To convert a fraction to a decimal, a percent, or a mixed number, pick the tool by what you already have. The same quantity can be written several ways: 3/4, 0.75, and 75% are the same value, and this page takes you to the calculator for each conversion.
| I have | I need | Tool | Example |
|---|---|---|---|
| A proper fraction | A decimal | Fraction to decimal | 3/4 = 0.75 |
| A proper fraction | A percent | Fraction to percent | 7/20 = 35% |
| A terminating decimal | Its fraction | Decimal to fraction | 0.125 = 1/8 |
| A repeating decimal | Its fraction | Repeating decimal to fraction | 0.3̅ = 1/3 |
| A percent | Its fraction | Percent to fraction | 12.5% = 1/8 |
| An improper fraction | A mixed number | Improper to mixed | 7/4 = 1 3/4 |
| A mixed number | An improper fraction | Mixed to improper | 1 3/4 = 7/4 |
Read the table from the left column: find the form you have, and the tool in the third column makes the change. Every one returns the same value written differently, so you can check a result by going back with the reverse tool. In the United States 0.75 is written with a decimal point; many other countries use a comma, 0,75. The calculator accepts both. For repeating decimals, type the repeating digits in parentheses, such as 0.(3); in the text you will see them with a bar over the digits, 0.3̅.
A full round trip, step by step
Worked example: 5/16 as a decimal, as a percent, and back
A quiz has 16 questions and you got 5 of them right. What percent of the quiz is that?
- Divide the numerator by the denominator. 5 ÷ 16 = 0.3125. The division ends because 16 = 2 × 2 × 2 × 2.
- Multiply by 100. 0.3125 × 100 = 31.25.
- Write the percent. 31.25%.
- Go back to the fraction. 0.3125 = 3125/10,000, and dividing top and bottom by 625 leaves 5/16.
Result: 5/16 = 0.3125 = 31.25%.
Check: 16 × 0.3125 = 5, which is the numerator you started with.
Fraction to decimal and fraction to percent do steps 1 to 3, and decimal to fraction does step 4.
When a decimal is exact and when it is an approximation
A fraction gives a terminating decimal when its denominator, in lowest terms, has only the prime factors 2 and 5. That is why 1/8 is 0.125 and 1/25 is 0.04. If another factor appears, like the 3 in 1/3, the digits repeat without end: 1/3 = 0.3̅, where the bar marks the digits that repeat. The rounded decimal 0.33 is a different number, a little smaller.
To work with the repeating digits, use repeating decimal to fraction. If the decimal is long or comes from a measurement and you want a convenient fraction, approximate a decimal as a fraction limits the denominator and shows how far the result is from the original value.
Percents and mixed numbers
A percent is a fraction with denominator 100. So 12.5% reads as 12.5/100, which in lowest terms is 1/8, and to go the other way you multiply by 100. The % sign does not change the unit of what you measure; it only expresses a proportion.
A mixed number combines a whole number and a proper fraction. To turn it into an improper fraction, multiply the whole number by the denominator and add the numerator: 2 × 5 + 2 = 12, so 2 2/5 = 12/5. With a negative mixed number, the sign applies to the whole value: −2 2/5 = −12/5. If you are going to keep calculating, the improper fraction is usually easier to work with than the mixed number.
What to look at next
Keep the fraction while you keep calculating, and convert only at the end. The fraction calculator accepts fractions and decimals in the same operation. When the unit changes too, as in fractional inches to millimeters, you need a factor that belongs to that unit, and these tools do not apply one.
- Which fractions give terminating or repeating decimals: you can tell by looking at the denominator, before dividing.
- Fraction, decimal, and percent table: the most common equivalents, from 1/100 to 3/2, to look up without calculating.
- Terminating and repeating decimals: why 0.333 and 0.333… are not the same, and why 0.999… = 1.