Free worksheet · Australian Curriculum

Fractions, decimals and percentages worksheets with answers

Fractions, decimals and percentages are three ways of writing the same number. Learn to move between them, including recurring decimals and percentages over 100%, then make a free worksheet with full solutions.

Choose your year ↓Make a worksheet ↓How to do it and a quick check ↓

Choose your year level

Fractions, decimals and percentages at each year level, matched to the textbook chapters most Victorian schools use: a free printable worksheet with answers, sample questions, and an auto-marked test teachers can share.

Free Year 7 fractions, decimals and percentages worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

Download the PDF

Auto-marked test for your class

Teachers: share one link and every student is marked straight away, with worked solutions.

Create a test

Printable practice exam

Mix in harder questions, with marks and a suggested time.

Build an exam

Year 7 topics covered

Fractions and percentages
Connecting decimals and fractions
Connecting decimals and percentages
Expressing proportions using decimals, fractions and percentages

Sample Year 7 fractions, decimals and percentages questions

Fractions and percentages
(a) Write $\dfrac{7}{20}$ as a percentage.

(b) Write $45\%$ as a fraction in simplest form.
Show the answer
Key idea: Percent means out of $100$ .
1. (a) $\dfrac{7}{20} = \dfrac{7 \times 5}{20 \times 5} = \dfrac{35}{100} = 35\%$
2. (b) $45\% = \dfrac{45}{100} = \dfrac{45 \div 5}{100 \div 5} = \dfrac{9}{20}$
Answer: (a) $35\%$ (b) $\dfrac{9}{20}$
Connecting decimals and fractions
Write $\dfrac{7}{8}$ as a decimal.
Show the answer
Key idea: Divide the numerator by the denominator.
1. $7 \div 8 = 0.875$
Answer: $0.875$
Connecting decimals and percentages
Write each decimal as a percentage: (a) $0.47$ (b) $0.6$ (c) $1.25$
Show the answer
Key idea: To change a decimal to a percentage, multiply by $100$ .
1. (a) $0.47 \times 100 = 47\%$
2. (b) $0.6 \times 100 = 60\%$
3. (c) $1.25 \times 100 = 125\%$
Answer: (a) $47\%$ (b) $60\%$ (c) $125\%$
Expressing proportions using decimals, fractions and percentages
A student scored $36$ out of $48$ on a maths test. Express the student's score as a percentage of the total, rounded to one decimal place.
Show the answer
Key idea: Write the score as a fraction of the total, then multiply by $100$ to convert to a percentage.
1. Write as a fraction: $\dfrac{36}{48}$
2. Multiply by $100$ : $\frac{36}{48} \times 100$
3. Simplify the fraction first: $\dfrac{36}{48} = 0.75$
4. Calculate: $0.75 \times 100 = 75$
Answer: The student scored $75\%$ .

Free Year 8 fractions, decimals and percentages worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

Download the PDF

Auto-marked test for your class

Teachers: share one link and every student is marked straight away, with worked solutions.

Create a test

Printable practice exam

Mix in harder questions, with marks and a suggested time.

Build an exam

Year 8 topics covered

Terminating decimals, recurring decimals and rounding
Converting fractions, decimals and percentages

Sample Year 8 fractions, decimals and percentages questions

Terminating decimals, recurring decimals and rounding
Convert $\dfrac{9}{16}$ to a decimal and state whether it is terminating or recurring.
Show the answer
Key idea: If the denominator's only prime factors are 2s and 5s, the decimal terminates. Divide to find the decimal.
1. Check the denominator: $16 = 2^4$ . Only 2s, so the decimal terminates.
2. Divide: $9 \div 16$ .\
$\begin{aligned} 9 \div 16 &= 0.5625 \end{aligned}$
1. Verify: $0.5625 \times 16 = 9$ ✓
Answer: $\dfrac{9}{16} = 0.5625$ (terminating decimal)
Converting fractions, decimals and percentages
Write $\dfrac{7}{8}$ as a percentage.
Show the answer
Key idea: Multiply by $100\%$ .
1. $\frac{7}{8} \times 100\% = \frac{700}{8}\% = 87.5\%$
Answer: $87.5\%$
Terminating decimals, recurring decimals and rounding
Convert $\dfrac{5}{12}$ to a recurring decimal. Write your answer using dot notation.
Show the answer
Key idea: Divide the numerator by the denominator. When a remainder repeats, the decimal recurs. Use a dot above the first and last repeating digit.
1. Check the denominator: $12 = 2^2 \times 3$ . It has a factor of 3 (not just 2s and 5s), so the decimal recurs.
2. Perform the division $5 \div 12$ :\
$\begin{aligned} 5 \div 12 &= 0.41666\ldots \end{aligned}$
1. The digit 6 repeats forever, so the recurring part is just 6.
2. In dot notation, place one dot above the 6: $0.41\dot{6}$
Answer: $\dfrac{5}{12} = 0.41\dot{6}$
Converting fractions, decimals and percentages
Write $0.045$ as a percentage.
Show the answer
Key idea: Multiply by $100\%$ , which moves the decimal point two places to the right.
1. $0.045 \times 100\% = 4.5\%$
Answer: $4.5\%$

Topic guide

Fractions, decimals and percentages, explained

Six conversions, each with a worked example. Percent means 'out of 100', which links all three.

1. Fraction to decimal

Divide the numerator by the denominator:

$\frac{3}{8} = 3 \div 8 = 0.375$

If the denominator goes into $10$ , $100$ or $1000$ , make an equivalent fraction instead: $\frac{7}{20} = \frac{35}{100} = 0.35$ .

2. Decimal to fraction

Write the decimal over $10$ , $100$ or $1000$ using its place value, then simplify:

$0.45 = \frac{45}{100} = \frac{9}{20} 2.125 = 2\frac{125}{1000} = 2\frac{1}{8}$

3. Recurring decimals

Some fractions give decimals that repeat forever. A dot goes over the repeating digit, or over the first and last digits of a repeating block:

$\frac{2}{3} = 0.\dot{6} \frac{1}{6} = 0.1\dot{6} \frac{5}{11} = 0.\dot{4}\dot{5}$

To change $0.\dot{4}\dot{5}$ back to a fraction, let $x = 0.\dot{4}\dot{5}$ . Two digits repeat, so multiply by $100$ and subtract:

$100x - x = 45.\dot{4}\dot{5} - 0.\dot{4}\dot{5}, 99x = 45, x = \frac{45}{99} = \frac{5}{11}$

4. Percentage to fraction or decimal

Write the percentage over $100$ and simplify, or divide by $100$ for the decimal:

$35\% = \frac{35}{100} = \frac{7}{20} = 0.35 12.5\% = 0.125 = \frac{1}{8}$

5. Fraction or decimal to percentage

Multiply by $100\%$ :

$\frac{3}{5} \times 100\% = 60\% 0.072 \times 100\% = 7.2\% \frac{1}{3} \times 100\% = 33\frac{1}{3}\%$

For a decimal, this moves the decimal point two places to the right.

6. Percentages over 100%

A percentage over $100\%$ is more than one whole, so its fraction and decimal are greater than $1$ :

$150\% = 1.5 = 1\frac{1}{2} 2.4 = 240\% \frac{7}{4} = 1.75 = 175\%$

These come up with growth and mark-ups, such as a price that is $120\%$ of what it was.

Quick check: 10 questions

Try each one, then open the answer.

Write $0.7$ as a percentage.
Answer
$70\%$
Write $\frac{3}{4}$ as a decimal.
Answer
$0.75$
Write $45\%$ as a fraction in simplest form.
Answer
$\frac{45}{100} = \frac{9}{20}$
Write $0.36$ as a fraction in simplest form.
Answer
$\frac{36}{100} = \frac{9}{25}$
Write $\frac{5}{8}$ as a percentage.
Answer
$62.5\%$
Write $0.035$ as a percentage.
Answer
$3.5\%$
Write $\frac{4}{9}$ as a recurring decimal.
Answer
$0.\dot{4}$
Write $\frac{7}{12}$ as a recurring decimal.
Answer
$0.58\dot{3}$
Write $225\%$ as a decimal and as a mixed numeral.
Answer
$2.25 = 2\frac{1}{4}$
Write $0.\dot{2}\dot{7}$ as a fraction in simplest form.
Answer
$99x = 27$ , so $x = \frac{27}{99} = \frac{3}{11}$

Generate a free maths worksheet

Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

Want more than a worksheet?

Practice built from mistakes.

A worksheet on fractions decimals and percentages is a good start. Tuterly goes further: it turns any question students get wrong into fresh practice, at the right level, on what’s likely to be in the next test or exam.

~90% of Bayside Academics students using it weekly improved their test marks

Based on the actual school test marks of 100+ Bayside Academics students in Years 7 to 10, before and after using Tuterly at least once a week.

Free worksheet Tuterly

The questionsFree worksheetThe same questions for every student on this topic.TuterlyWritten from the questions they got wrong in homework and school tests, at their level.

How manyFree worksheetOne sheet at a time.TuterlyAs many fresh questions as they need, each one different, never just the numbers swapped.*

Before a testFree worksheetPick a topic and hope it’s the right one.TuterlyA practice test covering every part of the topic. Upload the term planner and it focuses on what’s coming up.

MarkingFree worksheetCheck the answer key yourself.TuterlyMarked as they go, with the exact step that went wrong explained.

ProgressFree worksheetNothing is saved.TuterlyEvery question tracked until it’s mastered, and a weekly review for parents.

For Years 7 to 10: $8.99 a week or $29.99 a month at the launch price (from 1 April 2027, $17.99 a week or $59.99 a month), with a 7-day free trial on the monthly plan only. Better marks in 6 months, or your money back.

Or try it free now on one of their questions →

Coming soon on iPhone. Android soon after.

Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon

* Fair use applies with subscriptions.

These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetPercentages Year 7 worksheetFractions and decimals Year 8 worksheetFractions and decimals Year 8 worksheetPercentages

Questions

How do you convert a fraction to a percentage?

Multiply the fraction by 100 and add the percent sign. For example, three fifths times 100 is 60, so three fifths is 60%. You can also change the fraction to a decimal first, then multiply by 100.

Can a percentage be more than 100%?

Yes. A percentage over 100% means more than one whole. For example, 150% is 1.5, or one and a half times the original amount.

Which year level learns recurring decimals?

Converting fractions to decimals starts in Year 7. Recurring decimals, and changing them back into fractions, are part of Year 8 in the Victorian Curriculum.

More skill worksheets

Skill worksheetFraction Skill worksheetEquivalent fractions Skill worksheetArea of composite shapes Skill worksheetArea of a triangle Skill worksheetMultiplying fractions Skill worksheetLinear equations Skill worksheetAdding fractions Skill worksheetPercentage

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.