Rounding Numbers
Rounding Numbers is used to ease the calculation by adjusting the digits. For example, 541 rounded to the nearest hundred is 500 because 541 is much closer to 500 than 600. You can round a number to the nearest ten, hundred, thousand and so on. So, while rounding a number just ask yourself 'what are you rounding the number to?'. Suppose a number is 7456. When 7456 is rounded to the nearest ten, then we take 7460, but when 7456 is rounded to the nearest thousand, then we take 7000.
In this page, you will be learning about rounding numbers, followed by solved examples and practice questions which would further ease your calculations, giving a better idea of how you can round off a number to the nearest ten, hundred, thousand and so on.
What is Rounding Off Numbers?
"Rounding" 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 off a number, we consider the place value of digits in a number.
Let's 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 using that data easier. Here, Susan noted an easier value for her to keep a record of.
What are the 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 rather a smaller one?
To round off a number, there are a certain set of rules that need to be followed. The following table shows these rules for different cases:
S.No.  Rules 

1.  All the nonzero digits in the number are significant. 
2.  All the zeros that are between nonzero digits are significant. 
3.  The zeros on the right of a nonzero digit in a whole number are significant. 
4.  If the digit to be dropped while rounding off is less than 5, the following digit is left unchanged. 
5.  If the digit to be dropped while rounding off is 5 or greater than 5, the following digit is increased by 1. 
6.  While rounding off a digit at a higher place value, we ignore the lower place value digits. 
Example
Here is a reallife example to understand the above rules better:
Jennifer went grocery shopping with her mother. The cashier told Jennifer's mother that since he is out of change, they can pay the rounded off amount for the total. If the bill had a total of $172, can you help Jennifer help her mother calculated the rounded off value of the amount up to tens place?
The amount to be rounded off to the nearest tens is $172. To round off the number, we will mark the tens place, up to which we are supposed to round off the number. All the digits towards the right of this marked digit should be replaced with 0 in the final result. To do so, we will compare the first digit on its right side with 5. Since 2 is smaller than 5, we will replace 2 with 0, and digit 7 will remain unchanged. Thus, the rounded amount to be paid for the grocery = $170
How to Round Off Whole Numbers?
Whole numbers are rounded off by following the same rules as rounding numbers. To round off a whole number, remember the following points:
 Decide up to which place the number is to be rounded off.
 The digit preceding this place is to be compared with 5.
 If it is less than 5, all the digits towards its left including it will be replaced by 0. The digit in the place we decided in step 1 will remain unchanged.
 If 5 or greater than 5, all the digits towards its left will be replaced by 0. The digit in the place we decided in step 1 will be increased by 1.
 The digit thus obtained is the roundedoff number.
How to Round Off Fractions?
Fractions are written in the form of (p/q), where q not equal to zero. For rounding off the fractions, remember the following points:
 Both the numerator and denominator should be whole numbers to make the calculation easier.
 If not, follow the decimal point shifting rule of fractions to make them whole numbers.
 We will then take the numerator and denominator separately.
 The numerator and denominator are separately rounded off using the rules for rounding off numbers.
 The equal number of trailing zeros from the numerator and denominator can be ignored after rounding off.
 Simplify the fraction thus obtained.
Example
Fractions can be rounded off either by converting the fraction to a decimal and rounding off the number thus formed as a decimal number. Suppose, we have to round off a fraction (23.1/17).
We will rewrite this fraction as (231/170). Since, 1 is smaller than 5, after rounding off 231, we will get 230. Roundedoff value of 170 to nearest tens will be taken as 170 only. Thus, the obtained rounded off fraction becomes (230/170). Dropping the trailing zeros from both the numerator and denominator, we get, (231/17). Thus, the rounded fraction is 231/17
How to Round Off Decimals?
A decimal number is a combination of a whole and a fraction. To round off a decimal, remember the following points:
 Decide up to which place the number is to be rounded off.
 The digit preceding this place is to be compared with 5.
 If it is less than 5, all the digits towards its left including it will be replaced by 0. The digit in the place we decided in step 1 will remain unchanged.
 If 5 or greater than 5, all the digits towards its left will be replaced by 0. The digit in the place we decided in step 1 will be increased by 1.
 The training zeros after the decimal point in any number are insignificant and can be simply dropped.
 The digit thus obtained is the roundedoff number.
Example
Let's round off the decimal number 45.4784 up to 2 decimal places:
The initial steps while rounding off a decimal are similar to those for whole numbers. The decimal to be rounded off up to two significant places after the decimal point is 45.4784. To round off the number, we will mark the place up to which we are supposed to round off the number, that is, 7. All the digits towards the right of this marked digit should be replaced with 0. To do so, we will compare the first digit on its right side, 8 with 5.
Since 8 is greater than 5, we will replace 8 with 0, and digit 7 will be increased by 1 to give 8 in its place. So, the decimal number we get after rounding off is 45.4800. Since trailing zeros after the decimal point are insignificant, we will drop it here too. Thus, the rounded decimal is 45.68
Types of Rounding of Numbers
The most common three types of rounding of numbers are given below:

Rounding off a number to nearest tens
While comparing digits, we observe that the numbers 1, 2, 3, and 4 are nearer to 0. So, these numbers are rounded off to their lower ten value. Similarly, numbers 6, 7, 8, and 9 are nearer to 10. So, these numbers are rounded off to their higher ten value.
What about number 5? Since number 5 is equidistant from both 0 and 10, thus it is rounded off to the higher ten.
 Rounding off a number to nearest hundreds
Suppose, we have numbers from 201 to 249. All the numbers are closer to 200 in comparison to 300. So, these numbers will be rounded off to their nearest hundred, i.e. 200. Similarly, numbers 251 to 299 are closer to 300. So, these numbers will be rounded off to the higher hundreds, that is, 300.
 Estimation of the sum or difference
To estimate numbers during addition or subtraction, we should have an idea of a suitable place up to which the numbers can be rounded off. To estimate the sum of 19304 and 7814, we see that 19304 > 7814. Thus, both the numbers can be rounded off to the nearest thousands as 19300 and 8000.
Hence, 19000 + 8000 = 27000.
Solved Examples

Example 1: There are almost 321 pens in a pack. How many pens are there approximated to the nearest hundred?
Solution
The number of pens in the pack = 321. The digit at hundredth place = 3. The digit on the exact right of 3, i.e., 2 will be compared to 5. Since 2 is less than 5, 3 remains unchanged and the digits on the right of 3 are replaced with 0. Therefore, the required number of pens = 300.

Example 2: Can you help Miley estimate the sum of numbers 495 and 104 to its nearest hundred?
Solution
We know, 495 ≈ 500. Also, 104 ≈ 100. Thus adding 500 and 600, we get, 500 + 100 = 600. Therefore, the estimate sum = 600

Example 3: There were 4680 cherry trees in a park. Few workers were hired to plant 579 more trees. Can you estimate the total number of trees up to hundreds place, after the workers planted the trees?
Solution
Here, the number of trees in the yard = 4680. The number of new trees planted = 579. Total number of trees = 4680 + 579 = 5259 . After rounding off 5259 up to hundreds of places, we get 5300 trees. Therefore, the estimated number of tree planted = 5300

Example 4: Mandy and Sam were playing video games together. Mandy scored 2335 points and Sam scored 1023 points. What is the approximate total of the points they scored rounded up to hundreds place?
Solution
Here, total of Mandy and Sam's points = 2335 + 1023 = 3358 points. Rounding off 3358 to nearest hundred = 3400. Therefore, the estimated points = 3400
Practice Questions
Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.
FAQs on Rounding Numbers
How do you Explain Rounding Numbers?
"Rounding" means the process of making a number simpler such that its value remains close to what it was which makes the calculation easy.
What are the Rules for Rounding Off Decimal Numbers?
To round off a decimal number, remember the following points:
 Decide up to which place the number is to be rounded off.
 The digit preceding this place is to be compared with 5.
 If it is less than 5, all the digits towards its left including it will be replaced by 0. The digit in the place we decided in step 1 will remain unchanged.
 If 5 or greater than 5, all the digits towards its left will be replaced by 0. The digit in the place we decided in step 1 will be increased by 1.
 The training zeros after the decimal point in any number are insignificant and can be simply dropped.
 The digit thus obtained is the roundedoff number.
What is 62 to the Nearest 10?
If the last digit in the number is 5, 6, 7, 8, or 9, we always round up and if the last digit in the number is 1, 2, 3, or 4, we always round down. So, 62 to the nearest 10 is 60.
Where do we Use Rounding of Numbers in Real Life?
We usually use rounding of numbers in a grocery store, planning a party or while calculating the budget.
How to Round Off Numbers Ending in 5?
While rounding off a number ending in 5, we can replace 5 with 0, and the following digit is increased by 1.
How do you Round Off Numbers in Thousands?
To round off numbers in thousands, we compare the digit in hundreds place with 5. If the digit is greater than 5, the following digit is increased by 1.
And if the digit is less than 5, the following digit remains unchanged.
What does 2.5 Round To?
We will compare the digit to be dropped with 5. If the digit is greater or equal to 5, we increase the following digit by 1 and drop the digit that we compared.
Since 5 is equal to 5, we will increase 2 by 1 and drop 5. Thus, 2.5 is rounded off to 3.