Quick answer
A fraction converts to a decimal by long division: numerator ÷ denominator. 3/8 = 0.375. Repeating blocks are found from repeated remainders, up to 1,000 digits.
Enter a numerator and denominator. The calculator returns the decimal, with the repeating block marked, and a rounded value.
Related tools: Decimal to Fraction Calculator: Convert a terminating decimal to a simplified fraction. Fraction Simplifier: Reduce a fraction to lowest terms. Fraction to Percent Calculator: Convert a fraction to a percentage.
How to use the Fraction to Decimal Calculator
- Enter numerator (a whole number).
- Enter denominator (a whole number, between 1 and 1000000000).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Numerator | A whole number | — |
| Denominator | A whole number | ≥ 1, ≤ 1000000000 |
Formula and method
Formula
decimal = numerator ÷ denominator (long division, repeating block found from repeated remainders)
IEEE-754 double precision; shown to at most 6 decimal places.
Long division tracking remainders; the first repeated remainder marks the start of the repeating block.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Numerator = 3; Denominator = 8.
| Result | Value |
|---|---|
| Decimal | 0.375 |
| Rounded (6 dp) | 0.375 |
Example 2
Inputs: Numerator = 1; Denominator = 6.
| Result | Value |
|---|---|
| Decimal | 0.1(6) |
| Rounded (6 dp) | 0.166667 |
Example 3
Inputs: Numerator = 1; Denominator = 7.
| Result | Value |
|---|---|
| Decimal | 0.(142857) |
| Rounded (6 dp) | 0.142857 |
The first line is the headline result (decimal). Below it the fraction to Decimal Calculator lists rounded (6 dp), which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Terminating or repeating
A fraction in lowest terms terminates only if the denominator has no prime factors except 2 and 5. 3/8 terminates (8 = 2³), while 1/3 = 0.(3) and 1/7 = 0.(142857) repeat.
Where this estimate stops applying
The denominator must be a positive whole number. A repeating block can be up to 1,000 digits long. The rounded value is shown to six decimal places.
How the result changes with numerator
Holding every other input at the first worked example, this table changes only numerator. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Numerator | Decimal | Rounded (6 dp) |
|---|---|---|
| 2 | 0.25 | 0.25 |
| 3 | 0.375 | 0.375 |
| 6 | 0.75 | 0.75 |
| 12 | 1.5 | 1.5 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Denominator: entering "0" shows "Denominator must be at least 1." beside that field and no result.
Choosing between the Fraction to Decimal Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Decimal to Fraction Calculator](/math/decimal-to-fraction-calculator/) | decimal | Fraction |
| [Fraction Simplifier](/math/fraction-simplifier/) | numerator and denominator | Simplified |
| [Fraction to Percent Calculator](/math/fraction-to-percent-calculator/) | numerator and denominator | Percent |
| [Percent to Fraction Calculator](/math/percent-to-fraction-calculator/) | percent | Fraction |
| [Decimal to Fraction Calculator](/math/decimal/) | decimal | Fraction |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Denominator must be a positive whole number
- Repeating blocks up to 1,000 digits
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for denominator to confirm this.
Frequently asked questions
What is 1/3 as a decimal?
1/3 is 0.333… with the digit 3 repeating forever.
What is 5/8?
5/8 = 0.625, which terminates because 8 = 2³.
Why does 1/7 repeat?
Its remainders cycle through six values.
What does the Fraction to Decimal Calculator calculate?
Convert a fraction to a decimal, showing repeating digits. It returns Decimal and Rounded (6 dp).
What formula does the Fraction to Decimal Calculator use?
decimal = numerator ÷ denominator (long division, repeating block found from repeated remainders). Long division tracking remainders; the first repeated remainder marks the start of the repeating block.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Denominator must be a positive whole number.
What are the limits of this calculator?
Denominator must be a positive whole number. Repeating blocks up to 1,000 digits.
What is an example of a fraction to Decimal result?
With numerator 3 and denominator 8, the decimal is 0.375.
Related calculators
- Decimal to Fraction Calculator — Convert a terminating decimal to a simplified fraction.
- Fraction Simplifier — Reduce a fraction to lowest terms.
- Fraction to Percent Calculator — Convert a fraction to a percentage.
- Percent to Fraction Calculator — Convert a percentage to a simplified fraction.
- Decimal to Fraction Calculator — Exact fraction, percent and mixed number for a finite decimal.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Inch Fraction Calculator — Convert decimal inches to the nearest fractional inch.
- Decimal to Percent Calculator — Convert a decimal to a percentage.
- Compare Fractions Calculator — Which of two fractions is larger?
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.