Question

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) $2\frac{5}{12}$

Answer 1

(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) $\frac{11}{24}$
$\frac{11}{24}$ =
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$\frac{5}{12}$ = $\frac{29}{12}$ =
By actual division, we have:

It is non-terminating decimal expansion.