Math July 13, 2026 · 8 Min Read

Decimal to Fraction Calculator – Guide & Formulas

Convert any decimal number to a simplified fraction or mixed number. Shows repeating decimal conversion, terminating decimal conversion, and step-by-step simplification process.

Convert any decimal number to a simplified fraction or mixed number. Supports both terminating and repeating decimals with step-by-step conversion and GCD simplification.

Key Takeaway

Use the free Decimal to Fraction Calculator to convert any decimal number to a simplified fraction or mixed number. shows repeating decimal conversion, terminating decimal conversion, and step-by-step simplification process. Get instant results with step-by-step explanations.

How to Use the Decimal to Fraction Calculator

  1. Enter a decimal number in the input field (e.g., 0.75 or 0.333...).
  2. For repeating decimals, check the "Repeating" toggle and enter the repeating digits.
  3. Click "Convert to Fraction" to see the result.
  4. Review the step-by-step conversion showing place value, fraction form, and simplification.
  5. Copy the fraction or mixed number result.

The Formula

A terminating decimal with n digits after the point equals the integer formed by all digits divided by 10^n. For example, 0.75 = 75/100 = 3/4. For repeating decimals 0.̄r̄, multiply by 10^n (n = repeating length) and subtract the original to eliminate the repeating part.

Variable Definitions

  • d₁d₂...dₙ: The digits after the decimal point
  • 10ⁿ: Power of 10 equal to the number of decimal places
  • GCD: Greatest Common Divisor — used to simplify the fraction
  • LCM: Least Common Multiple — used in repeating decimal conversion

Example: Convert 0.625 to a Fraction

Convert the terminating decimal 0.625 to a simplified fraction.

  1. Step 1: Write 0.625 as a fraction: 625/1000 (three decimal places → divide by 1000).
  2. Step 2: Find GCD(625, 1000). Factor: 625 = 5⁴, 1000 = 2³ × 5³. GCD = 5³ = 125.
  3. Step 3: Divide both by 125: 625÷125 / 1000÷125 = 5/8.
  4. Step 4: Verify: 5 ÷ 8 = 0.625. The conversion is correct.
  5. Step 5: The simplified fraction is 5/8.

Frequently Asked Questions

How do you convert a decimal to a fraction?

Write the decimal as a fraction with the appropriate power of 10 as the denominator. For 0.75, write 75/100. Then simplify by dividing both numerator and denominator by their GCD. 75/100 → GCD = 25 → 3/4.

How do you convert a repeating decimal to a fraction?

Let x = the repeating decimal. Multiply x by 10ⁿ where n is the length of the repeating block. Subtract the original equation to eliminate the repeating part. Solve for x. For example, 0.̄3̄: 10x = 3.333... and x = 0.333..., so 9x = 3, x = 1/3.

What is the difference between terminating and repeating decimals?

Terminating decimals have a finite number of digits after the decimal point (e.g., 0.75). Repeating decimals have an infinite pattern of digits that repeats (e.g., 0.333...). Terminating decimals convert directly; repeating decimals require algebraic manipulation.

How do you convert a mixed number to a decimal?

Divide the numerator by the denominator to get the fractional part as a decimal, then add the whole number. For example, 3 1/4: 1 ÷ 4 = 0.25, so 3 1/4 = 3.25.

What is 0.5 as a fraction?

0.5 = 5/10 = 1/2. Since there is one decimal place, place the digit 5 over 10, then simplify by dividing both by 5 to get 1/2.

How do you convert a decimal greater than 1 to a fraction?

Separate the whole number and decimal parts. Convert the decimal part to a fraction, then combine. For example, 2.75: the whole number is 2, and 0.75 = 75/100 = 3/4. So 2.75 = 2 3/4 or 11/4 as an improper fraction.

Can all decimals be converted to fractions?

Terminating and repeating decimals can always be converted to fractions (they are rational numbers). Non-repeating, non-terminating decimals (like π or √2) are irrational and cannot be exactly expressed as fractions, though they can be approximated.

How do you know if a decimal will terminate or repeat?

A fraction in lowest terms terminates if and only if the denominator has no prime factors other than 2 and 5. For example, 1/8 = 0.125 terminates (8 = 2³), while 1/3 = 0.333... repeats (3 is not 2 or 5).

How do you convert 0.999... to a fraction?

0.999... = 1 exactly. Using algebra: let x = 0.999..., then 10x = 9.999..., so 10x - x = 9, 9x = 9, x = 1. This is not an approximation — 0.999... is mathematically equal to 1.

What is the decimal 0.125 as a fraction?

0.125 = 125/1000. GCD(125, 1000) = 125. Simplifying: 125÷125 / 1000÷125 = 1/8. So 0.125 equals 1/8.