Math & Algebra Tool

Decimal to Fraction

Convert decimal numbers (0.75) back into simplified fractions (3/4).

Σ The Formula

Convert to a/b form, then simplify using GCD

Real World Examples

Simple Conversion
0.75 = 75/100 = 3/4
Smaller Decimal
0.125 = 125/1000 = 1/8
Repeating Pattern
0.333... ≈ 1/3
Improper Fraction
2.5 = 5/2

# About This Calculator

Converting decimals to fractions is useful for finding the exact value representation of a number. While decimals (like 0.333) are approximations, fractions (like 1/3) are exact. This precision is crucial in algebra, carpentry, and science.

To convert a decimal to a fraction, write the decimal divided by 1 (e.g., 0.75/1), then multiply top and bottom by 10 for every digit after the decimal point (75/100). Finally, simplify the result by finding the Greatest Common Divisor (GCD).

For example, 0.75 becomes 75/100. Both are divisible by 25, so it simplifies to 3/4. This tool automates that entire process, handling simple decimals and complex ones instantly.

Perfect for schoolwork, converting digital measurements to ruler markings (like 0.125 inches to 1/8"), or ensuring exactness in mathematical proofs.

How To Use

  1. Enter a Decimal Number (e.g., 0.125).
  2. Click Convert.
  3. View the simplified Numerator and Denominator.

Frequently Asked Questions

How do I convert a decimal to a fraction manually?+

Write the decimal over 1. Multiply top and bottom by 10, 100, etc., to remove the decimal point. Then simplify. Example: 0.5 = 5/10 = 1/2.

Why convert decimals to fractions?+

Fractions are often more precise. For example, 1/3 is exact, while 0.333 is an approximation. Fractions are also preferred in algebra and baking.

Can any decimal be converted to a fraction?+

Any 'rational' number (terminating or repeating decimal) can be a fraction. 'Irrational' numbers like Pi (3.14159...) cannot be written as a simple fraction.

What if my decimal is greater than 1?+

You'll get an improper fraction. For example, 1.5 becomes 15/10 = 3/2. You can then convert that to a mixed number (1 1/2) if needed.

Does this tool simplify the result?+

Yes! It automatically finds the simplest form (lowest terms). 0.5 gives 1/2, not 5/10 or 50/100.

Is Decimal to Fraction free to use?+

Yes, Decimal to Fraction on Matheric is completely free to use. We believe in accessible education and utility for everyone.

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