Decimal Representation Math Example 3

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

easy

Write each fraction as a decimal and classify as terminating or repeating: (a)

\dfrac{3}{4}

, (b)

\dfrac{2}{9}

1
(a) $\dfrac{3}{4} = 3 \div 4 = 0.75$ . Denominator $= 2^2$ , only factor $2$ , so it terminates.
2
(b) $\dfrac{2}{9} = 2 \div 9 = 0.222\ldots = 0.\overline{2}$ . Denominator $= 3^2$ , factor $3 \neq 2,5$ , so it repeats.

Answer

(a)

0.75

(terminating); (b)

0.\overline{2}

(repeating)

A fraction terminates as a decimal exactly when its denominator (in lowest terms) has only

2

s and

5

s as prime factors. Any other prime factor in the denominator causes the decimal to repeat.

About Decimal Representation

Writing fractions as digits to the right of a decimal point, using place values of tenths, hundredths, thousandths, etc.

Convert [formula] to a decimal by long division, and determine whether it terminates or repeats.

Convert [formula] to a fraction in simplest form.

Convert [formula] to a fraction in simplest form. (Note: only the [formula] repeats.)