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Decimal to Fraction Calculator

Use this free online decimal to fraction calculator to convert any decimal number to its equivalent fraction in simplest form. Enter a decimal and get the simplified fraction instantly.

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Formula

decimal = numerator / denominator (simplified by GCD)

Multiply the decimal by a power of 10 to remove the decimal point, then simplify using the GCD.

Worked Example

Convert 0.75 to a fraction Step 1: 0.75 = 75/100 Step 2: GCD(75, 100) = 25 Step 3: 75/25 = 3, 100/25 = 4 Result: 3/4

How to Convert Decimals to Fractions

Converting a decimal to a fraction involves writing the decimal as a fraction over a power of 10, then simplifying. The number of decimal places determines which power of 10 to use as the denominator. This process works for any terminating decimal.
  • 0.5 has 1 decimal place, so it becomes 5/10, which simplifies to 1/2
  • 0.75 has 2 decimal places, so it becomes 75/100, which simplifies to 3/4
  • 0.125 has 3 decimal places, so it becomes 125/1000, which simplifies to 1/8
  • Repeating decimals (like 0.333...) require a different algebraic method to convert

Converting between decimals and fractions is a practical skill used in cooking (recipes often use fractions), construction (measurements), and mathematics (simplifying expressions).

You can also calculate changes using our Fraction Calculator or Percentage Calculator.

Frequently Asked Questions

How do I convert a decimal to a fraction?

Write the decimal over a power of 10 based on the number of decimal places, then simplify by dividing both numerator and denominator by their GCD. For example, 0.6 = 6/10 = 3/5.

Can all decimals be expressed as fractions?

Terminating decimals (like 0.25) and repeating decimals (like 0.333...) can be expressed as fractions. Irrational numbers (like pi = 3.14159... or sqrt(2) = 1.4142...) cannot.

What is a mixed number?

A whole number combined with a proper fraction, e.g. 1.75 = 1 3/4. To convert, separate the whole part and convert only the decimal part to a fraction.

How do I convert a repeating decimal to a fraction?

For 0.333..., let x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 3/9 = 1/3. The method involves multiplying by a power of 10 to shift the repeating part.

What are common decimal-to-fraction equivalents?

0.25 = 1/4, 0.5 = 1/2, 0.75 = 3/4, 0.125 = 1/8, 0.2 = 1/5, 0.333... = 1/3, 0.666... = 2/3. Memorizing these speeds up mental math.

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