Familiar fraction–decimal–percentage equivalents | Year 5

01 / LEARN

The idea, step by step

Percent means out of one hundred

A percentage is a fraction with a hundred as its reference whole. Twenty-five percent means twenty-five out of every hundred equal parts, written $\frac{25}{100}$ . Its decimal is $0.25$ . A hundred-square grid makes this connection visible.

The whole must stay the same when changing notation. If the shaded part is one quarter of the grid, it is also twenty-five hundredths and twenty-five percent of that same grid.

\frac{1}{4} = \frac{25}{100} = 0.25 = 25 %

Use familiar equivalents as anchors

Half a whole is $\frac{1}{2} = \frac{50}{100} = 0.5 = 50 %$ . A tenth is $\frac{1}{10} = \frac{10}{100} = 0.1 = 10 %$ . A fifth is $\frac{1}{5} = \frac{20}{100} = 0.2 = 20 %$ . Use these anchors to reason about quarters, three quarters and simple tenths.

To check an unfamiliar statement, rename the fraction as hundredths when you can. For three quarters, multiply three and four by twenty-five: $\frac{3}{4} = \frac{75}{100} = 0.75 = 75 %$ . These are different names for the same share, not four different quantities.

Useful equivalent shares
Fraction	Decimal	Percentage
1/10	0.1	10%
1/5	0.2	20%
1/4	0.25	25%
1/2	0.5	50%
3/4	0.75	75%

A common trap

Writing 50% as 50.0.

Instead: The percent sign means divide the whole into a hundred equal parts. Fifty out of a hundred is one half, or 0.5, not fifty wholes.

02 / WORKED EXAMPLES

See the thinking

Example 1

Rename three tenths

Write $\frac{3}{10}$ as a decimal and a percentage.

$\frac{3}{10}$ is three tenths, so the decimal is $0.3$ .
Multiply numerator and denominator by ten: $\frac{3}{10} = \frac{30}{100}$ .
Thirty hundredths means thirty percent.

\frac{3}{10} = 0.3 = 30 %

Example 2

Interpret a familiar percentage

A reading chart is 75% shaded. What fraction is shaded, and what decimal names that share?

Seventy-five percent means $\frac{75}{100}$ .
Divide numerator and denominator by twenty-five to get three quarters.
Seventy-five hundredths is the decimal 0.75.

\frac{3}{4}

and

0.75

Check your understanding

Write one fifth as a decimal and percentage.

Show answer

$0.2$ and $20 %$

$\frac{1}{5} = \frac{20}{100}$ , which is $0.20$ or $20 %$ .

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Write $\frac{1}{2}$ as a decimal and percentage.
1 mark
Write $\frac{1}{4}$ as a decimal and percentage.
1 mark
Write $0.7$ as a fraction with denominator ten and as a percentage.
2 marks
Write the shaded share as a decimal and percentage.
2 marks
Write 20% as a fraction in simplest form and as a decimal.
2 marks
Ari says $\frac{1}{4}$ and $0.25$ are different amounts because one uses a slash. Explain why Ari is mistaken.
2 marks

Read the worked solutions

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

Write $\frac{1}{2}$ as a decimal and percentage.
1 mark
$\frac{1}{2} = \frac{50}{100}$ .
$0.5$ and $50 %$
Write $\frac{1}{4}$ as a decimal and percentage.
1 mark
$\frac{1}{4} = \frac{25}{100}$ .
$0.25$ and $25 %$
Write $0.7$ as a fraction with denominator ten and as a percentage.
2 marks
Seven tenths equals seventy hundredths.
$\frac{7}{10}$ and $70 %$
Write the shaded share as a decimal and percentage.
2 marks
Forty of the hundred equal squares are shaded.
$0.4$ and $40 %$
Write 20% as a fraction in simplest form and as a decimal.
2 marks
$\frac{20}{100} = \frac{1}{5}$ , and twenty hundredths is $0.20$ .
$\frac{1}{5}$ and $0.2$
Ari says $\frac{1}{4}$ and $0.25$ are different amounts because one uses a slash. Explain why Ari is mistaken.
2 marks
Splitting each quarter into twenty-five pieces gives a hundred pieces in the whole. One quarter contains twenty-five of them.
They name the same amount: $\frac{1}{4} = \frac{25}{100} = 0.25$ .

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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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