Fraction ⇄ Decimal Converter

Convert fractions to decimals and decimals to fractions

Free online converter for fractions and decimals. Convert fractions to decimals (e.g., 1/2 → 0.5) and decimals to fractions (e.g., 0.75 → 3/4). Supports mixed numbers and automatic simplification. No registration required.

How to Use

Simple 2-way conversion process:

Step 1: Choose Conversion Direction
Choose whether to convert fraction to decimal or decimal to fraction
Step 2: Enter Values
For fraction to decimal: enter whole number (optional), numerator, and denominator. For decimal to fraction: enter decimal number
Step 3: Get Results
Click Convert button to see instant results. Fractions are automatically simplified

All conversions are performed in your browser. No data is sent to our servers.

Fraction ⇄ Decimal Converter Tool

1. Fraction → Decimal

Decimal Result:

2. Decimal → Fraction

Decimal:

Fraction Result (Simplified):

Practical Use Cases

Fraction-decimal converters are essential in various fields:

1. Cooking and Recipes

Convert recipe measurements. 1/4 cup = 0.25 cups, 2/3 cup = 0.667 cups, 3/4 teaspoon = 0.75 tsp. Convert between fractions and decimals for scaling recipes, converting between measurement systems, or using digital kitchen scales.

2. Construction and Woodworking

Convert measurements for precision cutting. 5/8 inch = 0.625 inches, 3/16 inch = 0.1875 inches. Tape measures use fractions (1/16, 1/8, 1/4) while digital tools use decimals. Converting ensures accurate measurements across different tools.

3. Financial Calculations

Convert stock prices and shares. Historically, stocks traded in fractions (1/8, 1/16). Convert to decimals for modern trading: 1/8 = $0.125, 3/8 = $0.375. Useful for understanding historical price data and calculating gains/losses.

4. Mathematics Education

Learning equivalence between fractions and decimals. 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/3 = 0.333..., 2/3 = 0.666... Understanding these conversions is fundamental for algebra, geometry, and real-world applications.

5. Engineering and Manufacturing

Convert technical specifications. CAD software uses decimals (0.375mm) while blueprints may show fractions (3/8 inch). Converting between formats ensures accuracy in manufacturing, quality control, and product specifications.

What is Fraction-Decimal Conversion?

Fractions and decimals are two ways to represent numbers that are not whole integers. Converting between them is essential for many practical applications.

Understanding Fractions and Decimals

A fraction represents a part of a whole: numerator/denominator (e.g., 3/4 means 3 parts out of 4). Mixed numbers combine whole numbers and fractions (e.g., 2 1/2). A decimal uses base-10 notation with a decimal point (e.g., 0.75, 2.5). Both represent the same values but in different forms: 3/4 = 0.75, 1/2 = 0.5, 1/4 = 0.25.

Conversion Methods

Fraction to decimal: Divide numerator by denominator. For mixed numbers, add the whole number: 2 3/4 = 2 + (3÷4) = 2.75. Decimal to fraction: Count decimal places to determine denominator (0.5 = 5/10 = 1/2, 0.75 = 75/100 = 3/4), then simplify by dividing numerator and denominator by their greatest common divisor (GCD).

Automatic Simplification

This converter automatically simplifies fractions to lowest terms using the GCD algorithm. 0.5 → 5/10 → 1/2 (divide by 5). 0.75 → 75/100 → 3/4 (divide by 25). 0.125 → 125/1000 → 1/8 (divide by 125). Simplified fractions are easier to understand and use in calculations.

Frequently Asked Questions

How do I convert a fraction to a decimal?

Divide the numerator (top number) by the denominator (bottom number). For example: 3/4 = 3 ÷ 4 = 0.75. For mixed numbers like 2 1/4, convert the fraction part first (1/4 = 0.25), then add the whole number: 2 + 0.25 = 2.25.

How do I convert a decimal to a fraction?

Count the decimal places to determine the denominator. 0.5 (1 decimal place) = 5/10 = 1/2. 0.75 (2 decimal places) = 75/100 = 3/4. 0.125 (3 decimal places) = 125/1000 = 1/8. Then simplify by finding the GCD of numerator and denominator.

What is a mixed number?

A mixed number combines a whole number and a fraction: 2 1/2, 3 3/4, 5 1/8. To convert to decimal: 2 1/2 = 2 + (1÷2) = 2.5. To convert from decimal: 2.75 = 2 + 0.75 = 2 + 3/4 = 2 3/4.

Why do some decimals become repeating fractions?

Some fractions create repeating decimals: 1/3 = 0.333..., 1/6 = 0.1666..., 1/7 = 0.142857142857... This happens when the denominator has prime factors other than 2 and 5. These fractions cannot be exactly represented as terminating decimals in base 10.

How do I simplify a fraction?

Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it. Example: 6/8 → GCD is 2 → 6÷2 / 8÷2 = 3/4. Example: 25/100 → GCD is 25 → 25÷25 / 100÷25 = 1/4. This converter automatically simplifies all results.

What is the GCD (Greatest Common Divisor)?

The GCD is the largest number that divides evenly into both the numerator and denominator. For 12/18: factors of 12 are 1,2,3,4,6,12; factors of 18 are 1,2,3,6,9,18; common factors are 1,2,3,6; GCD is 6. So 12/18 = 2/3 (dividing both by 6).

Are there fractions that equal whole numbers in decimal?

Yes, when the numerator is divisible by the denominator: 4/2 = 2.0, 10/5 = 2.0, 15/3 = 5.0. These are called improper fractions (numerator ≥ denominator). Convert to mixed numbers: 7/4 = 1 3/4 = 1.75.

How accurate is this converter?

This converter uses JavaScript's standard number precision (about 15-17 significant decimal digits). For most practical purposes this is sufficient. Very large or very small numbers may lose precision due to floating-point limitations. Simplified fractions are exact.