Decimal to Fraction Converter

Convert any decimal number to its fraction equivalent with our easy-to-use calculator. Perfect for students, teachers, and anyone working with decimals in daily life.

Enter Decimal

Enter decimal number or use repeating notation like 0.(3) or 1.1(6)

Quick Examples

Result

1/2
Simplified fraction
Original Decimal

0.5

Unsimplified Fraction

5/10

Simplified Fraction

1/2

Percentage

50%

How to Convert Decimals to Fractions

Converting decimals to fractions is a valuable mathematical skill. Our calculator makes this process simple by automatically determining the correct fraction and simplifying it to its lowest terms. If you need to perform other fraction operations, try our comprehensive fractions calculator for addition, subtraction, multiplication, and division.

Need the reverse conversion? Use our Fraction to Decimal Converter to convert fractions to decimal numbers.

The Conversion Method

To convert a decimal to a fraction, follow these steps:

  • Write the decimal as a fraction with the decimal number as the numerator and 1 as the denominator
  • Multiply both numerator and denominator by 10 for each decimal place
  • Simplify the fraction by finding the greatest common divisor (GCD)
  • Divide both numerator and denominator by the GCD to get the simplest form

Types of Decimal Numbers

Terminating Decimals

These decimals have a finite number of digits. Examples: 0.5, 0.25, 0.125. They can be easily converted to fractions.

Repeating Decimals

These decimals have repeating patterns. Examples: 0.333..., 0.142857142857... They require special techniques for conversion.

Common Decimal to Fraction Conversions

Decimal Fraction Simplified
0.55/101/2
0.2525/1001/4
0.7575/1003/4
0.22/101/5
0.125125/10001/8
0.333...333/10001/3

Why Convert Decimals to Fractions?

  • Exact Representation: Fractions can represent exact values that decimals might round.
  • Mathematical Operations: Some calculations are easier with fractions than decimals.
  • Educational Understanding: Understanding fractions helps with mathematical concepts.
  • Recipe Scaling: Cooking and baking often use fractional measurements.
  • Construction and Engineering: Many measurements are naturally expressed as fractions.

Frequently Asked Questions

How do I convert a decimal to a fraction?

To convert a decimal to a fraction, write the decimal as a fraction with the decimal number as the numerator and an appropriate power of 10 as the denominator, then simplify. Our calculator does this automatically.

What is the difference between simplified and unsimplified fractions?

An unsimplified fraction is the direct conversion (like 0.5 = 5/10), while a simplified fraction is reduced to its lowest terms (5/10 = 1/2). Our calculator shows both forms.

How do I handle repeating decimals?

Repeating decimals require special techniques. For simple repeating decimals like 0.333..., you can use algebraic methods. Our calculator includes options for repeating decimal conversion.

Can I convert very long decimals?

Yes, but very long decimals might result in fractions with large numerators and denominators. Our calculator handles up to 6 decimal places for optimal accuracy.

Why do some decimals create large fractions?

Decimals with many places create fractions with large denominators. For example, 0.123456 becomes 123456/1000000, which might simplify to a smaller fraction.

What if my decimal is a whole number?

Whole numbers like 5.0 convert to fractions like 5/1. The calculator will show this as the simplified result.

How accurate is the conversion?

Our calculator provides exact conversions for terminating decimals and highly accurate approximations for repeating decimals, showing both the unsimplified and simplified forms.

Can I convert negative decimals?

Yes, negative decimals work the same way as positive ones. For example, -0.5 becomes -1/2. The negative sign stays with the numerator.

How do I convert a fraction back to a decimal?

Use our Fraction to Decimal Converter! It supports mixed numbers, proper and improper fractions, and provides step-by-step solutions with multiple precision options. Simply divide the numerator by the denominator for manual conversion.