SOLUTION: What is 5.246246 as a fraction?? How did you convert this to a fraction? Thank you for your time!

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: What is 5.246246 as a fraction?? How did you convert this to a fraction? Thank you for your time!      Log On


   

Question 319167: What is 5.246246 as a fraction?? How did you convert this to a fraction? Thank you for your time!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the number is 5.246246246... where the '246' repeats forever.


Let x=5.246246246. Now multiply both sides by 1000 to get 1000x=5246.246246246. Why 1000? I wanted to move the decimal point to the next start of the block 246


Now subtract 'x' from 1000x to get 1000x-x=5246.246246246-5.246246246=5241


Note: notice how the decimal parts match perfectly and they subtract and cancel out completely.


So we now know that 1000x-x=5241


1000x-x=5241 Start with the given equation.


999x=5241 Combine like terms on the left side.


x=%285241%29%2F%28999%29 Divide both sides by 999 to isolate x.


x=1747%2F333 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is x=1747%2F333


Since we let x=5.246246246, this then means that 1747%2F333=5.246246246 where the '246' block repeats forever.