Fraction connections | Year 4

01 / LEARN

The idea, step by step

Read the denominator as a place name

A fraction with denominator ten counts tenths. A fraction with denominator one hundred counts hundredths. This lets us move directly between fraction and decimal notation.

Three tenths is 0.3. Three hundredths is 0.03. The denominator tells which column receives the digit.

Make a useful equivalent fraction

For a familiar fraction such as one half, rename it in tenths or hundredths first. One half is five tenths, so it is 0.5.

One quarter is twenty-five hundredths, so it is 0.25. Use equal strips or a hundred-grid to justify the conversion; the amount must stay unchanged.

A common trap

Writing $\frac{7}{100}$ as 0.7.

Instead: Seven hundredths needs two places after the point: 0.07. The zero shows there are no tenths.

02 / WORKED EXAMPLES

See the thinking

Example 1

Convert a fifth

Write $\frac{2}{5}$ as a decimal.

Multiply numerator and denominator by 2 to make tenths.
$\frac{2}{5} = \frac{4}{10}$ .
Four tenths is written 0.4.

0.4

Example 2

Convert three quarters

Write $\frac{3}{4}$ as a decimal.

Each quarter is twenty-five hundredths.
Three groups of twenty-five are seventy-five.
Three quarters equals seventy-five hundredths.

0.75

Check your understanding

What decimal equals $\frac{1}{4}$ ?

Show answer

$0.25$

One quarter equals twenty-five hundredths, $\frac{25}{100}$ .

03 / WORKSHEET

Your turn

6 questions · 9 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Write $\frac{3}{10}$ as a decimal.
1 mark
Write $\frac{7}{100}$ as a decimal.
1 mark
Write 0.23 as a fraction with denominator 100.
1 mark
Write 0.8 as a fraction in tenths and in hundredths.
2 marks
Write $\frac{1}{2}$ and $\frac{1}{4}$ as decimals.
2 marks
Which is larger, $\frac{2}{5}$ or 0.35? Explain.
2 marks

Read the worked solutions

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

Write $\frac{3}{10}$ as a decimal.
1 mark
The fraction counts three tenths.
$0.3$
Write $\frac{7}{100}$ as a decimal.
1 mark
Seven belongs in the hundredths place.
$0.07$
Write 0.23 as a fraction with denominator 100.
1 mark
The amount is twenty-three hundredths.
$\frac{23}{100}$
Write 0.8 as a fraction in tenths and in hundredths.
2 marks
Eight tenths contain eighty hundredths.
$\frac{8}{10} = \frac{80}{100}$
Write $\frac{1}{2}$ and $\frac{1}{4}$ as decimals.
2 marks
One half is five tenths; one quarter is twenty-five hundredths.
$0.5$ and $0.25$ .
Which is larger, $\frac{2}{5}$ or 0.35? Explain.
2 marks
$\frac{2}{5} = 0.4 = 0.40$ ; forty hundredths is more than thirty-five hundredths.
$\frac{2}{5}$

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Tenths/hundredths; representations; notation; fraction connections.

Official curriculum source ↗

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