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Question
Express the following in the form `p/q`, where p and q are integers and q ≠ 0:
`0.1bar34`
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Solution
Let `x = 0.1bar34`
⇒ `x = 0.bar134 = 0.13434`......... ...(i)
On multiplying both sides of equation (i) by 10, we get
10x = 1.3434......... ...(ii)
On multiplying both sides of equation (ii) by 100, we get
1000x = 134.3434........ ...(iii)
On subtracting equation (ii) from equation (iii), we get
1000x – 10x = 134.34... – (1.3434...)
⇒ 990x = 133
∴ `x = 133/990`
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