Year 8 Interactive Maths - Second Edition

## Rounding Off

Decimals numbers often contain more decimal places than we need in daily life.  For example, a builder may have calculated that 20.37 cubic metres of concrete is needed to make a driveway, but actually only needs a figure to the nearest tenth of a cubic metre to make the order.

From the number line, it is clear that 20.37 is closer to 20.4.  So, the amount ordered would be 20.4 cubic metres.  The builder has rounded off the calculated figure to one decimal place.  We say that the amount is rounded upwards since 20.4 is greater than 20.37.

Likewise, a builder may have calculated that 20.34 cubic metres of concrete is needed to make a driveway, but actually only needs a figure to the nearest tenth of a cubic metre to make the order.

From the number line, it is clear that 20.34 is closer to 20.3.  So, the amount ordered would be 20.3 cubic metres.  The builder has rounded off the calculated figure to one decimal place.  We say that the amount is rounded downward since 20.3 is less than 20.34.

###### To round off a decimal:
• Look at the digit to the right of the required decimal place.
• If the digit is less than 5, round down by ignoring the trailing digits.
• If the digit is 5 or more, round up by increasing the required decimal place by 1 and remove the trailing digits.

#### Example 16

Round 8.9463 kilograms to:
a.  one decimal place
b.  two decimal places
c.  three decimal places
d.  the nearest gram

##### Solution:

a.  The digit, 4, to the right of the required place is less than 5.  So, round down by ignoring the digits after the first decimal place.

b.  The digit, 6, to the right of the required place is more than 5.  So, round up by increasing the second decimal place by 1 and ignoring the trailing digits.

c.  The digit, 3, to the right of the required place is less than 5.  So, round down by ignoring the fourth decimal place.

The answer needs to be correct to 3 decimal places.