Math

Decimal to Fraction Calculator

Convert any decimal to a simplified fraction. Handles terminating and repeating decimals with step-by-step work.

Quick Answer

Write the decimal over the appropriate power of 10, then simplify. 0.75 = 75/100 = 3/4. For repeating decimals like 0.333..., use the notation 0.(3) and get 1/3.

Enter a Decimal

Decimal Number

For repeating decimals, use parentheses: 0.(3) = 0.333..., 0.1(6) = 0.1666...

Examples:

Results

3/4

Simplified Fraction

Step-by-Step

0.75 = 75/100

GCF(75, 100) = 25

Simplified: 3/4

About This Tool

The Decimal to Fraction Calculator converts any decimal number into its equivalent fraction in simplest form. It handles both terminating decimals (like 0.75) and repeating decimals (like 0.333...) and shows every step of the conversion process.

Converting Terminating Decimals

For terminating decimals, count the decimal places, write the number over the corresponding power of 10, then simplify. 0.625 has three decimal places, so it becomes 625/1000. The GCF of 625 and 1000 is 125, giving 5/8.

Converting Repeating Decimals

Repeating decimals require a different approach. Let x = 0.333... Multiply both sides by 10: 10x = 3.333... Subtract the original: 9x = 3, so x = 3/9 = 1/3. This calculator automates this process. Use parentheses to indicate the repeating part: 0.(3) for 0.333... or 0.1(6) for 0.1666...

Common Decimal-to-Fraction Conversions

Some conversions come up so often they are worth memorizing: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.125 = 1/8, 0.2 = 1/5, 0.333... = 1/3, 0.666... = 2/3, 0.1 = 1/10. Knowing these speeds up mental math significantly.

Why Fractions Matter

Fractions are exact representations. The decimal 0.333... is an approximation of 1/3 no matter how many digits you write. In engineering, cooking, woodworking, and mathematics, fractions often provide the precision needed. Understanding the conversion between decimals and fractions is a core math skill.

Frequently Asked Questions

How do I convert a decimal to a fraction?

For terminating decimals: write it over the appropriate power of 10 and simplify. 0.4 = 4/10 = 2/5. For repeating decimals, use algebra to eliminate the repeating part.

How do I enter a repeating decimal?

Put the repeating digits in parentheses. 0.333... becomes 0.(3). 0.142857142857... becomes 0.(142857). 0.1666... becomes 0.1(6).

What is 0.999... as a fraction?

0.999... = 1. This is mathematically proven. Let x = 0.999..., then 10x = 9.999..., subtract: 9x = 9, so x = 1. They are the same number.

Can every decimal be converted to a fraction?

Every terminating or repeating decimal can be converted to a fraction (rational number). Non-repeating, non-terminating decimals like pi (3.14159...) and the square root of 2 are irrational and cannot be expressed as exact fractions.

What is a mixed number?

A mixed number combines a whole number with a proper fraction, like 2 3/4. It represents 2 + 3/4 = 11/4 as an improper fraction. This calculator shows both forms when applicable.

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