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Decimal to Fraction Converter
A decimal to fraction calculator that turns a decimal, fraction, or percent into a simplified fraction, a decimal, and a percent, with the greatest common factor shown.
A terminating decimal such as 0.75 or 0.125
Check this when the digits continue forever. For 0.333..., enter 0.3 and set 1 repeating digit.
Enter a decimal such as 0.75 or 0.2 to see the simplified fraction and the percent.
Formula
Count the digits after the decimal point. Write the number over 1 followed by that many zeros, then divide the top and bottom by their greatest common factor (GCF).
Enter a decimal such as 0.75 or 0.2 to see the simplified fraction and the percent.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33 1/3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 2/5 | 0.4 | 40% |
| 3/4 | 0.75 | 75% |
| 1/6 | 0.1666... | 16 2/3% |
This converter turns a decimal into a simplified fraction, a fraction into a decimal and a percent, and a percent back into both. Terminating decimals stay exact, so 0.75 is 3/4 and 0.125 is 1/8, and a repeating checkbox turns a pattern such as 0.333... into 1/3. The greatest common factor is written on one line, an improper fraction is also shown as a mixed number, and a denominator of zero is explained in words. Students use it when a problem asks for the same value as a decimal, a fraction, and a percent.
Place value, then the greatest common factor
Count the digits after the decimal point and write them over 1 followed by that many zeros. Then divide the top and the bottom by their greatest common factor, the GCF on the step line. Two digits make 0.75 into 75/100, and the greatest common factor of 75 and 100 is 25, so the simplified fraction is 3/4. The same steps turn 0.125 into 125/1000 and then 1/8, and 0.2 into 2/10 and then 1/5.
A fraction uses a numerator and a denominator. The page simplifies it, names the greatest common factor, divides to get the decimal, and multiplies that decimal by 100 for the percent. So 1/8 is 0.125 and 12.5%, and 2/5 is 0.4 and 40%. An improper fraction is written as a mixed number too, so 7/4 is also 1 3/4. A percent is that number over 100: 25% is 25/100, which simplifies to 1/4 and equals 0.25. When the denominator is 0, the page explains that dividing by zero has no decimal or percent.
When the decimal repeats?
Check Repeating decimal when the digits continue forever, and enter how many digits at the end repeat. The fraction uses those digits, then the greatest common factor simplifies it. Enter 0.3 with one repeating digit for 0.333..., which is 3/9 and simplifies to 1/3. Enter 0.16 with one repeating digit for 0.1666..., which is 15/90 and simplifies to 1/6. With the box unchecked, 0.333 stops after three digits and equals 333/1000.
Frequently Asked Questions
How do you convert 0.75 to a fraction?
0.75 has two digits after the decimal point, so it is 75/100. The greatest common factor of 75 and 100 is 25. Dividing the top and bottom by 25 gives 3/4, which is also 75%.
What is 0.2 as a fraction?
0.2 has one digit after the decimal point, so it is 2/10. The greatest common factor of 2 and 10 is 2, and dividing both by 2 gives 1/5. As a percent, 1/5 is 20%.
How do you convert a fraction to a decimal and a percent?
Divide the numerator by the denominator for the decimal, then multiply by 100 for the percent. 1/8 is 0.125, which is 12.5%, and 2/5 is 0.4, which is 40%. The fraction is simplified first, and the greatest common factor appears on its own line.
How do you turn a repeating decimal into a fraction?
Mark how many digits repeat. For 0.333..., enter 0.3 and set one repeating digit, which is 3/9 and simplifies to 1/3. For 0.1666..., enter 0.16 with one repeating digit, which is 15/90 and simplifies to 1/6.
What happens when the denominator is 0?
A fraction means the numerator divided by the denominator. Division by zero has no result, so the page explains that and asks for a denominator other than 0. There is no decimal or percent to report until the denominator is a whole number such as 8.