Question

The value of 1.999… in the form p/q, where p and q are integers and q ≠ 0 , is

(A) 19/10

(B) 1999/1000

(C) 2

(D) 1/9

Answer 1

(C) 2

Explanation:

(A) 19/10 = 1.9

(B) 1999/1000= 1.999

(C) 2

(D) 1/9= 0.111….

Let x = 1.9999….. — ( 1 )

Multiply equation ( 1 ) with 10

10x = 19.9999….. — ( 2 )

Subtract equation (1) from equation(2)

We get,

9x = 18

x = 18 / 9

x = 2

Therefore,

x = 1.9999… = 2

Hence, (C) is the correct option.