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How to Make A Fraction A Decimal Without A Calculator

Reviewed by Calculator Editorial Team

Converting fractions to decimals is a fundamental math skill that's useful in many real-world situations. While calculators make this easy, knowing how to do it manually can help you understand numbers better and verify calculator results. This guide explains three reliable methods to convert fractions to decimals without a calculator.

Method 1: Long Division

The most straightforward method is using long division. Here's how to do it:

  1. Write the fraction as a division problem (numerator ÷ denominator).
  2. Divide the numerator by the denominator.
  3. If there's a remainder, add a decimal point and zeros to the numerator.
  4. Continue dividing until you either get a zero remainder or the decimal repeats.

Example: Convert 3/4 to a decimal using long division.

  1. 3 ÷ 4 = 0 with a remainder of 3.
  2. Add a decimal point and make the remainder 30.
  3. 30 ÷ 4 = 7 with a remainder of 2.
  4. Add another zero to make it 20.
  5. 20 ÷ 4 = 5 with no remainder.

The result is 0.75.

This method works for all fractions, including those that terminate (end) and those that repeat.

Method 2: Equivalent Fractions

This method works well for fractions with denominators that are factors of 10, 100, 1000, etc.

  1. Find an equivalent fraction with a denominator of 10, 100, or 1000.
  2. Multiply both the numerator and denominator by the same number to get the equivalent fraction.
  3. Write the numerator as a decimal by adding the appropriate number of zeros.

Example: Convert 1/8 to a decimal using equivalent fractions.

  1. Find an equivalent fraction with denominator 100 (since 8 × 12.5 = 100).
  2. Multiply numerator and denominator by 12.5: (1 × 12.5)/(8 × 12.5) = 12.5/100.
  3. Write 12.5/100 as 0.125.

This method is quick for simple fractions but may require more complex multiplication for less common denominators.

Method 3: Fraction to Decimal Conversion Chart

For common fractions, you can use a conversion chart to find the decimal equivalent quickly.

Common fraction-decimal equivalents:

  • 1/2 = 0.5
  • 1/3 ≈ 0.333...
  • 1/4 = 0.25
  • 1/5 = 0.2
  • 1/8 = 0.125
  • 1/10 = 0.1
  • 2/3 ≈ 0.666...
  • 3/4 = 0.75
  • 3/5 = 0.6
  • 3/8 = 0.375

For less common fractions, you can create your own chart by converting fractions to decimals using one of the other methods.

Worked Examples

Example 1: 5/8

Using long division:

  1. 5 ÷ 8 = 0 with remainder 5.
  2. Add decimal point: 50 ÷ 8 = 6 with remainder 2.
  3. Add another zero: 20 ÷ 8 = 2 with remainder 4.
  4. Add another zero: 40 ÷ 8 = 5 with no remainder.

Result: 0.625

Example 2: 7/16

Using equivalent fractions:

  1. Find equivalent fraction with denominator 100: 7 × 14.2857 ≈ 100.
  2. Multiply numerator and denominator by 14.2857: (7 × 14.2857)/(16 × 14.2857) ≈ 100/16.
  3. Write as decimal: 0.625.

Result: 0.4375

Frequently Asked Questions

How do I know when a fraction will terminate or repeat as a decimal?

A fraction will terminate (end) as a decimal if the denominator has no prime factors other than 2 or 5. If the denominator has other prime factors, the decimal will repeat.

What if I get a repeating decimal?

For repeating decimals, you can write them with a bar over the repeating digits (e.g., 1/3 = 0.333... or 0.3). Some repeating decimals can be expressed as fractions with denominators that are products of 2 and 5.

Can I use these methods for mixed numbers?

Yes, first convert the mixed number to an improper fraction, then use one of the methods above.