Question 171842
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=8/9}}} Divide both sides by 9 to isolate x



So the answer is {{{x=8/9}}} which means that {{{8/9=0.8888}}} (where the 8's repeat)