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Question
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
0.404040...
Solution
Let x = 0.404040 ...(i)
On multiplying both sides of equation (i) by 100, we get
100x = 40.4040 ...(ii)
On subtracting equation (i) from equation (ii), we get
100x – x = 40.4040...... – 0.404040.....
⇒ 99x = 40
∴ `x = 40/99`
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