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Alecsey [184]
3 years ago
8

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

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
8 0

1.999… is exactly the number 2.

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

1000<em>x</em> - <em>x</em> = 1999.999… - 1.999…

1000<em>x</em> - <em>x</em> = 1999 - 1

999<em>x</em> = 1998

<em>x</em> = 1998/999 = 2/1 = 2

So <em>p</em> = 2 and <em>q</em> = 1.

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