What is rounding off decimal numbers?
The decimal part of a decimal number as discussed in the chapter
Read, Write Decimal Numbers. Converting Decimals to Fractions.
can have any number of digits. Sometimes which may become so longer that may not be easy to read.
Such decimal numbers having longer decimal part can be reduced to a shorter decimal part with lesser number of
digits, this process is called rounding or rounding off decimals.
Let’s see next how it is processed with steps and their rules.
The digit to be rounded off must have another digit on its right.
Round off to the nearest whole number
To round off the decimal number to the nearest whole number only, the digit at the tenths place is checked.
If the digit at the tenths place is less than 5, then the whole part is the final answer of
rounding off leaving behind the decimal part.
If the digit at the tenths place is equal to or greater than 5, then the digit at ones place of the whole
part is increased by one.
Example 1: Round off 58.73 to the whole number only
The digit at the tenths place of 58.73 is 7
7 is greater than 5. So, the digit 8 at ones place of the whole part 58 will be increased by 1
which becomes 8 + 1 = 9
∴ the rounding of 58.73 to its the nearest whole number is 59
Example 2: Round off the 74.52 to the nearest ones place
The digit at the tenths place of 74.52 is 5, which is equal to 5
So, increase the digit 4 at ones place of the whole part 74
which becomes 4 + 1 = 5
∴ the rounding of 74.52 to its the nearest whole number is 75
Example 3: Round 92.37 to the nearest ones place
The digit at the tenths place is 3, which is less than 5
So, the whole part 92 of 92.37 will be the rounded off value
∴ the rounding of 92.37 to its the nearest whole number is 92
Round off to tenths place
In rounding of decimal numbers upto one decimal place the digit at the hundredths place is checked. If this
digit is equal to or greater than 5, then the digit at the tenth place is increased by one.
If the digit at the hundredths place is less than 5, then the digit at the tenths place remains intact,
not increased by one and the digit at the hundredths place is removed.
Example 1: Round 35.26 upto one decimal place only
The digit at hundredth place of 35.26 is 6
6 is greater than 5. So, 2 at tenths place will be increased by 1
which becomes 2 + 1 = 3
∴ the rounding of 35.26 upto one decimal place is 35.3
Example 2: Round 7.63 to the nearest tenth place
The digit at hundredth place is 3, which is less than 5
So, the tenths place digit 6 will not get increment of 1 and the 3 at the hundredths place will be
removed.
∴ the rounding of 7.63 to the nearest tenth place is 7.6
Example 3: Round off 49.85 to the nearest tenth place
49.85 has 5 at its hundredth place, which is equal to 5
So, the tenths place digit 8 will get increment of 1
i.e. 8 becomes 8 + 1 = 9
∴ the rounding of 49.85 to the nearest tenth place is 49.9
Rounding to hundredths place
To round a decimal number to hundredths place, the digit at the thousandths place is checked; if it
is equal to or greater than 5 then the digit at the hundredths place is increased by one.
If it is less than 5, then do not increase hundredths place digit by one but remove the digit at
thousandths place.
Example 1: Round 75.653 to the nearest hundredths place
The digit at thousandths place is 3
3 is less than 5. So, no increment to the hundredths place digit 5
In this case, remove the thousandths place digit 3
∴ the rounding of 75.653 to the nearest hundredths place is 75.65
Example 2: Round 1.269 upto only two decimal places
1.269 has 9 at the thousandths place
9 is greater than 5. So, increase hundredths place digit 6 by 1
i.e. 6 becomes 6 + 1 = 7
∴ the rounding of 1.269 upto two decimal place is 1.27
Example 3: Round off 94.475 to the nearest hundredths place
94.475 has 5 at the thousandths place
5 is equal to 5. So, increase hundredths place digit 7 by 1
i.e. 7 becomes 7 + 1 = 8
∴ the rounding of 94.475 upto two decimal place is 94.48
