Question

Express 0.00323232.... in the form of p/q where p , q are integers and q ≠0 .

Answer 1

Let x = 0.00323232.......(i)


Multiply equation (i) by 100 on both sides,

100 x = 0.323232.......(ii)


Multiply equation (i) by 10,000 on both sides,

10,000 x = 32.323232.......(iii)

Subtracting equation (ii) from (iii),

10,000 x = 32.323232.......(iii)
-- 100 x = 0.323232.......(ii)
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9900 x = 32

Thus, x = $\frac{32}{\text{9900}}$

$⟹$ x = $\frac{8}{2475}$

Therefore, x = $\frac{8}{2475}$