Mathematics 0580 · syllabus C1.4, E1.4
Cambridge IGCSE Mathematics 0580 — Fractions and decimals topical past papers
Equivalent fractions, decimals and percentages, converting between them, and on the Extended route turning recurring decimals into fractions.
- Questions
- 92
- Years
- 2009–2026
- With mark scheme
- 96%
- Questions 2022–2026
- 65
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What Fractions and decimals covers
Fractions, decimals and percentages are three ways of writing the same value, and this topic is about moving between them. A fraction becomes a decimal by division, a decimal becomes a percentage when multiplied by 100, and a terminating decimal becomes a fraction when written over a power of 10 and simplified: 0.375 = 375/1000 = 3/8. You need the words proper fraction, improper fraction and mixed number, and a fraction answer should be in its lowest terms.
On the Extended route you also work with recurring decimals. A dot over a digit shows that it repeats, and dots over the first and last digits of a block repeat the whole block, so 0.474747… is written with dots over the 4 and the 7. To turn a recurring decimal into a fraction, multiply it by powers of 10 to get two numbers with the same repeating tail after the point, then subtract one from the other, so that the tails cancel. Recurring decimals are not part of the Core content.
This is Core content, so it can be set on all four papers, and it is essential on the non-calculator papers, where a question can need 3/8 as a decimal or 0.35 as a fraction with no calculator to hand. Questions filed here also include calculating with decimals by hand, such as 0.6 × 0.04 = 0.024. The conversions lead into percentages and into probability, whose answers may be fractions, decimals or percentages, and every recurring decimal is rational, which links the topic to surds and irrational numbers.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- C1.4 Fractions, decimals and percentages
- E1.4 Fractions, decimals and percentages
What you should be able to do
- Convert between fractions, decimals and percentages in either direction
- Simplify fractions fully, and change between improper fractions and mixed numbers
- Order a mixed list of fractions, decimals and percentages by converting them to one form
- Write a terminating decimal as a fraction in its lowest terms
- Convert recurring decimals to fractions, and fractions to recurring decimals (Extended)
Key ideas
- a/b means a ÷ b, so 5/8 = 5 ÷ 8 = 0.625 = 62.5%
- Percent means per hundred: 35% = 35/100 = 7/20 = 0.35
- A fraction in its simplest form gives a terminating decimal only if its denominator has no prime factors other than 2 and 5
- For a recurring decimal x, multiply by powers of 10 until two multiples have the same repeating tail, such as 100x and x for 0.474747…, then subtract so the tails cancel
How Fractions and decimals has been examined
From 2022 to 2026, Fractions and decimals was on Paper 3 · Calculator (Core) in 6 of 14 exam series, worth about 2% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Non-calculator (Core) | 23 | 2% | 7 of 14 |
| Paper 2 · Non-calculator (Extended) | 13 | 1% | 6 of 14 |
| Paper 3 · Calculator (Core) | 20 | 2% | 6 of 14 |
| Paper 4 · Calculator (Extended) | 9 | 1% | 4 of 14 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 2.
Filed in Momentum under: Decimals.
A worked example
Write the recurring decimal 0.3888…, in which the 8 repeats, as a fraction in its lowest terms.
- Let x = 0.3888…
- Multiply by 10 so that the repeating part starts just after the point: 10x = 3.888…
- Multiply by 100 as well: 100x = 38.888…, which has the same repeating tail.
- Subtract: 100x − 10x = 38.888… − 3.888…, so 90x = 35.
- x = 35/90 = 7/18. Check: 7 ÷ 18 = 0.3888…
Answer: 7/18
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Leaving a fraction unsimplified, such as 45/60 for 3/4: answers are expected in their simplest form, and the final mark can depend on it.
- Ordering decimals by their number of digits, so that 0.45 is put above 0.6: compare place by place, or write them all with the same number of decimal places.
- Giving an answer that mixes the forms, such as a fraction with a decimal on top: a numerical answer must be written wholly as a fraction or wholly as a decimal.
- Multiplying by 10 instead of 100 for a two-digit repeating block, so the repeating parts do not line up and cancel.
- Placing the decimal point wrongly when multiplying decimals by hand: 0.6 × 0.04 has three decimal places in total, so it is 0.024.
Exam technique
- To order fractions without a calculator, convert them to decimals or rewrite them over a common denominator, then check whether the question wants the smallest or the largest first.
- For a recurring decimal, write x = …, show both multiplied lines and the subtraction, then simplify the fraction; the method marks are for those lines.
- Know the common equivalents, such as 1/8 = 0.125, 3/5 = 0.6 and 2/3 = 0.666…, so conversions without a calculator are quick.
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.