MISSION · Number sense
Fractions, Decimals, and Percents
Three costumes worn by the same number
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
Unlock the explanation
Open the chapters in any order. Try the examples as you go.
The idea in one sentence
A half, 0.5, and 50% are one number written three ways, and being able to switch between them at will is what makes percentage problems easy.
The conversions
Fraction → decimal. Divide the top by the bottom. \(\frac{3}{8} = 3 \div 8 = 0.375\).
Decimal → percent. Multiply by 100, which moves the point two places right. \(0.375 = 37.5\%\).
Percent → decimal. Divide by 100 — two places left. \(37.5\% = 0.375\).
Percent → fraction. Put it over 100 and simplify. \(37.5\% = \frac{37.5}{100} = \frac{375}{1000} = \frac{3}{8}\).
Decimal → fraction. Read the place value. \(0.375\) is 375 thousandths, so \(\frac{375}{1000}\), which simplifies to \(\frac{3}{8}\).
Everything goes through the other forms cleanly; there’s no conversion you can’t do in a step or two.
The ones worth memorising
Recognising these on sight saves more time than any method:
| Fraction | Decimal | Percent |
|---|---|---|
| \(\frac{1}{2}\) | 0.5 | 50% |
| \(\frac{1}{4}\) | 0.25 | 25% |
| \(\frac{3}{4}\) | 0.75 | 75% |
| \(\frac{1}{5}\) | 0.2 | 20% |
| \(\frac{1}{10}\) | 0.1 | 10% |
| \(\frac{1}{3}\) | 0.333… | 33.3% |
| \(\frac{1}{8}\) | 0.125 | 12.5% |
The ones that never finish
\(\frac{1}{3} = 0.3333\ldots\) goes on forever. That isn’t a flaw in the fraction — it’s a mismatch between thirds and a system built on tens. Three doesn’t divide 10, 100, or any power of ten, so the division never terminates.
Which fractions terminate is completely decided by their denominator: if, in lowest terms, it is built only from 2s and 5s, the decimal stops. \(\frac{3}{8}\) stops because \(8 = 2^3\). \(\frac{1}{6}\) doesn’t, because of the 3.
Recurring decimals are written with a dot or a bar over the repeating part, and in exact work you leave the fraction alone rather than rounding it.
Which form to use
Fractions for exact arithmetic, especially when thirds or sevenths are involved.
Decimals for calculators, measurements, and money.
Percents for comparing and for communicating. “Two thirds off” and “67% off” mean the same, but shops choose the percent because it lines up against every other offer in the street.
Being fluent in all three lets you pick whichever makes the problem easiest — and most percentage questions become simple the moment you convert to the fraction. Finding 25% of 64 is much easier read as a quarter.
Common mix-ups
- Moving the point one place instead of two between decimal and percent.
- Reading 0.5% as 0.5. It’s 0.005.
- Dividing the wrong way round. \(\frac{3}{8}\) is \(3 \div 8\), not \(8 \div 3\).
- Rounding a recurring decimal and calling it exact.
Check yourself
Write \(\frac{5}{8}\) as a decimal and a percent. Then write 12% as a fraction in lowest terms.
\(5 \div 8 = 0.625 = 62.5\%\). And \(12\% = \frac{12}{100} = \frac{3}{25}\).
LEVEL 3 · REFLECT
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