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

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Question 171842: how do you write 0.8...repeating as a fraction or mixed number in simplest form?
Answer by jim_thompson5910(21684) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=0.8888...


x=0.8888 Start with the given equation


10x=8.8888 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 x=0.8888 from 10x=8.8888 to get

10x-x=8.8888-0.8888


9x=8 Combine like terms. Notice how the decimal portions cancel out.


x=8%2F9 Divide both sides by 9 to isolate x


So the answer is x=8%2F9 which means that 8%2F9=0.8888 (where the 8's repeat)