Terminating and recurring decimals

Computing with decimals, converting fractions to terminating or recurring decimals, recurring decimal notation, and rounding.

Two kinds of decimal

A terminating decimal stops: $\tfrac{3}{8} = 0.375$. A recurring decimal repeats forever: $\tfrac{5}{11} = 0.454545\ldots = 0.\overline{45}$.

Example 1●●

Write $\tfrac{5}{6}$ as a decimal.

$5 \div 6 = 0.8333\ldots$

$= 0.8\dot{3}$ (only the $3$ repeats).

Example 2●

Find $3.2 \times 0.15$ and $4.68 \div 0.12$.

$32 \times 15 = 480$; three decimal places gives $0.480 = 0.48$.

$4.68 \div 0.12 = 468 \div 12 = 39$.

Flashcards

Terminating test

Denominator's prime factors are only 2s and 5s.

$ frac{1}{3}$

$0.\dot{3}$

$ frac{2}{11}$

$0.\overline{18}$

Practice