Fractions/decimals/percentages | Year 6

01 / LEARN

The idea, step by step

Three ways to write one chance

A fraction, decimal and percentage can describe the same position on the probability scale. One half equals 0.5 and 50%. The notation changes, but the chance does not.

Use equivalent fractions with denominator 10 or 100 when convenient. For example, three fifths equals six tenths, which is 0.6 or 60%. Probabilities cannot be negative or greater than one, and probability percentages cannot exceed 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, rewrite them in a common form. Compare 0.4 and 45% as 40% and 45%; the latter is greater. Do not compare the digits 4 and 45 without their place values.

A 25% chance means a quarter of equally likely outcomes in the model. In a repeated experiment it predicts a long-run pattern, not a promise of exactly one success in every block of four trials.

A common trap

0.8 is the same probability as 8%.

Instead: 0.8 is eight tenths or 80%. Eight percent is 0.08.

02 / WORKED EXAMPLES

See the thinking

Example 1

A fraction to a percentage

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

Multiply numerator and denominator by 2: $3 / 5 = 6 / 10$ .
Six tenths is 0.6.
Multiply the probability by 100 to express percent.

0.6 and 60%.

Example 2

A common form for comparison

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

Write $2 / 5 = 4 / 10 = 0.4 = 40 %$ .
Write $0.35 = 35 %$ .
Compare 40% with 35%.

The event with probability

2 / 5

Check your understanding

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

Show answer

0.25 and 25%.

$1 / 4 = 25 / 100$ , so its decimal is 0.25 and its percentage is 25%.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Write $1 / 2$ 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 $1 / 4$ ?
2 marks
Put $1 / 2$ , 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 $1 / 2$ as a decimal and a percentage.
2 marks
$1 / 2 = 5 / 10 = 50 / 100$ .
0.5 and 50%.
Write 0.75 as a fraction and a percentage.
2 marks
$0.75 = 75 / 100 = 3 / 4$ .
$3 / 4$ and 75%.
Write 20% as a fraction in simplest form.
2 marks
$20 / 100 = 1 / 5$ .
$1 / 5$ .
Which is larger: 30% or $1 / 4$ ?
2 marks
$1 / 4 = 25 %$ .
30% is greater than 25%.
30%.
Put $1 / 2$ , 0.2 and 75% in order from least likely to most likely.
2 marks
Convert to 20%, 50% and 75%.
0.2, $1 / 2$ , 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 ↗

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