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

Solution:

Let us simplify each option

a. 19/10 = 1.9

b. 1999/1000 = 1.999

c. 2

d. 1/9 = 0.111….

Consider x = 1.999 …. (1)

Let us multiply equation (1) with 10

10x = 19.99 …. (2)

Subtracting equation (1) from (2)

9x = 18

Dividing both sides by 9

x = 2

Therefore, the value of 1.999... is 2.

✦ Try This: The value of 1.666... in the form p/q, where p and q are integers and q ≠ 0 , is a. 16/10, b. 1666/1000, c. 2, d. 1/6

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 9

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

Summary:

The value of 1.999... in the form p/q, where p and q are integers and q ≠ 0 , is 2

☛ Related Questions:

• 2√3 + √3 is equal to a. 2√6, b. 6, c. 3√3, d. 4√6
• √10 x √15 is equal to a. 6√5, b. 5√6, c. √25, d.10√5
• The number obtained on rationalising the denominator of 1/(√7 - 2) is a. (√7 + 2)/3, b. (√7 - 2)/3, . . . .