Write each of the following in decimal form and say what kind of decimal expansion each has.
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.