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

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

Solution:

(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.