Math 8 min read

How to Convert Decimals to Fractions (Step-by-Step)

Learn the exact steps to convert any decimal to a fraction, including repeating decimals. Includes common conversions and worked examples.

The Quick Answer

To convert a decimal to a fraction:

  1. Write the decimal as a fraction over 1
  2. Multiply top and bottom by 10 for each decimal place
  3. Simplify by finding the greatest common divisor (GCD)

Example: 0.75 → 75/100 → 3/4

Step-by-Step Method

Step 1: Count Decimal Places

Look at how many digits appear after the decimal point.

  • 0.5 has 1 decimal place
  • 0.75 has 2 decimal places
  • 0.125 has 3 decimal places

Step 2: Write as a Fraction

Remove the decimal point and place the number over a power of 10:

  • 1 decimal place → divide by 10
  • 2 decimal places → divide by 100
  • 3 decimal places → divide by 1,000
Decimal Remove Decimal Denominator Fraction
0.5 5 10 5/10
0.75 75 100 75/100
0.125 125 1,000 125/1000

Step 3: Simplify the Fraction

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it.

Example: Simplify 75/100

  • Factors of 75: 1, 3, 5, 15, 25, 75
  • Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
  • GCD = 25

75 ÷ 25 = 3
100 ÷ 25 = 4

Result: 75/100 = 3/4

Worked Examples

Example 1: Convert 0.6 to a Fraction

  1. One decimal place → denominator is 10
  2. 0.6 = 6/10
  3. GCD of 6 and 10 is 2
  4. 6/10 = 3/5

Example 2: Convert 0.375 to a Fraction

  1. Three decimal places → denominator is 1,000
  2. 0.375 = 375/1000
  3. GCD of 375 and 1,000 is 125
  4. 375/1000 = 3/8

Example 3: Convert 2.25 to a Fraction

For decimals greater than 1, convert the decimal part and add the whole number:

  1. Whole number: 2
  2. Decimal part: 0.25 = 25/100 = 1/4
  3. Combined: 2 + 1/4 = 2 1/4 (mixed number) or 9/4 (improper fraction)

Common Decimal-to-Fraction Conversions

Memorizing these saves time:

Decimal Fraction Decimal Fraction
0.5 1/2 0.1 1/10
0.25 1/4 0.2 1/5
0.75 3/4 0.4 2/5
0.125 1/8 0.6 3/5
0.375 3/8 0.8 4/5
0.625 5/8 0.333... 1/3
0.875 7/8 0.666... 2/3

Converting Repeating Decimals

Repeating decimals (like 0.333... or 0.142857142857...) require a different approach.

Method for Repeating Decimals

Example: Convert 0.333... to a fraction

  1. Let x = 0.333...
  2. Multiply by 10: 10x = 3.333...
  3. Subtract: 10x - x = 3.333... - 0.333...
  4. Simplify: 9x = 3
  5. Solve: x = 3/9 = 1/3

Example: Convert 0.272727... to a fraction

  1. Let x = 0.272727...
  2. Two repeating digits, so multiply by 100: 100x = 27.272727...
  3. Subtract: 100x - x = 27.272727... - 0.272727...
  4. Simplify: 99x = 27
  5. Solve: x = 27/99 = 3/11

Quick Reference: Common Repeating Decimals

Decimal Fraction
0.333... 1/3
0.666... 2/3
0.111... 1/9
0.142857... 1/7
0.0909... 1/11
0.1666... 1/6
0.8333... 5/6

Converting Fractions Back to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator:

  • 3/4 = 3 ÷ 4 = 0.75
  • 1/3 = 1 ÷ 3 = 0.333...
  • 7/8 = 7 ÷ 8 = 0.875

Tip: If the denominator only has factors of 2 and 5, the decimal will terminate. Otherwise, it will repeat.

Practical Applications

Cooking and Recipes

Recipes often use fractions (1/2 cup, 3/4 teaspoon), but digital scales show decimals. Knowing that 0.5 cups = 1/2 cup helps you measure accurately.

Construction and Woodworking

Tape measures use fractions (inches divided into 1/8, 1/16, 1/32). Converting measurements like 0.375 inches to 3/8 inches ensures precision.

Finance

Interest rates, discounts, and percentages often need conversion. A 0.25% fee is the same as 1/400 of the total.

Education

Understanding the relationship between decimals and fractions builds number sense and helps with mental math.

Frequently Asked Questions

What is 0.75 as a fraction?

0.75 = 75/100 = 3/4 after simplifying by dividing both by 25.

What is 0.5 as a fraction?

0.5 = 5/10 = 1/2 after simplifying by dividing both by 5.

What is 0.125 as a fraction?

0.125 = 125/1000 = 1/8 after simplifying by dividing both by 125.

What is 0.333 as a fraction?

0.333 (if it terminates) = 333/1000. However, 0.333... (repeating) = 1/3.

How do I know if a decimal will repeat?

A fraction in lowest terms produces a terminating decimal only if the denominator has no prime factors other than 2 and 5. Otherwise, it repeats.

  • 1/4 = 0.25 (terminates — denominator is 4 = 2²)
  • 1/3 = 0.333... (repeats — denominator is 3)
  • 1/6 = 0.1666... (repeats — denominator is 6 = 2 × 3)

What is the difference between 0.3 and 0.333...?

  • 0.3 = 3/10 (exactly three tenths)
  • 0.333... = 1/3 (one third, which cannot be written as a terminating decimal)

Can all decimals be written as fractions?

All terminating and repeating decimals can be written as fractions (rational numbers). Non-repeating, non-terminating decimals like π (3.14159...) and √2 (1.41421...) cannot—they are irrational numbers.

Try It Yourself

Decimal to Fraction Converter

Convert any decimal to a simplified fraction instantly. Also converts fractions to decimals and shows percentages.

Open Converter

Summary

Conversion Type Method
Terminating decimal Write over power of 10, simplify
Repeating decimal Use algebra (let x = decimal, multiply, subtract)
Mixed number Convert decimal part, add whole number
Fraction to decimal Divide numerator by denominator

With practice, common conversions become automatic. For everything else, use the converter above.

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