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Question

Express the following in the form pq, where p and q are integers and q0
(i) 0.00323232...
(ii) 0.404040…

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Solution

(i) Let x = 0.00323232...
On multiplying the above equation by 100 we get
100x = 0.3232...
On multiplying the above equation by 100 we get
10000x = 32.3232...
10000x – 100x = (32.32...) - (0.3232…)
9900x=32
x=329900=82475 [ Dividing numerator and denominator by 4]

(ii) Let x=0.404040...
On Multiplying the above equation by 100, we get
100x=40.4040...
100x-x=(40.4040...) - (0.404040...)
99x=40
x=4099

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