Question

show that 0.14285742857...= 1/7

Answer 1

LHS = 0.142857142857...........
You see that , 142857 term is repeating infinite times .
so, you can write 0.142857142857...... = $\bold{0.\overline{142857}}$
$\bold{0.\overline{142857}}$ means to say 142857/999999
Hence, 0.142857142857..... = 142857/999999
when you divide by 142857 from 999999 , you get 7
I mean , 142857 × 7 = 999999

∴ 142857/7 × 142857 = 1/7 = RHS

Hence, 0.142857142857...... = 1/7