Question

Convert the following repeating decimal to a/b form where a and b are integers and b does not = 0

4.344444......

Answer 1

Example:
5.35555555555555................
=5+.355555555555555555555555555

Let x=.355555555........................
Now do 10x which is 10(.355555555555555...............)
I chose to multiply by 10 because after that that is where the repeating began
10x=3.5555555555555555555555555555

And do 10x-x=3.5555555555555555555555555....-.35555555555555555555....
9x=3.55-.35
9x=3.2
x=3.2/9
But you want an integer over an integer
So you need to multiply top and bottom by 10 like this:
x=3.2(10)/[9(10)]
x=32/90

Now recall we have 5.355555555555555............
=5+.35555555555555555555555
So we have
=5+32/90

You can combine the fractions by finding a common denominator

Answer 2

Let's look at yours when you have read through that example.