Comparing and ordering decimals

The process of comparing and ordering decimals is similar to the process of comparing and ordering whole numbers.

You must use your knowledge of place value and know how to find which digit is greatest or smallest in each place value column.

This place value chart shows you that 0.157 is greater than 0.146.

When you want to compare numbers, you look at the digit with the greatest value first.

You can see that the digits in each number are the same until you reach the hundredths column.

As 5 is greater than 4, you can say 0.157 is greater than 0.146.

Or you could write this using the 'greater than' symbol like this:

0.157 > 0.146

Test out your knowledge of comparing and ordering decimals with this quiz, then read on to complete the page.

Take the numbers 2.43 and 2.34.

Let's use a place value chart to find which is greater.

The chart on the left represents 2.43 and the chart on the right represents 2.34.

When you want to compare numbers, you always look at the greatest value first.

In this place value chart, the digit with the greatest value is the ones column.

Both of these numbers have 2 ones.

So now, you need to move to look at the next column - the tenths column.

2.43 has 4 in the tenths column. 2.34 has 3 in the tenths column.

4 is the greater value. So, you don’t need to keep going and look at the hundredths.

As 4 is greater than 3, so you can say:

2.43 > 2.34

The greater number is 2.43.

Ordering decimals

This place value chart has three rows containing three numbers.

Let’s find out if the numbers are ordered from smallest to greatest.

First, you need to look at the greatest value in the place value chart, which is the ones.

All three numbers have 1 in the ones column.

So, now you need to move to the tenths column.

1.03 has 0 in the tenths column.

1.3 and 1.32 both have 3 in the tenths column

So 1.03 is the smallest number.

As 1.3 and 1.32 both have 3 in the tenths column, you need to move to the next column. This is the hundredths column.

1.3 has the 0 in the hundredths column.

1.32 has 2 in the hundredths column, so that is the greatest number.

So, the numbers in the chart were ordered from smallest to greatest. You can use the greater than (>) and less than (<) signs to order them.

In ascending order (smallest to greatest) the numbers are:

1.03 < 1.3 < 1.32

In descending order (greatest to smallest) the numbers are:

1.32 > 1.3 > 1.03

Ordering decimals using a number line

You can use a number line to order decimals too.

This number line is split into tenths and has the numbers 0.6, 0.4, and 0.9 labelled on it.

The numbers are shown in ascending order (smallest to greatest).

You can say:

0.4 < 0.6 < 0.9

You can also order numbers with 2 decimal places on a number line.

, in between each tenth on a number line, there are ten hundredths.

If you look closely at the number line above you will the intervals for each tenth are marked with a line but they are not labelled.

If each of the missing intervals were labelled, it would look like this:

The next image shows a number containing two decimal places.

0.43 marked on this number line.

Placing numbers on a number line makes it easier to order them.

For example, if you wanted to order 0.43, 0.49 and 0.03, you would place all three numbers on the number line.

The number line above tells you that:

0.03 < 0.43 < 0.49