To convert a decimal to a fraction, write the digits after the decimal point over 10, 100 or 1,000 (one zero for each decimal place), then simplify. 0.75 = 75/100 = 3/4. To go the other way, divide the top number by the bottom number: 3/8 = 3 ÷ 8 = 0.375.
The Decimal to Fraction Calculator and the Fraction to Decimal Calculator do both with every step shown. This guide shows the method by hand, including repeating decimals, mixed numbers and simplifying.
How to convert a decimal to a fraction
- Count the decimal places. 0.75 has two.
- Write the digits over a power of 10 with that many zeros: 75/100.
- Simplify. Divide the top and bottom by their greatest common factor (GCF). The GCF of 75 and 100 is 25, so 75/100 = 3/4.
| Decimal | Over a power of 10 | GCF | Fraction |
|---|---|---|---|
| 0.5 | 5/10 | 5 | 1/2 |
| 0.25 | 25/100 | 25 | 1/4 |
| 0.6 | 6/10 | 2 | 3/5 |
| 0.75 | 75/100 | 25 | 3/4 |
| 0.125 | 125/1000 | 125 | 1/8 |
Trailing zeros make no difference: 0.50 is 50/100, which simplifies to the same 1/2.
Decimals greater than 1
Use the same steps on the whole number, then turn the result into a mixed number if you want one. 2.5 = 25/10 = 5/2, which is 2 1/2. Likewise 1.5 = 15/10 = 3/2 = 1 1/2, and 3.2 = 32/10 = 16/5 = 3 1/5.
Repeating decimals
A decimal that repeats forever, such as 0.333…, cannot be written over a power of 10, but a little algebra finds the fraction:
- Let x = 0.333…
- Multiply by 10 so the repeating part lines up: 10x = 3.333…
- Subtract the first line from the second: 9x = 3, so x = 3/9 = 1/3.
When the repeat starts later, multiply twice. For 0.1666…: 100x = 16.666… and 10x = 1.666…, so 90x = 15 and x = 15/90 = 1/6. For a two-digit block such as 0.363636…, multiply by 100: 99x = 36, so x = 36/99 = 4/11.
A calculator that shows 0.6666667 has rounded a repeating decimal. Typed as 0.6666667, it converts to 6666667/10000000; entered as the repeating decimal 0.(6), it is exactly 2/3. The Decimal to Fraction Calculator accepts that notation.
Negative decimals
Convert the number without the sign, then put the minus back: −0.75 = −3/4.
How to simplify a fraction
Divide the top (numerator) and bottom (denominator) by their greatest common factor. For 18/24, the factors of 18 are 1, 2, 3, 6, 9 and 18, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The largest one they share is 6, so 18/24 = 3/4. A fraction is in lowest terms when the only common factor left is 1.
Listing factors gets slow for large numbers. The GCF Calculator finds the greatest common factor with the Euclidean algorithm and shows each step.
Improper fractions and mixed numbers
An improper fraction has a top number at least as large as the bottom, such as 7/4 or 5/5. It is still a valid fraction; it just stands for 1 or more.
- Improper to mixed: divide. 7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4.
- Mixed to improper: multiply the whole number by the denominator and add the numerator. 2 2/3 = (2 × 3 + 2)/3 = 8/3.
Improper fractions are easier to calculate with, and mixed numbers are easier to read. The Fraction Calculator accepts both and gives the answer both ways.
How to convert a fraction to a decimal
Divide the numerator by the denominator. With a calculator, 3/8 is 3 ÷ 8 = 0.375. By hand, use long division: 8 goes into 3.000 to give 0.375. The Long Division Calculator writes out every step.
Will the decimal end or repeat?
Put the fraction in lowest terms and look at the denominator:
- If its only prime factors are 2 and 5, the decimal ends. 7/40 = 0.175, because 40 = 2 × 2 × 2 × 5.
- If it has any other prime factor, the decimal repeats forever. 1/12 = 0.08333…, because 12 = 2 × 2 × 3.
Repeating digits are written with a bar over them, or in parentheses: 1/7 = 0.(142857).
Mixed numbers
Convert to an improper fraction first, or divide the fraction part and add the whole number: 2 3/8 = 2 + 0.375 = 2.375.
Fraction, decimal and percent chart
To get the percent, multiply the decimal by 100.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 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% |
| 1/6 | 0.1666… | 16.67% |
| 5/6 | 0.8333… | 83.33% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/16 | 0.0625 | 6.25% |
The Fraction to Decimal Calculator has a printable version of this chart that can also list every 16th, 32nd or 64th.
Decimals to inch fractions
Tape measures and drill bits use sixteenths, so round to the nearest 1/16 instead of finding an exact fraction: multiply the decimal by 16, round to a whole number, and simplify. For 0.39 inch: 0.39 × 16 = 6.24, which rounds to 6, and 6/16 = 3/8 inch. Use 32 or 64 for finer work. The Decimal to Fraction Calculator's "Round to nearest 1/N" mode does this for any N.
Common questions
What is 1.5 as a fraction? 15/10 = 3/2, or 1 1/2 as a mixed number.
What is 2.5 as a fraction? 25/10 = 5/2, or 2 1/2.
What is 0.25 as a fraction? 25/100 = 1/4.
Is 0.999… equal to 1? Yes. With x = 0.999…, 10x = 9.999…, so 9x = 9 and x = 1.