Decimal to Fraction Converter
Convert any decimal number to a fraction in simplest form or Fraction to Decimal.
How to Convert Decimal to Fraction
Converting a decimal to a fraction takes three steps. First, count the number of decimal places — for 0.75, there are two. Second, write the decimal digits as the numerator over a denominator of 10 raised to that count: 75/100. Third, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. The GCD of 75 and 100 is 25, so 75 ÷ 25 = 3 and 100 ÷ 25 = 4. The simplified fraction is 3/4.
Decimal to Fraction Formula
For a decimal with n digits after the decimal point: Fraction = (decimal × 10ⁿ) / 10ⁿ, then simplify using GCD. In formula form: numerator = decimal digits as integer, denominator = 10ⁿ, simplified fraction = numerator/GCD ÷ denominator/GCD. For repeating decimals like 0.333..., the fraction is found algebraically: let x = 0.333..., then 10x = 3.333..., so 9x = 3, and x = 3/9 = 1/3.
Worked Example: Convert 0.625 to a Fraction
Step 1: Count decimal places — 0.625 has 3 decimal places. Step 2: Write as 625/1000. Step 3: Find GCD of 625 and 1000. Using the Euclidean algorithm: 1000 = 1 × 625 + 375, then 625 = 1 × 375 + 250, then 375 = 1 × 250 + 125, then 250 = 2 × 125 + 0. GCD = 125. Step 4: Divide both by 125: 625 ÷ 125 = 5, 1000 ÷ 125 = 8. Result: 0.625 = 5/8.
Common Decimal to Fraction Conversions
0.1 = 1/10 · 0.125 = 1/8 · 0.2 = 1/5 · 0.25 = 1/4 · 0.3 = 3/10 · 0.333... = 1/3 · 0.375 = 3/8 · 0.4 = 2/5 · 0.5 = 1/2 · 0.6 = 3/5 · 0.625 = 5/8 · 0.666... = 2/3 · 0.7 = 7/10 · 0.75 = 3/4 · 0.8 = 4/5 · 0.875 = 7/8 · 0.9 = 9/10. Memorizing these common equivalents speeds up mental math and is especially useful for standardized tests.
Technical Details
This converter handles terminating decimals with up to 15 significant digits, limited by JavaScript's IEEE 754 double-precision floating-point representation. For mixed numbers like 2.75, the tool separates the whole part (2) from the fractional part (0.75 = 3/4) and displays the result as 2 3/4. Negative decimals are fully supported. The GCD is computed using the Euclidean algorithm, which runs in O(log(min(a,b))) time. Note that true repeating decimals (like 0.333...) should be entered with enough digits for a close approximation — the tool will simplify to the nearest clean fraction.
Frequently Asked Questions
What is 0.75 as a fraction? 0.75 = 75/100 = 3/4 after dividing both by 25. How do you convert a repeating decimal to a fraction? For 0.666..., let x = 0.666..., multiply both sides by 10 to get 10x = 6.666..., subtract to get 9x = 6, so x = 6/9 = 2/3. Can every decimal be written as a fraction? Every terminating or repeating decimal can be expressed as a fraction. Non-repeating, non-terminating decimals like π (3.14159...) are irrational and cannot be written as exact fractions. What is the GCD and why does it matter? The greatest common divisor is the largest number that divides both the numerator and denominator evenly. Dividing by the GCD reduces the fraction to its simplest form.