Decimal to Fraction Converter

Convert Decimal to Fraction

What is a Decimal to Fraction Conversion?

Converting a decimal to a fraction means expressing a decimal number as a ratio of two integers. Every decimal number can be represented as a fraction, which is often more precise and easier to work with in mathematical calculations.

For example, the decimal 0.75 can be written as the fraction 3/4. This conversion is useful in many areas of mathematics, including algebra, calculus, and everyday calculations where fractions are preferred over decimals.

How to Convert Decimals to Fractions

Follow these steps to convert a decimal to a fraction:

  1. Write as fraction over 1: Place the decimal over 1 (e.g., 0.75/1)
  2. Multiply by power of 10: Multiply both numerator and denominator by 10 for each decimal place
  3. Simplify: Reduce the fraction by dividing by the GCD
  4. Check for repeating decimals: Some decimals (like 0.333...) require a different approach

Formula

For a decimal with n decimal places:

Decimal = (Decimal × 10ⁿ) / 10ⁿ

Then simplify by dividing by GCD

Example

Conversion Example

Problem: Convert 0.625 to a fraction

Solution:

  1. Write as fraction: 0.625/1
  2. Multiply by 1000 (3 decimal places): 625/1000
  3. Find GCD(625, 1000) = 125
  4. Divide both: 625/125 = 5, 1000/125 = 8
  5. Result: 5/8

Frequently Asked Questions

What about repeating decimals?

Repeating decimals like 0.333... convert to fractions using algebra. For 0.333..., let x = 0.333..., then 10x = 3.333..., and 10x - x = 3, so x = 1/3.

Can all decimals be converted to fractions?

Terminating and repeating decimals can be converted to fractions. Irrational numbers like pi (π) or sqrt(2) have non-repeating, non-terminating decimals that cannot be expressed as exact fractions.

How do I convert mixed numbers?

First convert the whole number separately, then add the fractional part. For example, 2.75 = 2 + 0.75 = 2 + 3/4 = 11/4.