The same value can wear four costumes — a fraction, a decimal, a percentage and a ratio. Olympiad questions mix them deliberately, so the first move is always to convert everything into one form.
Study Zone is free for our students — you just need to log in with your WhatsApp number first.
Log in with WhatsApp →The first two chapters of every book are free once you're logged in. To open this one, request an unlock and we'll get back to you on WhatsApp.
Learn the common ones by heart — you will not have time to divide during the paper.
🎭 Worth memorising
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/3 | 0.333… | 33⅓% |
| 2/3 | 0.666… | 66⅔% |
Decimal to fraction. Write the digits over the matching power of ten and cancel: 0.36 = 36/100 = 9/25. And 0.125 = 125/1000 = 1/8.
You can tell without dividing at all.
🔁 The test
Reduce the fraction to its lowest terms first — this step is essential.
Factorise the denominator.
If the only primes are 2 and 5, the decimal terminates. Any other prime and it recurs.
🔁 Worked out
| Fraction | Denominator | Decimal |
|---|---|---|
| 1/8 | 2³ | 0.125 — terminates |
| 3/40 | 2³ × 5 | 0.075 — terminates |
| 5/16 | 2⁴ | 0.3125 — terminates |
| 1/6 | 2 × 3 | 0.1666… — recurs |
| 2/7 | 7 | 0.285714… — recurs |
| 7/12 | 2² × 3 | 0.5833… — recurs |
Reduce first, or you will get it wrong. 6/12 looks as if it has a 3 in the denominator, but it is really 1/2 = 0.5, which terminates.
Cross-multiplication for comparing, common denominators for adding.
Cross-multiply to compare. For 5/6 and 7/8: 5 × 8 = 40 against 7 × 6 = 42. The larger product sits above the larger fraction, so 7/8 wins.
Dividing by a fraction means multiplying by its reciprocal. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. There is no such flip for addition.
A fraction of a fraction means multiply. "Two-thirds of three-quarters" is 2/3 × 3/4 = 6/12 = 1/2, not 2/3 + 3/4.
12 Olympiad questions on fractions and decimals. 🍀
