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Fraction Converter

Convert fractions to decimals, decimals to fractions, and mixed numbers to decimals. Automatically simplifies fractions using GCD.

✓ Tested formula & cited sources Checked against independent sources · Oct 13, 2026 Private: runs in your browser

The top number of the fraction

The bottom number of the fraction

Results

Decimal

0.75

Decimal type
Terminating
As Percentage
75%
Simplified Fraction
3/4

The formula

Fraction → Decimal: Numerator ÷ Denominator | Decimal → Fraction: multiply by 10^n / 10^n, simplify

GCD
Greatest Common Divisor
Numerator
Numerator
Denominator
Denominator

Worked example — Whole Number (mixed numbers only) 3, Numerator 3, Denominator 4, Decimal 0.75

Decimal = 0.75

Full explanation ↓

How Fraction Converter Works

Fraction → Decimal: Numerator ÷ Denominator | Decimal → Fraction: multiply by 10^n / 10^n, simplify

Converting between fractions and decimals uses basic division and the greatest common divisor (GCD) for simplification. The process is reversible: every fraction corresponds to exactly one decimal value, and every terminating decimal corresponds to a unique simplified fraction. The key insight is that fractions are division problems waiting to be solved, and decimals are fractions written in base-10 positional notation.

GCD
Greatest Common Divisor — The largest number that divides both the numerator and denominator evenly, used to simplify fractions. For example, GCD(12, 16) = 4, so 12/16 = 3/4.
Numerator
Numerator — The top number in a fraction. Represents how many parts of the whole you have.
Denominator
Denominator — The bottom number in a fraction. Represents how many equal parts the whole is divided into. Must be non-zero.
Fractions represent parts of a whole; dividing numerator by denominator gives the decimal equivalent.

Understanding the Result

Fraction-to-decimal conversion is one of the most fundamental operations in mathematics. Any fraction can be converted to a decimal by dividing the numerator by the denominator. Some fractions produce terminating decimals (1/4 = 0.25) because their denominator has only prime factors of 2 and 5. Others produce repeating decimals (1/3 = 0.333...) when the denominator has other prime factors. Converting decimals back to fractions requires multiplying by a power of 10 to clear the decimal, then simplifying using the GCD.

For example, 0.75 = 75/100 = 3/4 after simplification. A practical tip: common fractions like 1/2 = 0.5, 1/4 = 0.25, and 3/4 = 0.75 appear so frequently in daily life that memorizing them saves time. In carpentry, measurements are given in fractional inches (1/16, 1/8, 1/4) but digital tools often require decimal input, making this conversion essential on job sites. Similarly, in cooking, recipes use fractional cups but nutritional calculations use decimal values.

How to Use

  1. Select the conversion direction from the dropdown: Fraction to Decimal, Decimal to Fraction, or Mixed Number to Decimal.
  2. For fraction-to-decimal: enter the numerator (top) and denominator (bottom). The result is simply numerator divided by denominator.
  3. For decimal-to-fraction: enter the decimal value. The calculator multiplies by a power of 10 to clear decimal places, then simplifies using the GCD.
  4. For mixed numbers: enter the whole number along with the fractional part. The calculator converts to an improper fraction first, then to a decimal.
  5. Check the "As Percentage" column to see the decimal expressed as a percentage (multiplied by 100).

Frequently Asked Questions

What is a repeating decimal?
A decimal that repeats a pattern infinitely, like 0.333... (1/3) or 0.142857142857... (1/7). These fractions have denominators with prime factors other than 2 or 5. The repeating pattern is called the repetend and is often written with a vinculum (bar) over the repeating digits, or in bracket notation as this calculator does: 0.(3) for 1/3 and 0.(142857) for 1/7. Every rational number (fraction of integers) either terminates or repeats — there is no third possibility.
How do I simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, 12/16: the GCD is 4, so simplified is (12/4)/(16/4) = 3/4. Simplification makes fractions easier to compare and work with in further calculations.
Why do some decimals terminate while others repeat?
A decimal terminates when the denominator's only prime factors are 2 and 5 — the prime factors of 10 (our base-10 number system). For example, 1/8 = 0.125 because 8 = 2³. If the denominator has any other prime factor (like 3, 7, 11), the decimal repeats. This is a fundamental property of our base-10 number system.
How do I convert a mixed number like 2 3/4 to a decimal?
Convert the fraction part (3/4 = 0.75) and add it to the whole number: 2 + 0.75 = 2.75. Alternatively, convert to an improper fraction first: (2 × 4 + 3)/4 = 11/4, then divide 11 ÷ 4 = 2.75. Both methods give the same result.
What is the difference between a terminating and a repeating decimal?
A terminating decimal has a finite number of digits (e.g., 0.5, 0.125, 0.375). A repeating decimal has a pattern that repeats forever (e.g., 0.333..., 0.142857142857...). All fractions of integers produce either terminating or repeating decimals — there is no third category. A fraction produces a terminating decimal only when its denominator (in simplest form) has only 2 and 5 as prime factors.

Sources

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Cite this calculator

TheCalcUniverse. "Fraction to Decimal Converter — Auto-Simplifies with GCD." TheCalcUniverse, 2026, https://thecalcuniverse.com/math/fraction-to-decimal-calculator/. Accessed October 25, 2026.

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