Common Decimals Click to Convert
Click any decimal in the table below to convert it instantly.
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.5 | 1/2 | 50% |
| 0.25 | 1/4 | 25% |
| 0.75 | 3/4 | 75% |
| 0.333... | 1/3 | 33.3% |
| 0.666... | 2/3 | 66.7% |
| 0.125 | 1/8 | 12.5% |
| 0.375 | 3/8 | 37.5% |
| 0.625 | 5/8 | 62.5% |
| 0.875 | 7/8 | 87.5% |
| 0.2 | 1/5 | 20% |
| 0.4 | 2/5 | 40% |
| 0.6 | 3/5 | 60% |
| 0.8 | 4/5 | 80% |
| 0.1 | 1/10 | 10% |
| 0.01 | 1/100 | 1% |
Enter a decimal number to convert it to a fraction in simplest form.
How to Convert Decimals to Fractions
To turn a decimal into a fraction, write its digits over 10, 100 or 1,000 (one zero per decimal place) and simplify: 0.625 = 625/1000 = 5/8. A repeating decimal goes over nines instead, so 0.333... = 3/9 = 1/3. Type any decimal above, or put the repeating part in brackets like 0.(3), and the calculator returns the simplest fraction, mixed number and percent.
To convert a decimal to a fraction: (1) Count the decimal places. (2) Write the decimal digits as the numerator over 10 raised to the power of the decimal places as the denominator. (3) Simplify by dividing both numerator and denominator by their Greatest Common Divisor (GCD).
Example: 0.75. Two decimal places, so 75/100. GCD(75, 100) = 25. Divide both by 25: 75/25 = 3, 100/25 = 4. Result: 3/4.
Common Decimal Conversions
Simplifying Fractions
Mixed Number Form
Repeating Decimals
Repeating Decimals, Worked Out
A repeating decimal is always a fraction. The shortcut: put the repeating digits over as many nines as there are repeating digits. If some digits come before the repeat starts, add one zero after the nines for each of them, and subtract those leading digits from the top.
| Decimal | How to write it | Before simplifying | Simplest form |
|---|---|---|---|
| 0.333... | 0.(3) | 3/9 | 1/3 |
| 0.272727... | 0.(27) | 27/99 | 3/11 |
| 0.142857142857... | 0.(142857) | 142857/999999 | 1/7 |
| 0.1666... | 0.1(6) | (16 − 1)/90 = 15/90 | 1/6 |
| 0.8333... | 0.8(3) | (83 − 8)/90 = 75/90 | 5/6 |
| 0.58333... | 0.58(3) | (583 − 58)/900 = 525/900 | 7/12 |
| 2.4545... | 2.(45) | (245 − 2)/99 = 243/99 | 27/11 = 2 5/11 |
| 0.999... | 0.(9) | 9/9 | 1 |
Why the nines work
Take x = 0.1666... Multiply by 100 to get 100x = 16.666..., and by 10 to get 10x = 1.666... Subtracting removes the endless tail: 90x = 15, so x = 15/90 = 1/6. The calculator runs exactly this subtraction and shows it in the steps.
Inch Decimals to Sixteenths
Drawings, calipers and spreadsheets give inches as decimals, while tape measures are marked in sixteenths. Every sixteenth is a terminating decimal because 16 is a power of 2.
| Decimal (in) | Fraction | Decimal (in) | Fraction |
|---|---|---|---|
| 0.0625 | 1/16 | 0.5625 | 9/16 |
| 0.125 | 1/8 | 0.625 | 5/8 |
| 0.1875 | 3/16 | 0.6875 | 11/16 |
| 0.25 | 1/4 | 0.75 | 3/4 |
| 0.3125 | 5/16 | 0.8125 | 13/16 |
| 0.375 | 3/8 | 0.875 | 7/8 |
| 0.4375 | 7/16 | 0.9375 | 15/16 |
| 0.5 | 1/2 | 1.0 | 1 |
A value like 2.375 inches is 2 3/8 inches: 2.375 = 2375/1000, and dividing by the greatest common factor 125 gives 19/8.
Rounded Decimals and Common Mistakes
- 0.33 is not 1/3. Typed as 0.33 it is exactly 33/100, which is off from 1/3 by about 0.0033. If you mean one third, enter 0.(3). When you type a rounded value with four or more decimals, such as 0.3333 or 0.6667, the calculator adds a note with the likely simple fraction.
- 3.14 is not pi. 3.14 = 314/100 = 157/50. Pi never repeats, so no fraction equals it exactly; 22/7 is only an approximation.
- Stopping at the power of ten. 0.0625 = 625/10000 is correct but not finished. Divide by 625 to get 1/16.
- Mixing up 0.5 and 0.05. Each place matters: 0.5 = 1/2, 0.05 = 1/20, 0.005 = 1/200.
- Dropping the whole number. 1.2 is 12/10 = 6/5 = 1 1/5, not 1/5.
To go the other way, or to add and subtract the fractions you get, use the fraction calculator. For long numerators and denominators the GCF calculator shows how the fraction is reduced.