Round numbers with decimals

Exploration

When we round a number to the nearest thousandth, we first want to know about its decimal values. A number like $0.0537$0.0537 can be written in a place value table as shown below.

Units	.	Tenths	Hundredths	Thousandths	Ten-thousandths
$0$0	$.$.	$0$0	$5$5	$3$3	$7$7

We can see that the thousandths is the third decimal place.

To round this number, we look at the ten thousandths, or the fourth decimal place. If the place value is less than $5$5 we round down, and if it's greater or equal to $5$5 we round up.

The number $0.0537$0.0537 lies between $0.053$0.053 and $0.054$0.054, and because the place value in the fourth decimal place is $7$7, we round up to $0.054$0.054.

We can round to the nearest ten-thousandth, or to four decimal places, using the same procedure.

Worked example

Example 1

Round $45.43021$45.43021 to four decimal places.

Think: We want to look at the place value in the fifth decimal place.

Do: The place value in the fifth decimal place is $1$1. So we round the number $45.43021$45.43021 down to $45.4302$45.4302.

 

example 2

Round $45.09997$45.09997 to four decimal places.

Think: We want to look at the place value in the fifth decimal place.

Do: The place value in the fifth decimal place is $7$7. So we round the number $45.09997$45.09997 up.

Ordinarily this means we increase the place value by $1$1, but whenever there is a $9$9, we change it to zero $0$0 and add the $1$1 to the place value to the left.

So the number $45.09997$45.09997 rounds up to $45.1000$45.1000.

Practice questions

question 1

question 2

question 3