aligns them with standard currency denominations.

Rounding the mean in financial contexts aids in budgeting , forecasting , and making informed decisions based on rounded average values.

In industries that rely on quality control and manufacturing processes , rounding the mean can be useful for assessing product quality . By rounding the mean of measured parameters or quality metrics , such as dimensions or weights, it becomes easier to evaluate whether the product meets specific standards or falls within acceptable tolerances .

Rounding the mean is often employed in educational settings to calculate and report grades . It allows for simplifying complex grade calculations, making them more understandable for students and parents. Rounding the mean in grading ensures consistency and fairness in evaluating student performance across different assessments or assignments .

Rounding the mean is applied in analyzing survey data and polling results to present summary statistics . When reporting average ratings or responses , rounding the mean can help convey the overall sentiment or preference in a more concise and easily interpretable manner. It simplifies the representation of survey data while still providing meaningful insights .

In political or social research , rounding the mean can be useful for analyzing public opinion polls . It facilitates the reporting of average responses or aggregated sentiment , allowing for clear communication of trends or patterns in a way that is understandable to policymakers , analysts , and the general public .

Rounding the mean is often employed in market research to analyze and present consumer feedback or rating data . By rounding the mean of customer satisfaction scores or product ratings , market researchers can summarize and communicate the overall perception of a product or service in a more digestible format.

Rounding the mean is essential in statistical reporting and data visualization . When presenting summary statistics or creating charts and graphs , rounding the mean allows for cleaner and less cluttered visual representations . It ensures that the reported or visualized mean values are more easily understood and provide a clearer overall picture of the data.

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  5. What is Rounding Numbers? Rules, Definition, Examples, Facts

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COMMENTS

  1. Rounding Definition (Illustrated Mathematics Dictionary)

    Learn what rounding means and how to do it with examples. Find out the difference between rounding up, rounding down, rounding to the nearest, rounding to the nearest ten, and rounding to the nearest hundred.

  2. What is Rounding Numbers? Rules, Definition, Examples, Facts

    Learn what rounding off is and how to round off different numbers using different rules. See examples of rounding off numbers to the nearest ten, hundred, thousand, or decimal place. Practice problems and FAQs on rounding off numbers.

  3. Rounding Numbers

    Rounding numbers means adjusting the digits of a number in such a way that it gives an approximate value. This value is an easier representation of the given number. For example, the population of a town could be easily expressed as 700,000 rather than 698,869.

  4. Rounding

    Rounding or rounding off means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $23.4476 with $23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414. Rounding is often done to obtain a value that is easier to report and communicate than the original.

  5. What Is Rounding Numbers In Math? Explained For Elementary

    What is rounding in math? Rounding numbers makes them 'easier' to use or understand while also keeping the number close to its original value. Instead of using exact numbers, simpler values can be used. For example, 189.2 could be rounded to 189, 190 or 200, depending on the degree of accuracy required.

  6. Simple Rules for Rounding Numbers Correctly

    Rules for Rounding Whole Numbers . When rounding numbers, you must first understand the term "rounding digit." When working with whole numbers and rounding to the closest 10, the rounding digit is the second number from the right—or the 10's place.When rounding to the nearest hundred, the third place from the right is the rounding digit—or the 100's place.

  7. ROUNDING Definition & Usage Examples

    noun the act or process of making something round. Mathematics. the process of replacing a number by another number of approximately the same value but having fewer digits: To the nearest dollar, the rounding of $27.68 yields $28. a similar process that specifies one of various rules.

  8. Rounding Numbers

    1. Find the desired place value. 2. Look at the number to the right. 3. If that number is 4 or less, round down. If it is 5 or higher, round up. 4. Change the numbers to the right of the...

  9. 1.3: Rounding Whole Numbers

    The Method of Rounding Whole Numbers. From the observations made in the preceding examples, we can use the following method to round a whole number to a particular position. Mark the position of the round-off digit. Note the digit to the immediate right of the round-off digit. If it is less than 5, replace it and all the digits to its right ...

  10. Rounding Numbers

    Rounding off numbers is a mathematical technique of adjusting the number's digits to make the number easier to use during calculations. Numbers are rounded off to a particular degree of accuracy to make calculations simpler and the results easier to understand. Before rounding off any number, you should know the place of all digits of a number.

  11. Rounding Numbers

    Rounding number is the process of approximating the number to its closest value. It involves reducing the number of significant digits while retaining the general magnitude or size of the original number. The result of rounding is less accurate than the original number but simplifies calculations.

  12. What is Rounding Decimals? Definition, Examples, Facts

    1. Rounding to the Nearest Whole We follow the given steps to round numbers to the nearest whole number: Step 1- We look at the number we want to round. Step 2- As we are rounding our number to the nearest whole, we mark the digit in the one's place. Step 3- Now we look at the 'tenths' place (the digit to the right of the decimal point).

  13. 1.1.2: Rounding Whole Numbers

    1.1: Introduction to Whole Numbers 1.1.2: Rounding Whole Numbers

  14. What is Rounding Off Numbers in Math? How to do a Round Off (Definition

    7 Grade 8 Schedule a free class Table of Contents What are Numbers? What is a Number line? What is Place value? Rounding off a number using a Number line : Rounding off a number using Place value : Solved Examples : Frequently Asked Questions What are N umbers ?

  15. Kids Math: Rounding Numbers

    1) Round 3.895 to the nearest hundredths place: There 9 is in the hundredths place. The next number to the right is 5, so we want to round the 9 up. We must make the 9 a 0 and then round the 8 up. Answer: 3.90. Note: We keep the "0" even though it is to the right of the decimal place.

  16. Rounding Numbers : Definition, Facts & Examples

    A round number is mathematically described as an integer that is the product of a reasonable number of relatively small factors in comparison to its neighboring numbers, such as 56 = 2 × 2 × 2 × 7. A round number is informally regarded as an integer that ends with one or more "0"s in a provided base.

  17. Rounding Whole Numbers

    The standard way we approximate a number when given a collection of any object, by mentally considering the collection as in groups of tens, hundreds, or thousands, is rounding numbers. Rounding whole numbers is a way by which we make numbers look good.

  18. Rounding To The Nearest Tens

    Step 1: We look at the number we want to round. Step 2: To round off numbers to the nearest tens, we mark the digits in the ones column and tens column. Step 3: (i) If the digit in the ones column is between 0 and 4 (i.e., if the digit is less than 5), we replace this digit with 0. This is called rounding down.

  19. What is Rounding Decimals ⭐ Definition, Examples, Facts

    Rounding decimals involves reducing the number of digits in a decimal while trying to keep its value close to the original. It's like approximating, but with a rule that tells us how to do it systematically. This process is particularly useful in real-life scenarios where precision isn't as important as simplicity.

  20. Round Definition & Meaning

    1 a (1) : having every part of the surface or circumference equidistant from the center (2) : cylindrical a round peg b : approximately round a round face 2 : well filled out : plump, shapely 3 a : complete, full a round dozen a round ton b : approximately correct especially : exact only to a specific decimal or place

  21. Rounding the Mean

    Definition. Rounding the mean refers to the process of adjusting the calculated average of a set of numbers to a specified degree of precision. The mean, or average, is obtained by summing all the values in a dataset and dividing by the number of data points. However, the mean often results in a decimal value that may not be practical or ...