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

1.	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» (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.

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»

(C) 2

Explanation:

(A) 19/10 = 1.9

(B) 1999/1000= 1.999

(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.