​ The fractional value of 2.\bar 357 is A. 2355/1001 B. 2379/997 C. 2355/999 D. none of these ​

Question

The fractional value of \(2.\overline{357}\) is

A. 2355/1001

B. 2379/997

C. 2355/999

D. none of these

Answer 1

Let, x = \(2.\overline{357}\)

= 2.357357…… …(1)

Multiply by 1000 both sides

1000x = 2357.357357…… …(2)

Subtracting eq.(1) from eq.(2)

1000x – x = 2357.357357… - 2.357357…

999x = 2355

x = 2355/999

The fractional value of \(2.\overline{357}\) is 2355/999