Math
Decimal to Fraction Calculator
Turn any decimal into an exact fraction.
Terminating decimals use place value (0.375 = 375/1000 = 3/8) and repeating decimals use the classic subtraction method (0.1(6) = 1/6). Write repeating digits in parentheses or with trailing dots, and get the simplified fraction, mixed number, decimal check, and percent, with every step shown.
Terminating: 0.375, -2.5. Repeating: put the repeating digits in parentheses, 0.(3) or 0.1(6), or write trailing dots, 0.333...
Try an example
Result
Fraction (simplified)
—
- Mixed number
- —
- Before simplifying
- —
- Percent
- —
- Decimal type
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
Terminating decimals: use place value
A decimal that stops is a fraction over a power of 10. Count the digits after the decimal point: that many zeros go in the The bottom number of a fraction; it says how many equal parts make one whole.. 0.375 has three decimal places, so it is 375/1000, which simplifies by the The largest number that divides evenly into every number in a set. 125 to 3/8. A decimal with a whole part, such as 2.5, becomes 25/10 = 5/2 = 2 1/2.
Repeating decimals: the subtraction method
Let x be the decimal. Multiply by a power of 10 that shifts one full repeating block to the left of the point, and by a smaller power that lines up the non-repeating digits. Subtracting the two equations cancels the endless tail. For 0.1(6): 100x = 16.(6) and 10x = 1.(6), so 90x = 15 and x = 15/90 = 1/6. A pure repeat like 0.(45) gives 99x = 45, so x = 45/99 = 5/11.
| Decimal | Setup | Fraction |
|---|---|---|
| 0.(3) | 10x - x = 3 | 3/9 = 1/3 |
| 0.(45) | 100x - x = 45 | 45/99 = 5/11 |
| 0.1(6) | 100x - 10x = 16 - 1 | 15/90 = 1/6 |
| 2.(3) | 10x - x = 23 - 2 | 21/9 = 7/3 = 2 1/3 |
| 0.(9) | 10x - x = 9 | 9/9 = 1 |
How to type a repeating decimal
Put the repeating block in parentheses: 0.(3) means 0.333..., 0.1(6) means 0.1666..., and 0.(142857) means 1/7. You can also type the digits with trailing dots, such as 0.333... or 0.1666..., and the calculator will detect the repeating block. If it cannot tell which digits repeat, it asks you to use parentheses.
How to use it
- Type the decimal. Use a minus sign for negatives and a leading zero or not, as you like (.5 and 0.5 both work).
- For a repeating decimal, put the repeating digits in parentheses (0.1(6)) or add trailing dots (0.1666...).
- Read the simplified fraction, the A whole number written next to a fraction, like 2 1/3. for values above 1, and the percent.
- Open Show the work for the place-value or subtraction steps and the GCF simplification.
How to read the answer
The simplified fraction is exactly equal to the decimal you typed; the exact-decimal tile converts it back so you can confirm. The unsimplified fraction shows the raw place-value or algebra result before dividing by the GCF. A repeating block of 'none' means the decimal terminates.
Common mistakes and edge cases
- 0.333 (three digits, no dots) is 333/1000, not 1/3. Mark the repeat with parentheses or dots for the exact value.
- The parentheses go around only the repeating digits: 0.1(6), not 0.(16), which is 16/99.
- Do not drop the whole part. 2.5 is 5/2, not 1/2.
- Trailing zeros do not change the value: 0.50 = 0.5 = 1/2.
- Exact conversion is limited to about 15 decimal digits; longer inputs are rejected rather than rounded.
Worked examples
Terminating decimal
0.375
Fraction (simplified)
3/8
Pure repeating
0.(3) = 0.333...
Fraction (simplified)
1/3
Mixed repeating
0.1(6) = 0.1666...
Fraction (simplified)
1/6
Trailing dots
0.4545...
Fraction (simplified)
5/11
Greater than one
2.(3)
Fraction (simplified)
7/3
Negative decimal
-2.5
Fraction (simplified)
-5/2
Whole number
4.0
Fraction (simplified)
4
Ambiguous repeat
0.123... cannot be read
Fraction (simplified)
Error
Frequently asked questions
How do you convert a decimal to a fraction?+
Write the digits after the decimal point over a power of 10 with as many zeros as there are decimal places, then simplify. 0.375 = 375/1000 = 3/8.
What is 0.333... as a fraction?+
1/3. Let x = 0.333..., then 10x = 3.333..., subtract to get 9x = 3, so x = 3/9 = 1/3.
What is 0.1666... as a fraction?+
1/6. With x = 0.1(6): 100x = 16.(6) and 10x = 1.(6). Subtracting gives 90x = 15, so x = 15/90 = 1/6.
How do I enter a repeating decimal?+
Put the repeating digits in parentheses, such as 0.(3) or 0.1(6), or type the pattern with trailing dots, such as 0.333... The calculator detects the block.
Why is 0.(9) equal to 1?+
Let x = 0.999..., then 10x = 9.999..., and 10x - x = 9, so 9x = 9 and x = 1. Two decimals can name the same number.
Why does my decimal give a big denominator?+
Every terminating decimal starts as a power of 10 in the denominator. 0.123 is 123/1000, and since 123 = 3 × 41 shares no factor with 1000, it cannot simplify further.
Can I convert a decimal bigger than 1?+
Yes. 2.5 becomes 5/2, shown as the mixed number 2 1/2 as well.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Fraction to Decimal Calculator
Convert any fraction or mixed number to a decimal with long-division steps, automatic detection of repeating digits with overline notation, rounding to your chosen places, and the percent form.
Simplify Fractions Calculator
Reduce any fraction, mixed number, or decimal to lowest terms with prime-factor GCF steps, a list of equivalent fractions, mixed-number form, decimal, and percent, plus a strip picture showing both forms are equal.
Improper Fraction to Mixed Number Calculator
Convert an improper fraction to a mixed number by dividing numerator by denominator, with the quotient and remainder shown, the fraction part simplified, and decimal and percent forms.
Fraction Calculator
Add, subtract, multiply, divide, simplify, compare, or convert decimals to fractions with steps and visual fraction bars.
Decimal to Binary Converter
Convert decimal to binary with the repeated-division steps, fractional parts by repeated multiplication (0.625 → 0.101), repeating-fraction detection, and negatives as a sign or two's complement.
Partial Fraction Decomposition Calculator
Decompose a rational function into partial fractions with exact fractions: distinct and repeated linear factors, irreducible quadratics, long division for improper fractions, the cover-up method, the coefficient system, and every step.
Last updated: September 4, 2026