In the last section we dealt with rounding off to nearest 10 and now in this subtopic we will discuss about rounding off to nearest 100. When we were rounding number to 10 then we were considering the last digit that is the digit of the unit place. When we are rounding off to 100 then we will consider the tens digit.

**Rule I:** If the tens digit is 1, 2, 3, or 4 then the number will be rounded off to the previous nearest 100

**For example:**

Round off 826 to nearest hundred

Now the digit in the tens place is 2 hence the number will be rounded off to the previous hundred that is 800. 826 lie between 800 and 900 and the nearest hundred to 826 is 800.

**Rule II:** If the tens digit is 5, 6, 7, 8 or 9 then the number will be rounded off to the next nearest 100

**For example:**

Round off 876 to nearest hundred

We have 7 in the tens place hence the number is rounded to next nearest 100 that is 900. The two hundreds between which 876 lies is 800 and 900 and the nearest is 900. Hence 876 will be rounded off to 900.

**Here are few examples illustrating rounding off to nearest 100**

**1. Round off the following numbers to the nearest 100:**

(i) 632

(ii) 978

**Solution:**

(i) 600

Here tens digit number is 3 which is less than 5 hence the number will be rounded off to the previous hundred that is 600. 632 lie between 600 and 700 and hence the nearest hundred is 600.

(ii) 1000

In this example we can see that 7 is the tens digit number which is more than 5 and hence the number should be rounded off to the next nearest hundred. Now, 978 lie between 900 and 1000 hence the nearest hundred is 1000.

**2. Round off the following numbers to the nearest 100:**

(i) 5723

(ii) 2456

(iii) 13535

**Solution:**

(i) 5700

The tens digit in the number is 2 and we know that if the tens digit is 1, 2, 3, or 4 then we round it off to previous hundred. Hence 5723 will be rounded off to 5700 as the two hundred between which 5723 lie is 5700 and 5800 but it will rounded to 5700 as the tens digit (i.e. 2) is lees than 5.

(ii) 2500

In the number 2456 the tens digit is 5 and we know that if the tens digit is 5, 6, 7, or 9 then the number will be rounded off to next nearest hundred. Hence 2456 will be rounded off to 2500 as the tens digit is 5.

(iii) 13500

In 13535 tens digit is 3 that is less than 5 hence the number will be rounded off to the previous hundred. The two hundred between which 13535 lie is 13500 and 13600 but, 13535 is nearer to 13500. Hence, 13535 will be rounded off to 13500.

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