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.

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.

Steps	Observations	Working out
1	25.37134
2	3 is at the 10ths place. The next digit to it is 7.
3	7 > 5	So, we will round up the preceding number, i.e., 3.  ∴ 3 +1 = 4
4	After rounding up, we get 25.4	We write the number upto 4 and remove the rest.

Rounding 43.25 to its nearest 10ths.

Steps	Observations	Working out
1	43.25
2	2 is at the 10ths place. The next digit to it is 5.
3	5 = 5	So, we will round up the preceding number, i.e., 3.  ∴ 2 +1 = 3
4	After rounding up, we get 43.3	We write the number upto 3 and remove the rest.

To the Nearest Hundredths

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:

Steps	Observations	Working out
1	1.423
2	4 is at the 10ths place. The next digit to it is 2.
3	2 < 5	So, we will add 0 to the preceding number, i.e., 4.  ∴ 4 + 0 = 4
4	After rounding up, we get 1.4	We write the number upto 4 and remove the rest.

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:

Steps	Observations	Working out
1	6.835
2	3 is at the 100ths place. The next digit to it is 5.
3	5 = 5	So, we will add 1 to the preceding number, i.e., 3.  ∴ 3 + 1 = 4
4	After rounding up, we get 6.84	We write the number upto 4 and remove the rest.

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:

Steps	Observations	Working out
1	5.7829
2	2 is at the 1000ths place. The next digit to it is 9.
3	9 > 5	So, we will add 1 to the preceding number, i.e., 2.  ∴ 2 + 1 = 3
4	After rounding up, we get 5.783	We write the number upto 3 and remove the rest.

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:

Steps	Observations	Working out
1	38.17534
2	3 is at the 10000ths place. The next digit to it is 4.
3	4 < 5	So, we will add 0 to the preceding number, i.e., 3.  ∴ 3 + 0 = 3
4	After rounding up, we get 38.1753	We write the number upto 3 and remove the rest.