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Decimal to Fraction Calculator
Convert decimals to exact or simplified fractions

Limits the denominator for approximate fractions

Common Conversions
0.51/2
0.251/4
0.333...1/3
0.1251/8
0.21/5
0.753/4
0.666...2/3
0.8757/8
Conversion Method

For Terminating Decimals:

  1. Count decimal places (n)
  2. Multiply by 10^n to get numerator
  3. Use 10^n as denominator
  4. Simplify using GCD

Example: 0.75

0.75 = 75/100 = 3/4

What is Decimal to Fraction Conversion?

Decimal to fraction conversion is the process of expressing a decimal number as a ratio of two integers (a fraction). Every terminating decimal can be converted to an exact fraction, while repeating decimals can also be expressed as fractions using algebraic methods. For example, 0.75 equals 3/4, and 0.333... (repeating) equals 1/3.

This conversion is useful in many contexts, including cooking measurements, construction calculations, and mathematical problem-solving where fractions provide more precise or intuitive representations than decimals. Understanding both forms helps in choosing the most appropriate representation for any given situation.

How to Use This Calculator

Enter any decimal number (positive, negative, or zero) into the input field. The calculator will automatically convert it to a fraction in lowest terms. You can also see the mixed number representation when applicable (e.g., 7/4 = 1 3/4).

For very long decimals or irrational approximations like pi (3.14159...), you can set a maximum denominator to get a practical approximation. For example, limiting the denominator to 100 for pi gives you 22/7, a famous approximation used throughout history.

Disclaimer

Decimal to fraction conversions are approximate for repeating decimals within the specified tolerance. Results depend on input accuracy and selected options. For exact representations of repeating decimals, algebraic methods should be used to derive the precise fraction.

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