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Question
Show that 0.142857142857... = `1/7`
Solution
Let x = 0.142857142857 ...(i)
On multiplying both sides of equation (i) by 1000000, we get
1000000x = 142857.142857 ...(ii)
On subtracting equation (i) from equation (ii), we get
1000000x – x = (142857.142857...) – (0.142857...)
⇒ 999999x = 142857
∴ `x = 142857/999999 = 1/7`
Hence proved.
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