Decimal to Fraction Calculator
Convert a terminating decimal, scientific notation or repeating decimal to an exact reduced fraction. You can also enter a fraction or mixed number to see its decimal form.
How decimal-to-fraction conversion works
A terminating decimal becomes an integer divided by a power of ten. For example, 0.625 = 625/1000, and dividing both terms by 125 gives 5/8. Scientific notation moves the decimal point before the same exact reduction, so 1.2 × 10−3 = 12/10000 = 3/2500.
For a repeating decimal, subtract the nonrepeating prefix from the number formed by appending one full repeating block. The denominator contains one 9 for each repeating digit and one 0 for each nonrepeating decimal digit. Thus 1.2(34) = (1234 − 12)/990 = 611/495.
Checked examples
| Input | Exact fraction | Decimal or mixed form |
|---|---|---|
| 0.625 | 5/8 | 0.625 |
| −1.25 | −5/4 | −1 1/4 |
| 1.2e−3 | 3/2500 | 0.0012 |
| 0.(3) | 1/3 | 0.(3) |
| 0.1(6) | 1/6 | 0.1(6) |
| 1.2(34) | 611/495 | 1.2(34) |
| 7/8 | 7/8 | 0.875 |
How to use the calculator
- Enter a decimal, or use parentheses around the repeating block.
- Select Convert exactly.
- Read the reduced improper fraction, mixed number, decimal, percent and exact numerator and denominator.
Limits and notation
- Use a decimal point, not a comma, and omit thousands separators.
- Repeating digits must be inside parentheses: 0.(3), 0.1(6) or 1.2(34).
- Scientific exponents from −100 to 100 are supported.
- Inputs may contain up to 60 digits. All fraction reduction uses exact integer arithmetic.
- Decimal output shows a detected repeating cycle when it fits within 80 digits; longer expansions are truncated with an ellipsis while the fraction remains exact.
- A denominator of zero is undefined.
Frequently asked questions
Does the calculator round the fraction?
No. Typed terminating and repeating decimals are converted exactly, then reduced using the greatest common divisor.
What does 0.(3) mean?
The parentheses mean that 3 repeats forever: 0.3333… Its exact fraction is 1/3.
Can I convert a fraction back to a decimal?
Yes. Enter a fraction such as 7/8 or a mixed number such as 2 1/3. The calculator shows terminating or repeating decimal notation.
Related calculators
Use the Fraction Calculator for arithmetic with two fractions, the Inches to Fractions Calculator for ruler and tape-measure rounding, the Significant Figures Calculator for precision rules, or the Percentage Calculator for percent changes and proportions.