Question

Express $0.\overline{621}$ in the form of $\frac{p}{q}$.

• A. $\frac{7}{39}$
• B. $\frac{7}{11}$
• C. $\frac{21}{37}$
• D. $\frac{23}{37}$

Answer 1

The correct option is D $\frac{23}{37}$

$x=0.\overline{621}=\mathrm{0.621621621.....}10x=\mathrm{6.21621621......}100x=\mathrm{62.1621621.....}1000x=\mathrm{621.621621....}1000x=\mathrm{621.621621....}-x=\mathrm{0.621621621.....}999x=621.00000x=\frac{621}{999}=\frac{23}{37}$