Fraction, decimal and percent — three names for one number
A fraction, a decimal and a percent are three different outfits for the same number. The number itself — the part of the whole — doesn't change. Only the way it's written changes.
Why three?
Each form is useful in different places:
- Fractions are great for thinking ("half a pizza", "three quarters of the class").
- Decimals are great for calculator work and measurements ("3.5 metres", "0.25 of a litre").
- Percentages are great for comparing parts of different wholes ("the sale is 20 % off, but the other shop is 25 % off").
The number is the same — but the language fits the situation.
Decimal ↔ percent
Going between a decimal and a percent is the easiest move in maths:
- Decimal → percent: shift the decimal point two places to the right.
- Percent → decimal: shift the decimal point two places to the left.
Why? Because "%" means "out of 100", and shifting two places is multiplying or dividing by 100.
| Decimal | Percent |
| 0.07 | 7 % |
| 0.4 | 40 % |
| 0.5 | 50 % |
| 0.25 | 25 % |
| 1.25 | 125 % |
| 0.001 | 0.1 % |
Convert 0.6 to a percent. Shift the point two places right: 0.6 → 6.0 → 60. 60 %.
Convert 3 % to a decimal. Shift the point two places left: 3.0 → 0.30 → 0.03. 0.03.
Fraction ↔ percent
Fractions are slightly more work, but if the denominator is a friendly number, it's still mental arithmetic.
Easy case: denominator is 100
If the denominator is already 100, just read off the numerator:
37/100 = 37 %
Easy case: denominator divides 100
If the denominator is 2, 4, 5, 10, 20, 25 or 50, scale the fraction up so the denominator becomes 100. Then read off the numerator.
3/4 — multiply top and bottom by 25 → 75/100 = 75 %.
4/5 — multiply top and bottom by 20 → 80/100 = 80 %.
7/10 — multiply top and bottom by 10 → 70/100 = 70 %.
General case
For any fraction, divide the top by the bottom (the decimal form) and then move the point two places right.
5/8 → 5 ÷ 8 = 0.625 → 62.5 %.
A handy round-trip table
| Fraction | Decimal | Percent |
| 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 % |
| 3/5 | 0.6 | 60 % |
| 4/5 | 0.8 | 80 % |
| 1/10 | 0.1 | 10 % |
| 3/10 | 0.3 | 30 % |
| 1/8 | 0.125 | 12.5 % |
| 1/100 | 0.01 | 1 % |
| 1 | 1 | 100 % |
Learning the friendly half of this table by heart makes percent problems much faster.
Common mistakes
- "40 % is 0.40" — yes, but watch out: 0.4 is the same as 0.40. Both equal 40 %. The position of the digits is what matters, not the trailing zero.
- Forgetting the / 100. A percent is always "out of 100", even when the question doesn't say so.
- Confusing 100 % with 1 %. 100 % is the whole thing. 1 % is one hundredth. They look similar in writing — they're a hundred times apart.
- Going the wrong way. Decimal → percent shifts right (the number gets bigger). Percent → decimal shifts left (the number gets smaller — 50 % is less than 1).