Percent, decimal and fraction are three ways of writing the same number. "25%" and "0.25" and "1/4" all mean one quarter, so converting between them is really translation, not calculation. Get the direction right and every conversion is a single move of the decimal point or a single fraction to simplify.
The three-way rule
- Percent → decimal: divide by 100 (move the point two places left). 25% → 0.25.
- Decimal → percent: multiply by 100 (move the point two places right). 0.6 → 60%.
- Percent → fraction: put the number over 100 and simplify. 25% → 25/100 → 1/4.
- Fraction → percent: divide the top by the bottom, then multiply by 100. 3/8 → 0.375 → 37.5%.
The decimal is the bridge. Converting to a decimal first makes the other two conversions easy in either direction.
Worked example: 12.5%
- To decimal: 12.5 ÷ 100 = 0.125.
- To fraction: 12.5/100 is awkward with a decimal on top, so scale by 10: 125/1000.
- Simplify: divide top and bottom by 125 → 1/8.
- Check: 1 ÷ 8 = 0.125, and 0.125 × 100 = 12.5%. The loop closes.
Conversions worth memorising
| Percent | Decimal | Fraction |
|---|---|---|
| 10% | 0.10 | 1/10 |
| 20% | 0.20 | 1/5 |
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 12.5% | 0.125 | 1/8 |
| 33⅓% | 0.333… | 1/3 |
| 16⅔% | 0.1666… | 1/6 |
Repeating decimals
Some fractions never produce a tidy decimal. 1/3 is 0.333… repeating forever, and 2/3 is 0.666…. Written as a percent, 1/3 is 33.333…%. You round for display (33.33%) but the exact value is a repeating decimal. This is why "one third off" never equals exactly 33%: 33% of $90 is $29.70 saved, while one third is $30. The fraction is the precise form; the percent is an approximation.
Common mistakes
- Shifting the wrong way. Going from percent to decimal you move left; to percent you move right. 0.5% is 0.005, not 0.5.
- Forgetting the decimal on small percents. 0.5% and 50% are a hundred times apart.
- Not simplifying the fraction. 50/100 is correct but 1/2 is cleaner and easier to use.
- Leaving a decimal inside a fraction. Scale both parts by 10 until the numerator is a whole number, then simplify.
Handling percents bigger than 100
The same rules work when a percent exceeds 100. 150% becomes 1.5 as a decimal and 150/100 = 3/2 (or 1½) as a fraction. Once you are multiplying by a decimal above 1, the result grows, which is the correct behaviour for an increase. A "200% rise" is a tripling, not a doubling: 200% on top of 100% gives 300% of the original, so a $20 price becomes $60.
Negative and tiny percents
A decrease written as a negative percent behaves identically after conversion: −25% is −0.25, and multiplying by 0.75 gives the same reduction as "25% off". Very small values are where the decimal point matters most. 0.1% is 0.001, and 0.01% is 0.0001. Dropping a zero there changes the answer tenfold, so it pays to double-check the count of places when the percent is below 1.
Checking your conversion
A quick sanity test catches most errors: the decimal should be smaller than the percent whenever the percent is under 100, and a fraction should sit between 0 and 1 for the same range. If 40% converts to 4.0, the direction is wrong; if it converts to 0.4, it is right. Reading the result back with the reverse rule — multiply instead of divide, or vice versa — confirms the round trip closes.
Which form to use
Use percent to communicate a rate to people ("20% off"). Use decimal inside a calculation, because multiplying by 0.20 is one step and multiplying by 20 and dividing by 100 is two. Use a fraction when it is exact and simple, such as splitting a bill into thirds or reading a recipe. Choosing the right form makes the arithmetic shorter, not just prettier.
To take a percentage of a number, find the percent change, or check a ratio, use our percentage calculator. For related methods, see the guide to finding a percentage of a number and percentage points vs percent.