Question:
Show that $0.142857142857 \ldots=1 / 7 .$
Solution:
Let x = 0.142857142857 …………………..(i)
On multiplying both sides of Eq. (i) by 1000000, we get
1000000 x = 142857.142857…………………………(ii)
On subtracting Eq. (i) from Eq. (ii), we get
1000000 x – x = (142857.142857…) – (0.142857..) => 999999 x = 142857
∴ x = 142857/999999 = 1/7 Hence proved.