Topics
5. Decimals
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Australia
Year 5

5.06 Order decimals

Lesson
Practice

Are you ready?

We have previously  ordered decimals  that have digits in the tenths place. Let's practice.

Examples

Example 1

Arrange the following decimals from largest to smallest: 0.8, \, 0.3, \, 0.4.

Worked Solution
Create a strategy

Use a place value table and compare the numbers.

Apply the idea
Units.Tenths
0.8
0.3
0.4

In the tenths column we can see that 8 is greater than 4 which is greater than 3. So the numbers arranged from largest to smallest would be 0.8, \, 0.4, \, 0.3.

Idea summary

We can use a place value table to order decimals.

Order decimals with thousandths

This video starts looks at how to order numbers that have digits in the thousandths place.

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This video uses a place value table to compare numbers with thousandths.

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Examples

Example 2

Order these numbers in ascending order: 0.584, \, 0.936, \, 0.753.

Worked Solution
Create a strategy

Use a place value table and compare the numbers. Ascending means smallest to greatest.

Apply the idea
Units.TenthsHundredthsThousandths
0.584
0.936
0.753

In the tenths column we can see that 5 \lt 7 \lt 9. This means that 0.584 \lt 0.753 \lt 0.936 . So the number in ascending order would be 0.584, \, 0.753, \, 0.936.

Idea summary

To compare decimals with thousandths, we can use a place value table that includes the units, tenths, hundredths and thousandths columns.

Order decimals beyond thousandths

Let's look at ordering numbers that go beyond thousandths.

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Examples

Example 3

Order these numbers in ascending order: 0.4764, \, 0.2959, \, 0.5385.

Worked Solution
Create a strategy

Use a place value table and compare the numbers. Ascending means smallest to greatest.

Apply the idea
Units.TenthsHundredthsThousandthsTen thousandths
0.4764
0.2959
0.5385

In the tenths column we can see that 2 \lt 4 \lt 5. This means that 0.2959 \lt 0.4764 \lt 0.5385 . So the number in ascending order would be 0.2959, \, 0.4764, \, 0.5385.

Idea summary

If our numbers are not all expressed as thousandths, starting from the left of our number is one way to compare them. We can rename our numbers so they are all expressed as thousandths, which also helps us place them in order.

Outcomes

AC9M5N01

interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line

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