Fraction to Decimal Calculator
Convert fractions into exact decimals and percentages with recurring repeating decimal detection.
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How to Use the Fraction to Decimal Calculator – Convert Fractions
- 1Enter the numerator (top number) into the first box.
- 2Enter the denominator (bottom number) into the second box.
- 3Review the decimal representation, percentage equivalent, and recurring status.
- 4Check the step-by-step division explanation below.
Formula & How It Works
Fraction to Decimal Division Method
A fraction a/b represents the division of numerator a by denominator b. In base-10, if the prime factors of the reduced denominator consist solely of 2s and 5s, the decimal terminates; otherwise, it produces a repeating repeating decimal period.
Worked Examples
Standard Quarter Fraction
Input: 3/4
Explanation: 3 ÷ 4 = 0.75 (terminating decimal).
Repeating Third Fraction
Input: 1/3
Explanation: 1 ÷ 3 = 0.333333... with a repeating repetend of [3].
Eighths Division
Input: 5/8
Explanation: 5 ÷ 8 = 0.625 (terminating decimal).
Improper Fraction Conversion
Input: 7/2
Explanation: 7 ÷ 2 = 3.5 (mixed number 3 1/2).
Frequently Asked Questions
How do you convert a fraction to a decimal?▼
Divide the numerator (top number) by the denominator (bottom number) using long division.
What is a repeating or recurring decimal?▼
A repeating decimal is a decimal fraction where a digit or block of digits repeats infinitely (such as 1/3 = 0.333... or 1/7 = 0.142857142857...).
Can the denominator be zero?▼
No, division by zero is undefined in mathematics; denominators must be non-zero.
How do you convert a mixed fraction like 2 3/4 to decimal?▼
Convert 3/4 to 0.75, then add the whole integer 2 to get 2.75.
How do I convert a decimal back into a fraction?▼
Use our Decimal to Fraction Calculator to find the simplified ratio.
Does this tool work completely offline?▼
Yes, all calculation logic runs locally in your browser using pure client-side TypeScript.
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