Decimal Places


A number can be rounded off to a specified place value or number of decimal places.

When we round a number to a certain number of decimal places, the digits 0,1,2,3,4 round off leaving the digit in the preceding place unchanged.

4.3612=4.36 (rounded to two decimal places, the digit 6 is unchanged since the digit immediately on its right is 1).

4.36539=4.365, to 3 decimal places. The digit 5 is unchanged since the digit immediately on its right is 3).
But, if the digit immediately on the right is 5.6.7.8 or 9, then rounding up will increase the digit in the preceding place by 1).
4.35539=4.4, to 1 decimal place.(The digit 3 becomes 4 since the digit immediately on its right is 6).

4.36539=4.37, to 2 decimal places. (The digit 6 becomes 7 since the digit immediately on its right is 5).

Nearest Integer (Nearest 10, 100, 1000…)

We may wish to round a number to its nearest integer, that is, to zero decimal places. If the digits immediately on the right are 0, 1, 2, 3 or 4, then the number is unchanged but if the digits immediately on the right are 5, 6, 7, 8 or 9, then the number should be increased by 1.

567.123 = 567, to the nearest integer,

4.019 = 4, to the nearest integer,

567.745 = 568, to the nearest integer,

4.913 = 5, to the nearest integer,

27999.123 = 27999, to the nearest integer,

27999.875 = 28000, to the nearest integer,

-123.456 = -123, to the nearest integer,

-123.678 = -124, to the nearest integer and not -122, be careful with negative numbers.


Example

Write the following numbers correct to 3 decimal places:

i) 1.23456

ii) 0.99998

iii) -14.0195

iv) 123.45602

v) 1000.0001

To 3 decimal places, these are:

i) 1.235

ii) 1.000

iii) -14.020

iv) 123.456

v) 1000.000