parthsarthi748 parthsarthi748

04-03-2021
Mathematics

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Find the value of 1.999.... in the form of p
q
where p and q are integers.

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LammettHash LammettHash

04-03-2021

1.999… is exactly the number 2.

Let x = 1.999… . Then 1000x = 1999.999… . Subtract x from this to eliminate the fractional part, and you get

1000x - x = 1999.999… - 1.999…

1000x - x = 1999 - 1

999x = 1998

x = 1998/999 = 2/1 = 2

So p = 2 and q = 1.

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