SOLUTION: _ Express the (repeating) decimal 1.9 as a quotient of two integers. *NOTE it has to be set up something like t

Question 391682: _
Express the (repeating) decimal 1.9 as a quotient of two integers. *NOTE it has to be set up something like this:
_
n = 1.9
the answer is the fraction (2/1) but I do not know how this is. Please Help
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The number you're referring to is 1.99999....there are probably a dozen ways to prove this is equal to 2.

We could consider the infinite series + ...If you know that the sum of the terms of a convergent geometric sequence is we can replace a = 9, and r = 10 to get 9/9 or 1. Finally, add 1 (since the number is 1.9999 instead of .9999) to get 2.

Another possible way works like this:

1/9 = .11111....
9/9 = 9(.11111....) = .99999....

However 9/9 = 1 so .99999.... = 1, and 1.99999.... = 2 = 2/1.
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