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.
Solved Examples
Example 1: A recipe calls for 0.375 cups of sugar. What fraction is this? Count 3 decimal places → 375/1000. GCD(375, 1000) = 125. Simplify: 375÷125 = 3, 1000÷125 = 8. Answer: 3/8 cup. Example 2: A student scores 0.92 on a test. Express as a fraction. Two decimal places → 92/100. GCD(92, 100) = 4. Simplify: 92÷4 = 23, 100÷4 = 25. Answer: 23/25. Example 3: Convert 2.35 to a mixed number fraction. Whole part = 2, decimal = 0.35. Write 35/100, GCD(35, 100) = 5, simplify to 7/20. Answer: 2 7/20. Example 4: A machinist measures a part at 0.3125 inches. What fraction of an inch is this? Four decimal places → 3125/10000. GCD(3125, 10000) = 625. Simplify: 3125÷625 = 5, 10000÷625 = 16. Answer: 5/16 inch — a standard drill bit size.
Practice Questions
1. Convert 0.45 to a fraction in simplest form. (Answer: 9/20) 2. What is 0.875 as a fraction? (Answer: 7/8) 3. Express 1.6 as a mixed number fraction. (Answer: 1 3/5) 4. Convert 0.06 to a fraction. (Answer: 3/50) 5. What fraction is 0.4375? (Answer: 7/16) 6. Convert 3.125 to a mixed number fraction. (Answer: 3 1/8)
Common Mistakes to Avoid
The most frequent error is forgetting to simplify the fraction after writing it over a power of 10. For example, writing 0.8 as 8/10 and stopping there — the correct simplified answer is 4/5. Another common mistake is miscounting decimal places: 0.05 has two decimal places (giving 5/100 = 1/20), not one (which would incorrectly give 5/10). Students also confuse the process for repeating decimals — you cannot simply write 0.333 as 333/1000 and expect to get 1/3 exactly; the algebraic method (let x = 0.333..., then 10x − x = 3) is required. Finally, when converting mixed decimals like 2.75, always separate the whole number first and convert only the decimal portion to a fraction.
Key Takeaways
The core formula is: write the decimal digits over 10ⁿ (where n = number of decimal places), then divide both by GCD. Every terminating decimal can be expressed as a fraction with a denominator whose only prime factors are 2 and 5. The Euclidean algorithm efficiently finds the GCD for simplification. Repeating decimals require an algebraic approach — set up an equation and solve for x. Mixed numbers are handled by converting only the decimal part. Common fractions (1/2, 1/4, 1/8, 3/4, 7/8) appear constantly in cooking, construction, and finance — memorize their decimal equivalents to save time.