Fraction to Decimal Converter
Convert any fraction to its decimal equivalent or Decimal to Fraction.
How to Convert a Fraction to a Decimal
To convert any fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). You can do this with long division or a calculator. For mixed numbers like 2 3/4, convert the fractional part first (3 ÷ 4 = 0.75), then add the whole number to get 2.75. The result is either a terminating decimal (like 3/4 = 0.75) or a repeating decimal (like 1/3 = 0.333...).
Fraction to Decimal Formula
Decimal = Numerator ÷ Denominator. For a mixed number: Decimal = Whole + (Numerator ÷ Denominator). This works because a fraction is simply a division problem written in a different notation. The fraction bar means "divided by," so 7/8 literally means 7 divided by 8.
Worked Example: Convert 7/8 to a Decimal
Divide 7 by 8 using long division. 8 goes into 7 zero times, so write 0. and carry 70. 8 goes into 70 eight times (64), remainder 6. Carry to get 60. 8 goes into 60 seven times (56), remainder 4. Carry to get 40. 8 goes into 40 exactly 5 times. Result: 7/8 = 0.875. Verification: 0.875 × 8 = 7 ✓.
Common Fraction to Decimal Conversions
1/2 = 0.5 · 1/3 = 0.333... · 1/4 = 0.25 · 1/5 = 0.2 · 1/6 = 0.166... · 1/7 = 0.142857... · 1/8 = 0.125 · 1/9 = 0.111... · 1/10 = 0.1 · 2/3 = 0.666... · 3/4 = 0.75 · 2/5 = 0.4 · 3/5 = 0.6 · 4/5 = 0.8 · 3/8 = 0.375 · 5/8 = 0.625 · 7/8 = 0.875 · 5/6 = 0.833... · 7/9 = 0.777...
Technical Details
A fraction produces a terminating decimal only when the denominator's prime factors are limited to 2 and 5 (the prime factors of 10). For example, 1/8 terminates because 8 = 2³, and 1/20 terminates because 20 = 2² × 5. Any other prime factor in the denominator produces a repeating decimal: 1/3 repeats because 3 is prime and not 2 or 5. The length of the repeating cycle for 1/p (where p is prime) divides p−1. This tool uses JavaScript's 64-bit floating-point arithmetic, which provides about 15-17 significant decimal digits of precision.
Frequently Asked Questions
What is 5/8 as a decimal? 5 ÷ 8 = 0.625. How do you know if a fraction will be a repeating decimal? If the denominator (in lowest terms) has any prime factor other than 2 or 5, the decimal will repeat. For example, 1/6 repeats because 6 = 2 × 3, and the factor of 3 causes repetition. What is a mixed number in decimal form? A mixed number like 3 1/4 converts to 3 + 0.25 = 3.25. Convert the fraction part and add it to the whole number. Why does 1/3 equal 0.333...? Because 3 does not divide evenly into any power of 10. No matter how many decimal places you calculate, there is always a remainder, producing an infinite repeating sequence.