Fraction to Decimal Converter
Convert fractions to decimals quickly and accurately. Supports whole numbers, proper fractions, improper fractions, and mixed numbers.
How do you convert a fraction to a decimal?
Divide the numerator (top number) by the denominator (bottom number). Formula: Decimal = Numerator ÷ Denominator. Example: 3/4 = 3 ÷ 4 = 0.75. For mixed numbers, convert the whole number first, then add the fraction: 2 3/4 = 2 + (3 ÷ 4) = 2 + 0.75 = 2.75. This works for all fractions: proper (1/2), improper (5/4), and mixed numbers (1 1/2).
What are common fraction to decimal conversions?
Common conversions: 1/2 = 0.5, 1/3 = 0.333..., 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125, 2/3 = 0.666..., 3/4 = 0.75, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8, 1/10 = 0.1, 1/100 = 0.01. Halves: 1/2 = 0.5, 3/2 = 1.5. Quarters: 1/4 = 0.25, 3/4 = 0.75. Eighths: 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875.
What is a repeating decimal?
A repeating decimal has digits that repeat infinitely. Examples: 1/3 = 0.333... (3 repeats), 2/3 = 0.666... (6 repeats), 1/6 = 0.1666... (6 repeats), 1/7 = 0.142857142857... (142857 repeats), 1/9 = 0.111... (1 repeats), 5/11 = 0.454545... (45 repeats). These occur when the denominator has prime factors other than 2 or 5. In notation, use a bar over repeating digits: 0.3̄ = 0.333...
How do you convert a mixed number to a decimal?
Add the whole number to the decimal value of the fraction. Steps: 1) Convert fraction to decimal (numerator ÷ denominator), 2) Add to whole number. Example: 3 2/5 = 3 + (2 ÷ 5) = 3 + 0.4 = 3.4. More examples: 1 1/2 = 1.5, 2 3/4 = 2.75, 5 1/8 = 5.125, 10 2/3 = 10.666... Alternative: Convert to improper fraction first: 3 2/5 = 17/5 = 3.4.
Why do some fractions have terminating decimals and others repeat?
A fraction produces a terminating decimal if the denominator (in lowest terms) has only 2 and/or 5 as prime factors. Examples: 1/2 = 0.5 (2), 1/4 = 0.25 (2²), 1/5 = 0.2 (5), 1/8 = 0.125 (2³), 3/10 = 0.3 (2×5). If the denominator has other prime factors (3, 7, 11, etc.), the decimal repeats: 1/3 (3), 1/6 (2×3), 1/7 (7). This is because our decimal system is base 10 (2×5).
How do you convert improper fractions to decimals?
Same method: divide numerator by denominator. Improper fractions (numerator > denominator) give decimals greater than 1. Examples: 5/4 = 5 ÷ 4 = 1.25, 7/2 = 7 ÷ 2 = 3.5, 11/3 = 11 ÷ 3 = 3.666..., 9/5 = 9 ÷ 5 = 1.8, 22/7 = 3.142857... (approximation of π). Or convert to mixed number first: 5/4 = 1 1/4 = 1.25, both methods give the same result.
How accurate should I round fraction-to-decimal conversions?
Depends on use: Money: 2 decimal places ($0.75). Measurements: 2-3 decimals (2.75 inches). Science: 3-4+ decimals (3.1416). Percentages: 1-2 decimals (75.5%). For repeating decimals, use reasonable precision: 1/3 ≈ 0.333 (3 decimals) or 0.33 (2 decimals). When exact values matter, keep the fraction form or use many decimals. Calculator and computer programs can handle 10+ decimal places for precision.