Question

Express each of the following decimals in the form $\frac{p}{q}:$
(i) $0.\overline{4}$

(ii) $0.\overline{37}$

(iii) $0.\overline{54}$

(iv) $0.\overline{621}$

(v) $125.\overline{3}$

(vi) $4.\overline{7}$

(vii) $0.\overline{47}$

Answer 1

(i) Let

Hence,

(ii) Let

Hence,

(iii) Let

Hence,

(iv) Let

Hence,

(v) Let

Hence,

(vi) Let

Let

Therefore,

Hence,

(vii) Let

Since,

Therefore,

Hence,