Question

Express $3.12\overline{7}$ in the $\frac{p}{q}$ form.

Answer 1

Let $x=3.12\overline{7}=3.12777$....................................(1)

Multiply (1) by 100 we get

$100x=312.777$......................................................(2)

Multiply (1) by 1000 we get

$1000x=3127.777$..........................................................(3)

Substruct (3) by (2) we get

$900x=2815$

$x=\frac{2815}{900}=\frac{563}{180}$

Hence $x=3.12\overline{7}=\frac{563}{180}$