Fractions to Decimals and Percent
Learn how to convert between fractions, decimals, and percentages. These three formats represent the same values in different ways, each useful in different contexts.
Fraction to Decimal
Divide Numerator by Denominator
Perform the division: numerator ÷ denominator
Example: 3/4 = 3 ÷ 4 = 0.75
Decimal to Percent
Multiply by 100
Multiply the decimal by 100 and add the % symbol
Example: 0.75 × 100 = 75%
Fraction to Percent (Direct)
Convert to Decimal First
Divide numerator by denominator
Multiply by 100
Multiply the result by 100 and add %
Example: 3/4 = 0.75 = 75%
Common Conversions to Memorize
- 1/2 = 0.5 = 50%
- 1/4 = 0.25 = 25%
- 3/4 = 0.75 = 75%
- 1/3 ≈ 0.333 ≈ 33.3%
- 2/3 ≈ 0.667 ≈ 66.7%
- 1/5 = 0.2 = 20%
- 1/8 = 0.125 = 12.5%
- 1/10 = 0.1 = 10%
When to Use Each Format
- Fractions: Exact values, recipes, construction measurements
- Decimals: Money, scientific calculations, computer data
- Percents: Statistics, discounts, test scores, comparisons
Repeating Decimals
Some fractions produce repeating decimals that never end. Common examples include 1/3 = 0.333... and 1/6 = 0.1666... Different contexts handle these differently—some round to a specific number of decimal places, while others use bar notation (0.3̄) or keep the fraction form.
For more on repeating decimals and their properties, see Wikipedia's article on repeating decimals.
Frequently Asked Questions
This depends on your context. For money, use 2 decimal places. For most practical purposes, 2-4 decimal places are sufficient. Scientific work may require more precision.
All terminating and repeating decimals can be written as fractions. Non-repeating, non-terminating decimals (like π) cannot be expressed as simple fractions.
Fractions with denominators that are powers of 2 and 5 (like 2, 4, 5, 8, 10, 16, 20, 25, etc.) produce terminating decimals. Other denominators typically produce repeating decimals.