Question

Prove algebraically that the recurring decimal 0.72 (both recurring) =8/11.

Write your proof in the box, below, and use x in the working.

The concluding line has been written for you, 'Therefore x=8/11'.

Answer 1

Given:

$0.\overline{72} = \dfrac{8}{11}$

To Find:

$\text{Prove it}$

$\boxed {\textbf{Solution}}$

Define x:

$\text{Let } x = 0.\overline {72}$

FInd 100x:

$x = 0.\overline{72}$

$100x = 0.\overline{72} \times 100$

$100x = 72.\overline{72}$

Find 99x:

$100x - x = 72.\overline{72} - 0.\overline{72}$

$99x = 72$

$x = \dfrac{72}{99}$

$x = \dfrac{8}{11}$

$\emph {\boxed{\boxed{\textbf{Answer = } \frac{8}{11} }}}$