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

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) (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 . Now multiply both sides by 1000 to get . Why 1000? I wanted to move the decimal point to the next start of the block 246

Now subtract 'x' from 1000x to get

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

So we now know that

Start with the given equation.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

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Answer:

So the solution is

Since we let , this then means that where the '246' block repeats forever.
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