Fractions, decimals and percentages
Test equivalence and conversion between fractions, decimals and percentages, or a simple operation using them (a percentage discount or increase, a fraction of an amount).
Three ways to say the same number
A fraction, a decimal and a percentage can all describe the exact same amount — they are just different notations for it. 3/4, 0.75 and 75% are three names for one number.
The 100 you keep coming back to
Percent literally means "per hundred", so converting between a decimal and a percentage is just moving the decimal point two places (× 100 or ÷ 100). Converting a fraction to a percentage means finding an equivalent fraction over 100, or multiplying by 100.
Worked example: What is 3/8 as a decimal and a percentage? 3/8 = 3 ÷ 8 = 0.375. Then 0.375 × 100 = 37.5%.
Comparing across the three forms
When comparing fractions with different denominators, it can be quicker to convert everything to decimals first — put every value into the SAME form before you compare size.
How to attack this question type
- 1
To compare fractions with different denominators, convert to a common denominator or convert both to decimals — whichever is faster for the specific numbers in front of you.
- 2
Learn the common conversions by heart: halves, quarters, fifths and tenths, and their decimal/percentage equivalents. Recognising 3/5 = 60% instantly saves real time.
- 3
"Of" means multiply. "20% of 45" means 0.2 × 45, not 45 ÷ 20 — mixing these up is the single most common percentage error.
- 4
Always simplify a fraction to its lowest terms unless the question allows otherwise — 3/12 and 1/4 are the same value, but only one is "simplest form".
- 5
Sense-check your answer: a percentage between 0 and 100% should correspond to a fraction between 0 and 1. If your converted fraction is bigger than 1, something has gone wrong.
Practice · untimed
Which fraction, in simplest form, is equal to 0.35?
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