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# Rounding Numbers to the nearest 100

In order to ease our calculations, we often approximate the numbers to some extent. It helps us give approximate answers where exact values are not required. For instance, we may say that there are around 600 students in a school. That does not necessarily mean that there are exactly 600 students in a school. The exact number of students in the school may be somewhere around 600 which, for convenience we have round off to 600. Rounding off can also be termed as a shortcut method.

So, how do we decide how to round off a number to the nearest 100?

Before understanding the rules to round off a number, it is important to understand what does rounding off to 100 mean?

It means that we wish to round off the last three digits of a number, i.e. up to the hundreds place of a number.

## Rounding Up vs Rounding Down

### Rounding Up

If the number at the hundred’s place is followed by 5, 6, 7, 8, or 9, the number is rounded up.

Example  – We want to round off 54897 to the nearest 100.

1. Look for the digit at the hundred’s place. It is 8.

2. Now look for the digit to the right of the digit at the hundred’s place. The number is 9

3. Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 97 becomes 100 which on adding to 8 at the hundred’s places, becomes 900.

Hence, the number 54897 after being rounded off to the nearest 100 is 54900

Note : Here we moved up the number to the nearest hundred, which is why it is called rounding up.

Let us take another example.

Example  – We want to round off 71367 to the nearest 100.

1. Look for the digit at the hundred’s place. It is 3.

2. Now look for the digit to the right of the digit at the hundred’s place. The number is 6

3. Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 67 becomes 100 which on adding to 3 at the hundred’s places, becomes 400.

Hence, the number 71367 after being rounded off to the nearest 100 is 71400

### Rounding Down

If the number at the hundred’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up.

Example  – We want to round off 24615 to the nearest 100.

1. Look for the digit at the hundred’s place. It is 6.

2. Now look for the digit to the right of the digit at the hundred’s place. The number is 1.

3. Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 15 becomes 00 which on adding to 6 at the hundred’s places, becomes 600.

Hence, the number 24615 after being rounded off to the nearest 100 is 24600.

Note : Here we moved down the number to the nearest hundred, which is why it is called rounding down.

Let us consider another example

Example  – We want to round off 4738 to the nearest 100.

1. Look for the digit at the hundred’s place. It is 7.

2. Now look for the digit to the right of the digit at the hundred’s place. The number is 3.

3. Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 38 becomes 00 which on adding to 7 at the hundred’s places, becomes 700.

Hence, the number 4738 after being rounded off to the nearest 100 is 4700.

## Graphical Representation

Rounding off to the nearest 100 can also be understood graphically as shown below

First it should be understood that when you are rounding off to the nearest 100, the digit at the hundred’s place needs to be looked into.

Let us take a number 748

This number lies between 700 and 800. To round off this number, either we take it back to 700 or move it forward to 800. How do we decide where to go?

Look at the number line below:

The numbers that lie in the red areas will be rounded down to 700. Similarly, the numbers that lie in the blue areas will be rounded up to 800. This is because the numbers that lie in red areas, i.e. the numbers between 701 and 749 are closer to 700 as compared to 800. Hence they will be rounded down.

However, the numbers that lie between 750 and 799 are closer to 800 due to which they would be rounded up to 800.

## Remember

When rounding off a number to the nearest hundred, look at the TENS DIGIT of the number.

• If that digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred. (Round down)
• If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred. (Round Up)

## Some More Examples

Let us round off these numbers to the nearest 100

1.         6216                Number after rounding off to the nearest 100                      6200

2.         845                  Number after rounding off to the nearest 100                      800

3.         9562                Number after rounding off to the nearest 100                      9600

4.         10160              Number after rounding off to the nearest 100                      10200

5.         601                  Number after rounding off to the nearest 100                      600

6.         4945                Number after rounding off to the nearest 100                      5000

7.         2264                Number after rounding off to the nearest 100                      2300

8.         1419                Number after rounding off to the nearest 100                      1400

9.         22366              Number after rounding off to the nearest 100                      22400

10.       14158              Number after rounding off to the nearest 100                      14200

A graphical representation of rounding off to the nearest 100 has been presented below for better understanding.

Think of how many students are at your school. Unless it is a small school you would probably think of a number to the nearest hundred. Below are three examples of rounding an exact number to the nearest hundred.

Note: You can use this rounding calculator at the foot of this page to round a number to the nearest 100.

## Rule for rounding to the nearest 100

Look at the number in the tens’ place and…

View the examples below showing how to round to the nearest 100