Question

Convert the repeating decimal to a/b form, where a,b are integers and b≠0

Answer 1

Love this question, wonder why it's not taught in most schools.

Answer 2

There is a general way of doing this. Let's try to convert 0.898989... to the rational form (the correct term for a/b).
Firstly, we will assume that x is the number with recurring digits, that's 0.898989... in this case. Since the repeating part is the part we need to get rid of, we multiply x by the number of digits the repeating bit has (in this case, 2). Hence we yield 100x = 89.898989 (notice that the recurring digits are still there)
Now we subtract x from 100x, getting 99x = 89. (What happened during this process is that the recurring part was cancelled out from the subtraction)
Now do simple algebra and you get x = 89/99. Make sure at the end you mention the relation between 0.898989... and 89/99, for clarity.

Answer 3

Oh, I am sorry I forgot to give you the rest of the problem, here it goes;Convert the repeating decimal to a/b form, where a,b are integers and b≠0

Answer 4

Use what tyteen4a03 suggested: