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Question
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... (i)
Multiply (i) by 10, we get
10x = 19.999... (ii)
On subtracting (i) from (ii), we get
10x – x = (19.999...) – (1.9999...)
⇒ 9x = 18
∴ x = 2
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