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Question
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
0.00323232...
Solution
Let x = 0.00323232 ...(i)
On multiplying both sides of equation (i) by 100, we get
100x = 0.3232......... ...(ii)
On multiplying both sides of equation (ii) by 100, we get
10000x = 32.3232......... ...(iii)
On subtracting equation (ii) from equation (iii), we get
10000x – 100x = 32.32....... – 0.3232....
⇒ 9900x = 32
∴ `x = 32/9900 = 8/2475` ...[Dividing numerator and denominator by 4]
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