11+ Fractions, Decimals and Percentages: Conversions and Questions
Learn to convert and compare fractions, decimals and percentages, with an equivalence table, worked examples and eight explained practice questions.
Original learning material for families preparing for 11-plus exams taken in 2027. These examples are not official exam questions; check your school’s current assessment guidance for the skills and format it uses.
A fraction, decimal and percentage can name exactly the same number. The job in a conversion question is to change its form while keeping its value. That is different from finding a fraction of a quantity: rewriting 3/4 as 75% does not require an amount such as £40.
Understand what each form means
In 3/4, the denominator 4 tells you that a whole has four equal parts; the numerator 3 tells you how many parts are counted. In 0.75, the digits describe seven tenths and five hundredths. The percentage 75% means 75 out of every 100. Each represents the same position on a number line.
Keep the whole in mind. If one whole is a litre, 0.75 of that whole is 750 ml. If the whole is a group of 20, 75% of it is 15. The representation stays the same; the quantity depends on the whole.
A useful conversion table
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
Use these as landmarks rather than eight unrelated facts. For example, half of 1/4 is 1/8, so half of 0.25 is 0.125 and half of 25% is 12.5%. Deriving a forgotten fact is more useful than guessing.
Three worked examples
Fraction to decimal and percentage: 3/20
Make an equivalent fraction with denominator 100: multiply both numerator and denominator by 5. This gives 15/100, so 3/20 = 0.15 = 15%. Check that the result is below 1/4: 15% is below 25%, as expected. You can also divide 3 by 20 to obtain the decimal.
Decimal to a simplified fraction: 0.36
The final digit is in the hundredths place, so write 36/100. Divide both numbers by 4 to get 9/25. Do not write 36/10: that would be 3.6, which is greater than one. Checking the size of the result catches the place-value error.
Compare mixed forms: 0.62, 5/8 and 61%
Choose decimals for all three. They become 0.620, 0.625 and 0.610. From smallest to largest: 61%, 0.62, 5/8. Write the original forms in the final answer so it is clear which item goes where. Adding a zero after the last decimal digit does not change its value.
Choose the right conversion route
- 1Fraction to decimal: divide the numerator by the denominator, or make an equivalent denominator of 10, 100 or 1000 when convenient.
- 2Decimal to fraction: use place value to write tenths, hundredths or thousandths, then simplify.
- 3Decimal to percentage: multiply the numerical value by 100 and include the % sign. Reverse this by dividing by 100.
- 4Percentage to fraction: write the percentage over 100 and simplify. Keep decimal percentages accurate; 12.5% = 12.5/100 = 125/1000 = 1/8.
Some fractions produce recurring decimals. A third is 0.333… rather than exactly 0.33. If a question asks for an exact value, retain 1/3 or the recurring form. Round only when instructed. Numbers can also exceed one: 1.2 = 6/5 = 120%; a percentage need not be below 100%.
Eight questions: try before opening each answer
1. Write 7/20 as a decimal and a percentage.
Show answer and explanation
0.35 and 35%.
7/20 = 35/100. Thirty-five hundredths is 0.35, and 35 per hundred is 35%.
2. Write 0.045 as a fraction in its simplest form and as a percentage.
Show answer and explanation
9/200 and 4.5%.
0.045 = 45/1000. Divide numerator and denominator by 5 to get 9/200. Multiplying the decimal by 100 gives 4.5%.
3. Write 18% as a decimal and a simplified fraction.
Show answer and explanation
0.18 and 9/50.
18% = 18/100 = 0.18. Dividing 18 and 100 by 2 gives 9/50.
4. Order 3/8, 0.37 and 38% from smallest to largest.
Show answer and explanation
0.37, 3/8, 38%.
Convert to decimals: 0.375, 0.370 and 0.380. Compare the thousandths after aligning decimal places.
5. Express 1.2 as an improper fraction in simplest form and as a percentage.
Show answer and explanation
6/5 and 120%.
1.2 = 12/10 = 6/5. As a percentage it is 1.2 × 100 = 120%. Both are greater than one whole.
6. A pupil writes 3/5 = 0.35. Explain the mistake and correct it.
Show answer and explanation
3/5 = 0.6.
The digits of a numerator and denominator cannot simply be put after a decimal point. Multiply both by 2: 3/5 = 6/10 = 0.6. Three fifths is also greater than half, whereas 0.35 is below half.
7. Is 0.6 larger than 0.60, smaller, or equal? Explain.
Show answer and explanation
They are equal.
Six tenths is sixty hundredths. A trailing zero after a decimal does not change the value; 0.6 = 0.60 = 60%.
8. Write 1/3 as a percentage rounded to the nearest whole percent.
Show answer and explanation
33%.
1 ÷ 3 × 100 = 33.333…%. The next digit after the whole percent is 3, so round down. Here 33% is a rounded answer, not an exact equivalent of 1/3.
What should you practise next?
If the conversion is secure but applying it is difficult, use fractions of amounts and percentages of amounts. For mixed contexts, try multi-step word problems. Return to the Maths hub to choose another skill.
Source and scope
The DfE mathematics programme provides the curriculum reference for equivalence and place value. It is not a promise about an individual school’s 11-plus syllabus. Source checked 21 October 2026; examples and answers are our original practice.
Ready to practise?
Choose original practice and use the answer explanations to decide what to work on next. These are not official school papers.