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

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=9.77777...

x=9.7777 Start with the given equation


10x=97.7777 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.


10x-x=97.7777-x Now subtract "x" from both sides (since we did this to both sides, this does NOT change the equation)


10x-x=97.7777-9.7777 Plug in x=9.7777 (the original equation) on the right side


9x=88 Subtract. Notice how decimal portion of the numbers go away.


x=88%2F9 Divide both sides by 9 to isolate "x"


So the answer is x=88%2F9 which means that 88%2F9=9.77777 (where the 7's repeat)