Fractions/decimals/percentages | Year 6

01 / LEARN

Understand the idea.

Three ways to write one chance

Fractions, decimals and percentages can describe the same probability: $\frac{1}{2} = 0.5 = 50 %$ . A percentage means a number per hundred, so converting changes the notation rather than the chance.

Use an equivalent fraction with denominator $10$ or $100$ when possible. For example, $\frac{3}{5} = \frac{6}{10} = \frac{60}{100}$ . This gives $0.6$ or $60 %$ . Check that a probability stays between $0$ and $1$ , or between $0 %$ and $100 %$ .

Equivalent probability descriptions
Fraction	Decimal	Percentage
0	0	0%
1/4	0.25	25%
1/2	0.5	50%
3/4	0.75	75%
1	1	100%

Compare after matching forms

To compare chances, express both in a common form. For $0.4$ and $45 %$ , write $0.4 = 40 %$ . Now the larger value is clear. Comparing digits alone ignores the units of the percentage and the place values of the decimal.

A probability of $25 %$ is one quarter, but it does not schedule successes. It predicts the proportion over many trials under the same chance rule, without promising exactly one success in each set of four trials.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A fraction to a percentage

Write $3 / 5$ as a decimal and a percentage.

Worked solution

1
Make an equivalent fraction in tenths.
$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$
Multiplying numerator and denominator by the same number preserves the fraction's value.
2
Read the decimal place value.
$\frac{6}{10} = 0.6$
Six tenths is written with six in the tenths place.
3
Express the fraction per hundred.
$\frac{3}{5} = \frac{60}{100} = 60 %$
Sixty out of one hundred means sixty percent, so the decimal and percentage are 0.6 and sixty percent.

Answer

0.6 and 60%.

EXAMPLE 02

A common form for comparison

Which is more likely: an event with probability 0.35 or an event with probability $2 / 5$ ?

Worked solution

1
Convert two fifths to a decimal.
$\frac{2}{5} = \frac{4}{10} = 0.40$
Equivalent tenths give a decimal; the final zero makes the hundredths places easy to compare.
2
Compare like place values.
$0.40 > 0.35$
Forty hundredths is greater than thirty-five hundredths.
3
Identify the more likely event.
$\frac{2}{5} > 0.35$
A greater probability means a more likely event, so the event with probability two fifths is more likely.

Answer

The event with probability $2 / 5$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

Write $1 / 4$ as a decimal and percentage.

Show answer & reasoning

0.25 and 25%.

Multiply the numerator and denominator by $25$ : $\frac{1}{4} = \frac{25}{100}$ . Twenty-five hundredths is $0.25$ , which is $25 %$ .

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Write $\frac{1}{2}$ as a decimal and a percentage.
2 marks
Write 0.75 as a fraction and a percentage.
2 marks
Write $20 %$ as a fraction in simplest form.
2 marks
Which is larger: $30 %$ or $\frac{1}{4}$ ?
2 marks
Put $\frac{1}{2}$ , 0.2 and $75 %$ in order from least likely to most likely.
2 marks
A student writes a probability as $140 %$ . Explain why this cannot be correct.
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 a percentage.
2 marks
$\frac{1}{2} = \frac{5}{10} = \frac{50}{100}$ .
0.5 and $50 %$ .
Write 0.75 as a fraction and a percentage.
2 marks
$0.75 = \frac{75}{100} = \frac{3}{4}$ .
$\frac{3}{4}$ and $75 %$ .
Write $20 %$ as a fraction in simplest form.
2 marks
$\frac{20}{100} = \frac{1}{5}$ .
$\frac{1}{5}$ .
Which is larger: $30 %$ or $\frac{1}{4}$ ?
2 marks
$\frac{1}{4} = 25 %$ .
$30 %$ is greater than $25 %$ .
$30 %$ .
Put $\frac{1}{2}$ , 0.2 and $75 %$ in order from least likely to most likely.
2 marks
Convert to $20 %$ , $50 %$ and $75 %$ .
0.2, $\frac{1}{2}$ , $75 %$ .
A student writes a probability as $140 %$ . Explain why this cannot be correct.
2 marks
$100 %$ already includes all possible outcomes.
Check that favourable outcomes were not counted more than once or compared with the wrong total.
A probability cannot exceed $100 %$ .

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Mathematics Curriculum 2026

Numerical likelihood; fractions/decimals/percentages; expected versus observed outcomes; larger simulations and variation.

Official curriculum source ↗

In this lesson

Understand the idea.

Three ways to write one chance

Compare after matching forms

See the method in action.

A fraction to a percentage

Make an equivalent fraction in tenths.

Read the decimal place value.

Express the fraction per hundred.

A common form for comparison

Convert two fifths to a decimal.

Compare like place values.

Identify the more likely event.

Try it yourself.

Check your understanding

Keep practising