Math
Fraction to Decimal Calculator
Divide the numerator by the denominator with long division, digit by digit.
The calculator finds the exact decimal, detects repeating digits and writes them with bar notation, rounds to as many places as you want, explains why the decimal terminates or repeats, and gives the percent as well.
Type a fraction (3/4), a mixed number (2 1/3), a whole number, or a decimal (1.75). Repeating decimals work too: 0.(3).
Used for the rounded value only. The exact decimal is always shown.
Try an example
Result
Exact decimal
—
- With repeating bar
- —
- Rounded
- —
- Percent
- —
- Mixed number
- —
- 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.
Fraction to decimal by long division
A fraction is a division problem: 5/12 means 5 ÷ 12. Divide, and whenever there is a remainder, bring down a 0 and keep going. The digits you write after the decimal point are the decimal expansion. The division either ends with remainder 0 (a terminating decimal) or a remainder repeats, after which the digits repeat too.
Terminating or repeating?
Simplify the fraction first. If the The bottom number of a fraction; it says how many equal parts make one whole.'s only A whole number above 1 whose only factors are 1 and itself. factors are 2 and 5, the decimal terminates; otherwise it repeats. 5/12 has denominator 12 = 2^2 × 3, so it repeats: 0.41(6). 3/8 has denominator 8 = 2^3, so it terminates: 0.375. The length of the repeating block is at most denominator minus 1.
| Fraction | Denominator factors | Decimal | Type |
|---|---|---|---|
| 3/8 | 2^3 | 0.375 | terminating |
| 1/3 | 3 | 0.(3) | repeating, period 1 |
| 5/12 | 2^2 × 3 | 0.41(6) | repeating, period 1 |
| 1/7 | 7 | 0.(142857) | repeating, period 6 |
| 2/11 | 11 | 0.(18) | repeating, period 2 |
| 7/4 | 2^2 | 1.75 | terminating |
Reading bar and parentheses notation
0.41(6) and 0.416̅ both mean 0.416666... with the 6 repeating forever. The calculator shows both notations plus a rounded value. Rounded decimals are approximations; the parentheses or bar form is exact.
How to use it
- Type the fraction (5/12), A whole number written next to a fraction, like 2 1/3. (2 1/3), or A fraction whose top number is at least as big as its bottom number, like 7/3. (7/4).
- Choose how many decimal places to round to for the rounded value.
- Read the exact decimal, the bar-notation version, and the rounded value.
- Open Show the work to follow each long-division digit and see where the remainder repeats or reaches 0.
How to read the answer
The exact decimal is the true value; parentheses or a bar mark digits that repeat forever. The rounded value is what a calculator display would show. The percent is the decimal multiplied by 100, and the denominator's prime factors explain why the decimal terminates or repeats.
Common mistakes and edge cases
- Divide The top number of a fraction; it counts how many parts you have. by denominator, not the other way around: 5/12 is 5 ÷ 12 = 0.41(6), not 2.4.
- A calculator's 0.4166667 is rounded; the exact value is 0.41(6).
- Convert mixed numbers by keeping the whole part and converting the fraction: 2 1/4 = 2.25.
- Simplify before deciding whether a decimal terminates: 6/12 = 1/2 terminates even though 12 has a factor of 3.
- A denominator of 0 is undefined and cannot be converted.
Worked examples
Repeating decimal
5/12
Exact decimal
0.41(6)
Terminating decimal
3/8
Exact decimal
0.375
Long repeating block
1/7
Exact decimal
0.(142857)
Mixed number
2 1/3
Exact decimal
2.(3)
Negative improper
-7/4
Exact decimal
-1.75
Whole number result
12/4
Exact decimal
3
Zero
0/9
Exact decimal
0
Undefined
4/0
Exact decimal
Error
Frequently asked questions
How do you convert a fraction to a decimal?+
Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. Use long division and bring down zeros until the remainder is 0 or starts repeating.
How do I know if a fraction gives a repeating decimal?+
Simplify it. If the denominator has any prime factor other than 2 or 5, the decimal repeats. 5/12 repeats because 12 = 2^2 × 3.
What does the bar over a digit mean?+
The digits under the bar repeat forever. 0.416̅ is 0.416666..., the same as 0.41(6) in parentheses notation.
How do you convert a mixed number to a decimal?+
Keep the whole part and convert the fraction part: 2 1/3 = 2 + 0.(3) = 2.(3). The calculator accepts mixed numbers directly.
Why is 1/7 so long?+
The repeating block of 1/n can be as long as n - 1 digits. For 7, it is the full 6 digits: 0.(142857).
Is the rounded decimal the same as the exact one?+
No. Rounding cuts off the repeating tail. 0.416667 is close to 5/12 but 0.41(6) is exact.
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
Decimal to Fraction Calculator
Convert any terminating or repeating decimal to an exact fraction with steps: powers of 10 for terminating decimals, the subtraction trick for repeating ones like 0.1(6), plus simplified, mixed-number, and percent forms.
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