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.
Solved Examples
Example 1: A recipe calls for 3/8 cup of oil. What is that on a digital measuring cup? Divide 3 by 8: 3 ÷ 8 = 0.375 cups. Answer: Set the measuring cup to 0.375 cups. Example 2: A student scores 17/20 on a quiz. What is the decimal equivalent? 17 ÷ 20 = 0.85. Answer: 0.85 (or 85%). Example 3: Convert the mixed number 5 2/3 to decimal. Whole part = 5. Fraction: 2 ÷ 3 = 0.6666... Total: 5.6667 (rounded to 4 decimal places). Answer: 5.6667. Example 4: A bolt has diameter 7/16 inch. Express in decimal for a digital caliper. 7 ÷ 16 = 0.4375 inches. Answer: 0.4375 inches exactly.
Practice Questions
1. Convert 5/6 to a decimal. (Answer: 0.8333...) 2. What is 11/4 as a decimal? (Answer: 2.75) 3. Express 2/7 as a decimal (to 4 places). (Answer: 0.2857) 4. Convert 9/16 to decimal. (Answer: 0.5625) 5. What is the mixed number 3 5/8 in decimal? (Answer: 3.625) 6. Convert 1/11 to a decimal. (Answer: 0.090909... repeating)
Common Mistakes to Avoid
The most frequent error is dividing the denominator by the numerator instead of the other way around. Remember: numerator ÷ denominator (top divided by bottom). Dividing backwards gives you the reciprocal. Another common mistake is with mixed numbers — students sometimes multiply the whole number by the fraction instead of adding. The correct process: 2 3/4 = 2 + (3÷4) = 2 + 0.75 = 2.75, NOT 2 × 0.75. When dealing with repeating decimals, don't round too early in intermediate calculations — carry extra digits and round only the final answer. Also, students sometimes assume all fractions with odd denominators are repeating, but 1/5 = 0.2 (terminates) because 5 is a factor of 10. The key rule: only denominators with factors of 2 and/or 5 (in lowest terms) give terminating decimals.
Key Takeaways
Fraction to decimal conversion is simply division: numerator ÷ denominator. Terminating decimals occur only when the simplified denominator has no prime factors other than 2 and 5. Repeating decimals are marked with an overbar (0.3̄) or ellipsis (0.333...). Mixed numbers: add the whole part to the decimal fraction. Common fractions worth memorizing: 1/2=0.5, 1/4=0.25, 1/8=0.125, 3/4=0.75, 1/3=0.333..., 2/3=0.667. This conversion is fundamental to understanding percentages, since percent = decimal × 100.