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Convert fractions to terminating decimals

A fraction represents a terminating decimal when, after reduction to lowest terms, its denominator has no prime factors other than 2 and 5; factors of 2 and 5 can be paired or scaled to produce a denominator of 10, 100, 1,000, or another power of ten. The resulting decimal preserves the fraction’s value and place-value meaning, supporting comparison, computation, and connections among fractions, decimals, and percents. Repeating-decimal representations and more advanced proofs about decimal expansions are outside this scope.

Detailed Explanation: Convert fractions to terminating decimals

To convert a fraction to a terminating decimal:

  1. Reduce the fraction to lowest terms.
  2. Look at the denominator. If its only prime factors are 2 and/or 5, the fraction can be written as a terminating decimal.
  3. Multiply the numerator and denominator by the same number to make the denominator a power of 10, such as (10)(10), (100)(100), or (1,000)(1{,}000).
  4. Write the numerator as a decimal using the denominator’s place value.

Example: Convert 320\frac{3}{20} to a decimal

The fraction is already in lowest terms.

The denominator is (20)(20), and

20=2⋅2⋅5.20=2\cdot 2\cdot 5.

Its only prime factors are 22 and 55, so it will have a terminating decimal.

To change (20)(20) into (100)(100), multiply by 55:

320⋅55=15100.\frac{3}{20}\cdot\frac{5}{5}=\frac{15}{100}.

A denominator of (100)(100) means hundredths. Therefore,

15100=0.15.\frac{15}{100}=0.15.

So,

320=0.15.\boxed{\frac{3}{20}=0.15}.

The value stays the same because the numerator and denominator were multiplied by the same number.

Learn by doing: Convert fractions to terminating decimals

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    Fraction to Decimals - Standard

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