Decimal to Fraction Calculator

Convert decimals to fractions

For 0.333... enter 1

About Converting Decimals to Fractions

Converting decimals to fractions is a fundamental math skill that helps you work with numbers in different forms.

Every decimal can be expressed as a fraction. Terminating decimals (like 0.75) convert easily, while repeating decimals (like 0.333...) require a special algebraic method.

Understanding this conversion helps with cooking measurements, construction work, and mathematical calculations.

Types of Decimals

• Terminating: Decimals that end (0.75, 2.625)

• Repeating: Decimals with repeating patterns (0.333..., 0.142857...)

• Non-repeating: Irrational numbers (π, √2)

How to Convert Decimals to Fractions

For Terminating Decimals

  1. Write the decimal divided by 1 - Place the decimal over 1
  2. Multiply to remove decimal point - Multiply both top and bottom by 10, 100, 1000, etc.
  3. Find the GCD - Find the greatest common divisor of numerator and denominator
  4. Simplify the fraction - Divide both by the GCD
  5. Convert to mixed number if needed - If improper, convert to mixed number

For Repeating Decimals

  1. Let x equal the decimal - x = 0.333...
  2. Multiply by power of 10 - 10x = 3.333...
  3. Subtract the equations - 10x - x = 3.333... - 0.333...
  4. Solve for x - 9x = 3, so x = 3/9 = 1/3

Example 1: 0.75

Step 1: 0.75/1

Step 2: (0.75 × 100)/(1 × 100) = 75/100

Step 3: GCD(75, 100) = 25

Step 4: 75÷25 / 100÷25 = 3/4

Result: 3/4

Example 2: 2.625

Step 1: 2.625/1

Step 2: 2625/1000

Step 3: GCD(2625, 1000) = 125

Step 4: 2625÷125 / 1000÷125 = 21/8

Step 5: 21/8 = 2 5/8

Result: 2 5/8

Common Decimal to Fraction Conversions

DecimalFractionType
0.51/2Terminating
0.251/4Terminating
0.753/4Terminating
0.333...1/3Repeating
0.666...2/3Repeating
0.1251/8Terminating
0.21/5Terminating
0.1666...1/6Repeating

Real-World Applications

Cooking & Recipes

Convert decimal measurements to fractions for easier measuring with cups and spoons (e.g., 0.375 cups = 3/8 cup).

Construction & Carpentry

Convert decimal inch measurements to fractional inches for precise cuts and measurements (e.g., 2.625" = 2 5/8").

Finance & Accounting

Express decimal percentages as fractions for easier calculations and understanding of proportions.

Tips for Success

Remember These Patterns:

  • • 0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000
  • • Count decimal places to find denominator power of 10
  • • Always simplify to lowest terms
  • • Repeating decimals often have 3, 6, 9, or 11 in denominator

Common Mistakes to Avoid:

  • • Forgetting to simplify the fraction
  • • Not recognizing repeating patterns
  • • Miscounting decimal places
  • • Confusing terminating with repeating decimals