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How to Turn Decimal Into Fraction Without A Calculator

Reviewed by Calculator Editorial Team

Converting decimals to fractions is a fundamental math skill that's useful in many areas of life. Whether you're working with measurements, ratios, or financial calculations, knowing how to convert decimals to fractions without a calculator can save you time and help you understand mathematical concepts better.

Method to Convert Decimal to Fraction

Converting a decimal to a fraction involves a few simple steps. Here's the process:

  1. Write down the decimal as a fraction with a denominator of 1 (e.g., 0.75 becomes 75/100).
  2. Multiply both the numerator and denominator by 10 for each digit after the decimal point (e.g., 0.75 has two digits after the decimal, so multiply by 100).
  3. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Formula: For a decimal number with n digits after the decimal point, the fraction is (decimal × 10ⁿ)/10ⁿ.

Let's walk through an example to make this clearer.

Worked Examples

Example 1: Converting 0.5 to a Fraction

  1. Write 0.5 as 5/10.
  2. Notice there are one digit after the decimal, so multiply by 10: (5 × 10)/(10 × 10) = 50/100.
  3. Simplify by dividing numerator and denominator by 50: 50 ÷ 50 = 1, 100 ÷ 50 = 2.
  4. Final fraction: 1/2.

Example 2: Converting 0.75 to a Fraction

  1. Write 0.75 as 75/100.
  2. There are two digits after the decimal, so multiply by 100: (75 × 100)/(100 × 100) = 7500/10000.
  3. Simplify by dividing numerator and denominator by 25: 7500 ÷ 25 = 300, 10000 ÷ 25 = 400.
  4. Final fraction: 3/4.

Tip: Remember that 0.5 is equivalent to 1/2, 0.25 is 1/4, and 0.75 is 3/4. These are common fractions you should memorize for quick reference.

How to Simplify Fractions

After converting a decimal to a fraction, you'll often need to simplify it. Here's how to do it:

  1. Find the greatest common divisor (GCD) of the numerator and denominator.
  2. Divide both the numerator and denominator by the GCD.
  3. The result is the simplified fraction.

For example, to simplify 8/16:

  1. The GCD of 8 and 16 is 8.
  2. Divide numerator and denominator by 8: 8 ÷ 8 = 1, 16 ÷ 8 = 2.
  3. Simplified fraction: 1/2.

If the numerator and denominator have no common divisors other than 1, the fraction is already in its simplest form.

Common Decimal-Fraction Conversions

Here's a table of common decimal to fraction conversions that you might find useful:

Decimal Fraction Simplified Fraction
0.1 1/10 1/10
0.2 2/10 1/5
0.25 25/100 1/4
0.333... 333/1000 1/3
0.5 5/10 1/2
0.666... 666/1000 2/3
0.75 75/100 3/4
0.9 9/10 9/10

FAQ

Can I convert any decimal to a fraction?
Yes, any decimal number can be converted to a fraction, whether it's terminating (like 0.5) or repeating (like 0.333...).
What if the decimal has more than two digits after the decimal point?
For decimals with more than two digits, simply multiply numerator and denominator by 10 for each digit after the decimal point. For example, 0.125 becomes 125/1000, which simplifies to 1/8.
How do I know if a fraction is simplified?
A fraction is simplified when the numerator and denominator have no common divisors other than 1. You can check this by finding the GCD of the numerator and denominator.
Can I convert a fraction back to a decimal?
Yes, you can convert a fraction back to a decimal by dividing the numerator by the denominator. For example, 3/4 becomes 0.75 when converted to a decimal.
Why is it important to simplify fractions?
Simplifying fractions makes them easier to work with in calculations and helps you understand the relationship between the numerator and denominator more clearly.