Decimal to Fraction Converter
Convert decimal numbers to fractions quickly and accurately. Automatically simplifies fractions to lowest terms and shows both proper and improper fraction forms.
How do you convert a decimal to a fraction?
Count decimal places, use as denominator power of 10, simplify. Steps: 1) Write decimal as fraction over 1 (0.75 = 0.75/1), 2) Multiply by 10 for each decimal place (0.75 × 100/100 = 75/100), 3) Simplify by dividing by GCD (75/100 = 3/4). Examples: 0.5 = 5/10 = 1/2, 0.25 = 25/100 = 1/4, 0.125 = 125/1000 = 1/8. For mixed decimals like 2.75: whole number + fraction = 2 + 75/100 = 2 3/4.
What are common decimal to fraction conversions?
Common conversions: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.2 = 1/5, 0.4 = 2/5, 0.6 = 3/5, 0.8 = 4/5, 0.125 = 1/8, 0.375 = 3/8, 0.625 = 5/8, 0.875 = 7/8, 0.1 = 1/10, 0.01 = 1/100, 0.333... = 1/3, 0.666... = 2/3, 0.167 = 1/6. Memorizing these speeds up conversions for cooking, construction, and math problems.
How do you simplify fractions?
Divide numerator and denominator by their Greatest Common Divisor (GCD). Example: 75/100 - GCD of 75 and 100 is 25, so 75÷25 / 100÷25 = 3/4. Finding GCD: List factors of each number, find largest common one. 75: 1,3,5,15,25,75; 100: 1,2,4,5,10,20,25,50,100; GCD = 25. Or use Euclidean algorithm. Always simplify to lowest terms: 50/100 = 1/2, not 5/10 or 25/50.
How do you convert repeating decimals to fractions?
Use algebraic method. Example: 0.333... = 1/3. Method: Let x = 0.333..., then 10x = 3.333..., subtract: 10x - x = 3, so 9x = 3, x = 3/9 = 1/3. For 0.454545...: Let x = 0.454545..., 100x = 45.454545..., 100x - x = 45, 99x = 45, x = 45/99 = 5/11. For 0.1666...: 0.1666... = 1/6. Common: 0.142857... = 1/7, 0.111... = 1/9.
How do you convert decimals greater than 1 to fractions?
Separate whole number from decimal part. Example: 2.75 = 2 + 0.75. Convert decimal: 0.75 = 75/100 = 3/4. Result: 2 3/4 (mixed number) or convert to improper fraction: 2 3/4 = (2×4 + 3)/4 = 11/4. More examples: 1.5 = 1 1/2 = 3/2, 3.25 = 3 1/4 = 13/4, 5.8 = 5 4/5 = 29/5. Both forms are correct; mixed numbers are easier to visualize, improper fractions easier for calculations.
Why convert decimals to fractions?
Fractions are exact, decimals can be approximate. Example: 1/3 is exact, but 0.333... is rounded. Uses: Cooking (1/2 cup vs 0.5 cup), construction (3/4 inch easier than 0.75"), music (1/4 note, not 0.25 note), math (exact answers in algebra/calculus). Fractions show relationships: 3/4 means 3 parts of 4, clearer than 0.75. Some contexts require fractions: measuring cups, wrench sizes, sheet music, stock prices.
What is the difference between proper and improper fractions?
Proper fraction: numerator < denominator, value < 1. Examples: 1/2, 3/4, 5/8. Improper fraction: numerator ≥ denominator, value ≥ 1. Examples: 5/4, 7/3, 9/2. Mixed number: whole number + proper fraction. Examples: 1 1/4, 2 1/3. Conversions: 5/4 = 1 1/4 (improper to mixed), 1 1/4 = 5/4 (mixed to improper). All forms represent same value: 1.25 = 5/4 = 1 1/4.