# Rounding Decimals

Rounding is necessary when the decimal number is too long. We round a decimal number to estimate it to its nearest whole number. To round a number, we consider the next digit to the right; if it is lesser than (<)  5, we round down, and if it is equal (=) to or greater than (>) 5, then we round up.

## To the Nearest Whole Number

Rounding a decimal to its nearest whole means converting a decimal with one digit after the point to a whole number closest to the original.

Round 54.7 to its nearest whole number.

Solution:

As we know, the place we would round is 4.
7 is at the 10ths place.
7 > 5, adding 1 to 4 in 54, we get 55
The nearest whole number is 55

We can also round a decimal number to its nearest tenth, the hundredth.

## To the Nearest Tenths

For rounding a decimal number to its tenths (10ths), we consider the digit at the thousandths (1000ths) place, i.e., the exact next decimal place. So, rounding a decimal to its 10ths means rounding a decimal number to one decimal place.

Let us round 25.37134 to its nearest tenths.

Rounding 43.25 to its nearest 10ths.

Round the decimal numbers 89.3613 and 62.2124 to their nearest 10ths.

Solution:

As we know,
In 89.3616, at the 100th place, 6 > 5
∴ 89.3616 = 89.4
As we know, the place we would round is 3
6 is at the 100ths place
6 > 5, adding 1 to 3 in 89.3616, we get 89.4
The nearest tenths is 89.4
Rounding 62.2124 ot its nearest tenths
1 is at the 100ths place
1 < 5, adding 0 to 2 in 62, we get 62.2
The nearest tenths is 62.2

Round 25.23 to its nearest 10ths.

Solution:

Rounding 25.23 ot its nearest 10ths
3 is at the 100ths place
3 < 5, adding 0 to 2 in 25.23, we get 25.2, removing the rest after 2.
The nearest tenths is 25.2

## To the Nearest Hundredths

Round 41.6458 to its nearest 100ths.

Solution:

The digit at the 1000th place is 5.
So, adding 1 with 4 in 6458,
∴ Rounded to its nearest 100ths, it becomes 41.65
Rounding 41.6458ot its nearest 100ths
5 is at the 1000ths place
5 = 5, adding 1 to 4 in 6458, we get 41.65, removing the rest
The nearest hundredths is 41.65

## Rounding Decimals to Given Places

We might not be directly given the place to be rounded to. Sometimes, we might have to round a decimal to certain places.

### Round to One Decimal Place

One decimal place means the digit at the 10ths place. So rounding a decimal upto one decimal place means rounding it to its nearest 10ths.

Rounding 1.423 to one decimal place:

### Round to Two Decimal Places

Two decimal places means the digit at the 100ths place. So rounding a decimal upto two decimal places means rounding it to its nearest 100ths.

Rounding 6.835 to two decimal places:

### Round to Three Decimal Places

Three decimal places means the digit at the 1000ths place. So rounding a decimal upto three decimal places means rounding it to its nearest 1000ths.

Rounding 5.7829 to three decimal places:

### Round to Four Decimal Places

Four decimal places means the digit at the 10000ths place. So rounding a decimal upto four decimal places means rounding it to its nearest 10000ths.

Rounding 38.1752 to four decimal places: