Fraction ↔ Decimal Converter

Instantly convert between fractions, decimals, percentages, and mixed numbers. Simplify fractions, see step-by-step calculations, and get precise results.

Fraction ↔ Decimal Converter

Enter a fraction, decimal, percentage, or mixed number to convert it to all other formats. Get simplified fractions and step-by-step explanations.

Convert Between Formats

3
4
Enter a decimal number (up to 6 decimal places)
Enter a percentage value (without the % sign)
1 1/2

Understanding Fraction-Decimal Conversions

Fractions and decimals are two different ways to represent the same value. Here's how they relate to each other:

Fractions
Parts of a Whole

A fraction represents a part of a whole, written as a/b where 'a' is numerator and 'b' is denominator.

  • Proper: Numerator < Denominator
  • Improper: Numerator ≥ Denominator
  • Example: 3/4 = three quarters
  • To decimal: Divide numerator by denominator
Decimals
Base-10 Number System

Decimals use the base-10 system with a decimal point to separate whole from fractional parts.

  • Place values: tenths, hundredths, etc.
  • Terminating: Ends after finite digits
  • Repeating: Has repeating pattern
  • To fraction: Write as fraction over 10ⁿ
Percentages
Parts per Hundred

A percentage represents a fraction with denominator 100, shown with the % symbol.

  • Meaning: "per hundred"
  • Conversion: % = Decimal × 100
  • Example: 75% = 75/100 = 0.75
  • Common: 50% = 1/2, 25% = 1/4
Mixed Numbers
Whole + Fraction

A mixed number combines a whole number with a proper fraction (e.g., 2½).

  • Format: a b/c
  • To improper: (a×c + b)/c
  • Example: 1¾ = 1 + 3/4
  • To decimal: Add whole to fraction

How to Use the Fraction-Decimal Converter

Follow these simple steps to convert between different number formats:

Step 1: Choose Input Type

Select the tab that matches your input format:

  • Fraction: Enter numerator and denominator
  • Decimal: Enter decimal number (e.g., 0.75)
  • Percentage: Enter percentage (e.g., 75)
  • Mixed Number: Enter whole number, numerator, denominator
Step 2: Set Options

Choose your conversion preferences:

  • Simplify Fraction - Reduce to lowest terms
  • Round Decimals - Control decimal precision
  • Include Percentage - Show % equivalent
  • Show Steps - See calculation process
Step 3: Convert & View Results

Click "Convert Now" to see all equivalent forms:

  • Fraction (simplified if requested)
  • Decimal (rounded if requested)
  • Percentage (if enabled)
  • Mixed number (if applicable)
  • Step-by-step calculations
  • Copy any result with one click
Step 4: Learn & Practice

Use the converter to understand relationships:

  • Study the calculation steps
  • Try common fractions (1/2, 1/4, 3/4)
  • Explore repeating decimals
  • Practice simplifying fractions
  • Check your math homework answers
  • Learn conversion patterns

Common Fraction-Decimal-Percentage Conversions

Memorize these common conversions for quick reference in everyday math:

Fraction Decimal Percentage Mixed Number Description
1/2 0.5 50% - One half
1/4 0.25 25% - One quarter
3/4 0.75 75% - Three quarters
1/3 0.333... 33.33% - One third (repeating)
2/3 0.666... 66.67% - Two thirds (repeating)
1/5 0.2 20% - One fifth
1/8 0.125 12.5% - One eighth
3/2 1.5 150% 1½ One and a half
5/4 1.25 125% 1¼ One and a quarter
7/4 1.75 175% 1¾ One and three quarters
Quick Conversion Tip: To convert a fraction to a decimal, simply divide the numerator by the denominator. For percentages, multiply the decimal by 100. For example: 3/4 = 3 ÷ 4 = 0.75 = 75%.

Real-World Applications

Everyday Life & Shopping
  • Discounts: 25% off = 1/4 reduction
  • Recipes: 3/4 cup flour = 0.75 cups
  • Measurements: 1/2 inch = 0.5 inches
  • Financial: 5% interest = 0.05 rate
  • Cooking: Doubling 1/3 recipe = 2/3
  • Time: 3/4 hour = 45 minutes
Education & Exams
  • Test scores: 18/20 = 90% = 0.9
  • GPA: Convert letter grades to decimals
  • Statistics: 3 out of 4 = 3/4 = 75%
  • Ratios: Simplify 16:24 to 2:3
  • Probability: Chance = favorable/total
  • Math homework: Check fraction answers
Important: When working with fractions, always simplify to lowest terms for the clearest representation. For repeating decimals, use the bar notation or round to an appropriate number of decimal places based on your needs.

Fraction Conversion Tips & Tricks

Simplify Fractions

Find the Greatest Common Divisor (GCD) of numerator and denominator, then divide both by it. Example: 8/12 = (8÷4)/(12÷4) = 2/3.

Repeating Decimals

For repeating decimals like 0.333..., the fraction is 1/3. For 0.666..., it's 2/3. For 0.142857142857..., it's 1/7.

Quick Conversions

1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125, 1/10 = 0.1. Memorize these for faster calculations.