Fraction ↔ Decimal Converter

Fraction ↔ Decimal Converter Live

Common Fraction ↔ Decimal Reference

What is a Fraction?

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many parts you have. For example, ¾ means 3 out of 4 equal parts.

Types of Fractions

• Proper fraction: Numerator < Denominator (e.g. 3/4). Value is always less than 1.
• Improper fraction: Numerator ≥ Denominator (e.g. 7/4). Value is 1 or more.
• Mixed number: A whole number plus a proper fraction (e.g. 1¾). Equivalent to an improper fraction.
• Equivalent fractions: Different fractions that represent the same value (e.g. 1/2 = 2/4 = 4/8).
• Terminating decimal: A fraction whose decimal representation ends (e.g. 1/4 = 0.25).
• Repeating decimal: A fraction whose decimal repeats infinitely (e.g. 1/3 = 0.333…).

How to Convert Fraction to Decimal

Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. For mixed numbers, convert to an improper fraction first: 1¾ = (1×4 + 3)/4 = 7/4 = 1.75.

How to Convert Decimal to Fraction

Count the decimal places (n), write the decimal over 10ⁿ, then simplify using the GCD. For example: 0.75 = 75/100 = 3/4. For repeating decimals, use the algebraic method: let x = 0.333…, then 10x = 3.333…, subtract: 9x = 3, so x = 3/9 = 1/3.