Ordering/number lines | Year 5

01 / LEARN

The idea, step by step

Compare from the greatest place

Compare whole-number parts first. If they match, compare tenths, then hundredths, then thousandths. Stop at the first different place. For $0.58$ and $0.6$ , the tenths are five and six, so $0.58 < 0.6$ . The length of the written number is not a measure of its size.

Trailing zeros can help line up the places: compare $0.580$ with $0.600$ . This is the same comparison written in thousandths. Add zeros only at the end of the decimal part, not between existing digits.

Read the interval before the point

On a number line, equal spaces show equal changes. Between $0.3$ and $0.4$ , ten equal intervals are hundredths because the total difference is one tenth. The fifth step after $0.3$ is $0.35$ .

Count the spaces, not the tick marks. Include the unit if a line represents a measurement. Before plotting, decide which two labelled values the decimal lies between; then count the correct number of equal steps.

A common trap

Saying 0.125 is bigger than 0.9 because 125 is bigger than 9.

Instead: Compare decimal places, not the digits as whole numbers. Nine tenths is 900 thousandths, which is more than 125 thousandths.

02 / WORKED EXAMPLES

See the thinking

Example 1

Compare three decimal places

Which is greater: $0.405$ or $0.45$ ?

Write $0.45$ as $0.450$ .
Both numbers have four tenths.
The hundredths are zero and five, so 0.450 is greater.

0.45 > 0.405

Example 2

Read a thousandths scale

The line runs from 0.12 to 0.13 in ten equal intervals. Which value is at the seventh step after 0.12?

The full change is 0.01. Ten equal intervals make each step 0.001.
Write the left end as 0.120.
Seven steps add seven thousandths, reaching 0.127.

0.127

Check your understanding

Put $0.46$ , $0.406$ and $0.6$ in increasing order.

Show answer

$0.406 < 0.46 < 0.6$

Compare 406, 460 and 600 thousandths.

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Insert $<$ , $>$ or $=$ : $0.8 ? 0.75$ .
1 mark
Insert $<$ , $>$ or $=$ : $0.50 ? 0.5$ .
1 mark
Order $0.306$ , $0.36$ and $0.063$ from smallest to largest.
2 marks
A line from 0.4 to 0.5 has ten equal intervals. What value is at the third tick after 0.4?
2 marks
Point A is shown on the number line. Write its decimal value.
2 marks
Two toy cars travel 0.709 metre and 0.79 metre. Which travels farther? Explain using equal decimal places.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Insert $<$ , $>$ or $=$ : $0.8 ? 0.75$ .
1 mark
Eight tenths is eighty hundredths, more than seventy-five hundredths.
$>$
Insert $<$ , $>$ or $=$ : $0.50 ? 0.5$ .
1 mark
A trailing zero does not change the value.
$=$
Order $0.306$ , $0.36$ and $0.063$ from smallest to largest.
2 marks
Compare 63, 306 and 360 thousandths.
$0.063 < 0.306 < 0.36$
A line from 0.4 to 0.5 has ten equal intervals. What value is at the third tick after 0.4?
2 marks
Each interval is one hundredth. Three hundredths after 0.40 is 0.43.
$0.43$
Point A is shown on the number line. Write its decimal value.
2 marks
Each interval is 0.001. Six intervals after 0.250 is 0.256.
$0.256$
Two toy cars travel 0.709 metre and 0.79 metre. Which travels farther? Explain using equal decimal places.
2 marks
Write 0.79 as 0.790.
790 thousandths is greater than 709 thousandths.
The car travelling 0.79 metre.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

Beyond hundredths; ordering/number lines; familiar fraction–decimal–percentage equivalents.

Official curriculum source ↗

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