Will that always work? Do you basically just take the original repeating number s, multiply it by 100, subtract s from it to make it 99s and then divide by 99?
Also, the number was 10.9090909091, the 1 at the end is throwing me off, because I don't know if that trick still applies or not.
The trick is to count how many repeating decimals you have,
For instance in
Muliply both sides of this equation by , where n is the number of digits in the repeating string. Here, the single digit 4 repeats infinitely, so n = 1
Subtract the original equation (x=0.9444444...) from the modified equation (10x = 9.444444...) which equals
Ok, that makes sense. But what about the number in my problem, I am confused by the way its written.
10.9090909091... I don't know what is repeated. Is it the 1? Is is the whole thing? The problem is that there is no teacher or anything to help me clarify that problem.
So I will have to do it multiple times until the computer accepts the answer.
So would I take 10.9090909091 and multiply it by what? By 1? Or by 10?
Express as a rational number, in the form
where and are positive integers with no common factors.
This is how the problem is written out on webwork (I despise webwork, I wish our school would stop using it). I tried using 1080 and 99 but those didn't work.
10 + 0.909090909 + 0.0000000001111........ (I assume)
Obviously 0.909090909 = 909090909/1000000000
Let S = 0.00000000011111.....
Then 1000000000S = 0.1111111 and 10000000000S = 1.1111111
Therefore 9000000000S = 1 => S = 1/9000000000.
So your number is 10 + (909090909/1000000000) + (1/9000000000).
Now add the fractions in the usual way to get the required representation.