Decimal-Fraction Conversion Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Convert 0.360.36 to a fraction in simplest form.

Solution

  1. 1
    Write using place value: 0.36=361000.36 = \frac{36}{100} (hundredths place).
  2. 2
    Simplify: gcd⁡(36,100)=4\gcd(36, 100) = 4, so 36100=925\frac{36}{100} = \frac{9}{25}.
  3. 3
    Check: 9÷25=0.369 \div 25 = 0.36 \checkmark

Answer

925\frac{9}{25}
A terminating decimal with nn decimal places can be written as a fraction over 10n10^n. Then simplify using the GCD. The check by dividing confirms the conversion is correct.

About Decimal-Fraction Conversion

Converting between fraction form and decimal form of a number: divide numerator by denominator for fraction-to-decimal, and use place value to go the other way.

Learn more about Decimal-Fraction Conversion →

More Decimal-Fraction Conversion Examples

Example 1 easy

Convert [formula] to a decimal.

Example 3 easy

Convert [formula] to a decimal.

Example 4 hard

Convert [formula] to a fraction, then determine whether [formula] and [formula] are equal by compari

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