Decimal-Fraction Conversion Math Example 4

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

Example 4

hard
Convert 0.1250.125 to a fraction, then determine whether 18\frac{1}{8} and 0.1250.125 are equal by comparing their decimal equivalents.

Solution

  1. 1
    Write 0.125=12510000.125 = \frac{125}{1000}. Simplify: gcd⁡(125,1000)=125\gcd(125, 1000) = 125, so 1251000=18\frac{125}{1000} = \frac{1}{8}.
  2. 2
    Convert 18\frac{1}{8} to decimal: 1÷8=0.1251 \div 8 = 0.125.
  3. 3
    Both represent 0.1250.125, so 18=0.125\frac{1}{8} = 0.125 \checkmark

Answer

0.125=18 (they are equal)0.125 = \frac{1}{8} \text{ (they are equal)}
Converting both representations to the same form and comparing is the most reliable way to test equality of a fraction and a decimal. Simplifying 125/1000 by the GCD of 125 gives the clean fraction 1/8.

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 2 medium

Convert [formula] to a fraction in simplest form.

Example 3 easy

Convert [formula] to a decimal.

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