Familiar fraction–decimal–percentage equivalents | Year 5

01 / LEARN

Understand the idea.

Percent means out of one hundred

Percent means “out of one hundred”. A hundred-square grid represents one whole, so shading $25$ equal squares gives $\frac{25}{100}$ of the grid, or $25 %$ . The decimal $0.25$ names the same twenty-five hundredths.

Changing between fraction, decimal and percentage changes the notation, not the share. Keep the reference whole fixed: one quarter of a grid is also $25 %$ of that same grid, regardless of how large the grid is drawn.

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

Use familiar equivalents as anchors

Use familiar equivalents as anchors. One half is $0.5$ or $50 %$ ; one tenth is $0.1$ or $10 %$ ; one fifth is $0.2$ or $20 %$ . Each equality can be checked by rewriting the fraction in hundredths.

For three quarters, each quarter is twenty-five hundredths, so $\frac{3}{4} = \frac{75}{100} = 0.75 = 75 %$ . Multiply numerator and denominator by the same number when renaming a fraction. The percent sign is essential: $75$ and $75 %$ are different numbers.

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%

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Rename three tenths

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

Worked solution

1
Name three tenths as a decimal.
$\frac{3}{10} = 0.3$
The first decimal place counts tenths.
2
Rename the same fraction in hundredths.
$\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}$
Multiplying both numerator and denominator by 10 preserves the share.
3
Write the equivalent percentage.
$\frac{3}{10} = 0.3 = 30 %$
Thirty out of one hundred means thirty percent.

Answer

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

EXAMPLE 02

Interpret a familiar percentage

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

Worked solution

1
Translate the percentage into hundredths.
$75 % = \frac{75}{100}$
Percent expresses the shaded share out of one hundred equal parts.
2
Simplify the fraction.
$\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}$
Dividing both counts by 25 preserves the share and gives simplest form.
3
Name the same hundredths as a decimal.
$\frac{75}{100} = 0.75$
Seventy-five hundredths has 7 tenths and 5 hundredths.
4
State both requested names.
$\frac{3}{4} and 0.75$
The fraction and decimal describe the same shaded portion of the reading chart.

Answer

$\frac{3}{4}$ and $0.75$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

Write one fifth as a decimal and percentage.

Show answer & reasoning

$0.2$ and $20 %$

Multiply numerator and denominator by $20$ : $\frac{1}{5} = \frac{20}{100}$ . Twenty hundredths is $0.20 = 0.2$ , which is also $20 %$ .

Keep practising

6 worksheet questions · 10 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Percent means out of one hundred

Use familiar equivalents as anchors

See the method in action.

Rename three tenths

Name three tenths as a decimal.

Rename the same fraction in hundredths.

Write the equivalent percentage.

Interpret a familiar percentage

Translate the percentage into hundredths.

Simplify the fraction.

Name the same hundredths as a decimal.

State both requested names.

Try it yourself.

Check your understanding

Keep practising