# The value of 1.999... in the form p/q, where p and q are integers and q ≠ 0 , is ______. - Mathematics

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

#### Options

• 19/10

• 1999/1000

• 2

• 1/9

#### Solution

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

Explanation:

Let x = 1.999...

Now, 10x = 19.999...

On subtracting equation (i) from equation (ii), we get

10x - x = (19.999...) - (1.9999...)

⇒ 9x = 18

∴ x = 18/9 = 2

Concept: Real Numbers and Their Decimal Expansions
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#### APPEARS IN

NCERT Mathematics Exemplar Class 9
Chapter 1 Number Systems
Exercise 1.1 | Q 9 | Page 4

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