Ordering/number lines | Year 5

01 / LEARN

Understand the idea.

Compare from the greatest place

Compare decimals from the greatest place: whole numbers, tenths, hundredths, then thousandths. The first different digit decides. In $0.58$ and $0.6$ , five tenths is less than six tenths, so $0.58 < 0.6$ , even though it has more digits.

Trailing zeros can make matching places easier to see: $0.58 = 0.580$ and $0.6 = 0.600$ . Now compare $580$ and $600$ thousandths. Add zeros only at the end; inserting one between digits can change their place values.

Read the interval before the point

A number line needs a known interval size before you can read a point. Find the difference between two labelled ends and divide it by the number of equal spaces. Ten intervals across a change of $0.1$ make steps of $0.01$ .

Count spaces rather than tick marks. Starting at $0.30$ , the fifth step of $0.01$ lands at $0.35$ . Check that your point lies between the labelled ends; a step calculation outside that range signals a place-value or counting error.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Compare three decimal places

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

Worked solution

1
Give both numbers matching decimal places.
$0.45 = 0.450$
A trailing zero changes the name but not the value.
2
Compare matching places from left to right.
$0.405 < 0.450$
The tenths match, but 0 hundredths is less than 5 hundredths.
3
State which original number is greater.
$0.45 > 0.405$
The first different place already settles the comparison; the thousandths cannot reverse it.

Answer

$0.45 > 0.405$ .

EXAMPLE 02

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?

Worked solution

1
Find the total change across the line.
$0.13 - 0.12 = 0.01$
The ten equal intervals together cover one hundredth.
2
Calculate one interval.
$0.01 \div 10 = 0.001$
Each of the ten spaces is one thousandth wide.
3
Find the change over seven intervals.
$7 \times 0.001 = 0.007$
The seventh step means seven equal spaces after the starting point.
4
Add the change to the starting value.
$0.120 + 0.007 = 0.127$
0.127 is seven thousandths beyond 0.12 and still below 0.13.

Answer

$0.127$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

$0.406 < 0.46 < 0.6$

Use matching thousandths: $0.406$ , $0.460$ and $0.600$ . Since $406 < 460 < 600$ , the increasing order is $0.406 < 0.46 < 0.6$ .

Keep practising

6 worksheet questions · 10 marks

Open worksheet 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.

Checking saved progress…

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 ↗

In this lesson

Understand the idea.

Compare from the greatest place

Read the interval before the point

See the method in action.

Compare three decimal places

Give both numbers matching decimal places.

Compare matching places from left to right.

State which original number is greater.

Read a thousandths scale

Find the total change across the line.

Calculate one interval.

Find the change over seven intervals.

Add the change to the starting value.

Try it yourself.

Check your understanding

Keep practising