SOLUTION: how do you write 0.8...repeating as a fraction or mixed number in simplest form?

Question 171842: how do you write 0.8...repeating as a fraction or mixed number in simplest form?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=0.8888...

Start with the given equation

Multiply both sides by 10. The goal is to move the decimal point to the next repeating portion (which is just one spot to the right)

Now subtract the equation from to get

Combine like terms. Notice how the decimal portions cancel out.

Divide both sides by 9 to isolate x

So the answer is which means that (where the 8's repeat)
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