Question

Prove algebraically that the recurring decimal 0.472 can be written as 17 36

Answer 1

Given:

The recurring decimal is $0.47\overline{2}$.

To prove:

Algebraically that the recurring decimal $0.47\overline{2}$ can be written as $\dfrac{17}{36}$.

Proof:

Let,

$x=0.47\overline{2}$

$x=0.472222...$

Multiply both sides by 100.

$100x=47.2222...$     ...(i)

Multiply both sides by 10.

$1000x=472.2222...$        ...(ii)

Subtract (i) from (ii).

$1000x-100x=472.2222...-47.2222...$

$900x=425$

Divide both sides by 900.

$x=\dfrac{425}{900}$

$x=\dfrac{17}{36}$

So, $0.47\overline{2}=\dfrac{17}{36}$.

Hence proved.