SOLUTION: I arrived at a problem on my math homework on rational numbers that looked like this: (9.7...repeated.) I followed the steps that a previous tutor gave me, and i have been doing fi

Question 171887: I arrived at a problem on my math homework on rational numbers that looked like this: (9.7...repeated.) I followed the steps that a previous tutor gave me, and i have been doing fine. I did N=9.7... and thenmultiplied each side by 10 and got 9N=?. 9.7x10=? I do not understand this concept whatsoever, please explain.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=9.77777...

Start with the given equation

Multiply both sides by 10. Notice how when we move the decimal one spot, the numbers after the decimal are EXACTLY the same as the numbers after the decimal above.

Why is this important? When we go to subtract 9.7777 from 97.7777, the numbers must match in order to completely cancel out the decimal portion.

Now subtract "x" from both sides (since we did this to both sides, this does NOT change the equation)

Plug in (the original equation) on the right side

Subtract. Notice how decimal portion of the numbers go away.

Divide both sides by 9 to isolate "x"

So the answer is which means that (where the 7's repeat)
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