Write each of the following in decimal form and say what kind of decimal expansion each has.
(i) $\frac{5}{8}$
(ii) $\frac{7}{25}$
(iii) $\frac{3}{11}$
(iv) $\frac{5}{13}$
(v) $\frac{11}{24}$
(vi) $\frac{261}{400}$
(vii) $\frac{231}{625}$
(viii) $2 \frac{5}{12}$
(i) $\frac{5}{8}=0.625$
By actual division, we have
It is a terminating decimal expansion.
(ii) $\frac{7}{25}$
$\frac{7}{25}=0.28$
By actual division, we have:
It is a terminating decimal expansion.
(iii) $\frac{3}{11}=0 . \overline{27}$
It is a non-terminating recurring decimal.
(iv) $\frac{5}{13}=0 . \overline{384615}$
It is a non-terminating recurring decimal.
(v) $\frac{11}{24}$
$\frac{11}{24}=0.458 \overline{3}$
By actual division, we have:
It is nonterminating recurring decimal expansion.
(vi) $\frac{261}{400}=0.6525$
It is a terminating decimal expansion.
(vii) $\frac{231}{625}=0.3696$
It is a terminating decimal expansion.
(viii) $2 \frac{5}{12}$
$2 \frac{5}{12}=\frac{29}{12}=2.41 \overline{6}$
By actual division, we have:
It is non-terminating decimal expansion.