Example 1 · Make the denominator 100
- Start with 34.
- Multiply the numerator and denominator by 25: 3/4 = 75/100.
- 75 hundredths is 0.75. This decimal terminates (ends).
Mathematics · Decimals · Topic 8 · 1 of 5
Fractions as Decimals
Convert fractions and recognize terminating and repeating decimals.
Two ways to write a fraction as a decimal
A fraction means division: the numerator is divided by the denominator. A decimal shows the same amount using place value.
Example 2 · Divide when you cannot easily make a power of 10
For 5/8, calculate 5.000 ÷ 8.
- 50 tenths ÷ 8 gives 6 tenths, with 2 tenths left.
- Bring down 0: 20 hundredths ÷ 8 gives 2 hundredths, with 4 left.
- Bring down 0: 40 thousandths ÷ 8 gives 5 thousandths.
So 5/8 = 0.625. Check: 0.625 × 8 = 5.
Example 3 · A repeating remainder
5 ÷ 6 = 0.8333… . After the first decimal digit, the same remainder keeps returning. Only the 3 repeats.
5/6 = 0.83. Type 0.8(3) in the exercises. For 2/11, type 0.(18), meaning 0.181818… .
Remember: Terminating decimals end. Repeating decimals continue forever with a repeating block. Every fraction with a nonzero whole-number denominator has a decimal that either terminates or repeats. A repeating decimal is one kind of nonterminating decimal.
Try explaining it
Why are 0.5 and 0.50 equal? Why is 0.33 only an approximation to 1/3?