Express the recurring decimal 0.125125125 … as a rational number.
Let,
x = 0.125125125 ….equation 1
As 125 is the repeating term, so in all such problems multiply both sides of the equation with a number such that complete repetitive part of number comes after the decimal.
∴ multiplying equation 1 with 1000 in both sides, we have –
1000x = 125.125125125… …equation 2
Subtracting equation 1 from equation 2,we get-
1000x – x = 125.125125125… - 0.125125125….
⇒ 999x = 125
∴ x = 125/999