There is a paper bundle of 500 papers.The height of this paper bundle is 5cm.I took 1 paper from the paper bundle and folded it into 50 times then what is the height of that folded paper?


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So, here's how thick one paper is:

5 cm $\div$ 500 pages = .01 cm

And here is how the folding is done:

Remember, OP is doing the folding, not someone in a vacuum who could fold a piece of paper to be millions of kilometers thick!

So the rest of the math is:

One fold is 2 $\cdot$ sheet thickness.
Two folds is 3 $\cdot$ sheet thickness.
... N folds is N + 1 $\cdot$ sheet thickness.
... 50 folds is 51 $\cdot$ sheet thickness.
51 $\cdot$ .01 cm = .51 cm


Pretty standard question.

If there are 500 sheets of total thickness 1cm, each sheet is .1mm thick. Assuming uniform thickness and no air between sheets, each successive fold doubles the sheet's thickness. Thus, after 50 folds, the thickness of one sheet will be 0.01*(2^50)cm. This is 1.1258999e+13, or approximately 113 gigameters. I'm not sure if you also want to place this on top of the initial stack, but it would make very little difference to the final sum.


So, naively, the answer seems to be:

113 million km.

This makes a bunch of assumptions, not the least of which is that a paper can be folded 50 times, and that the thickness of a bundle does not have any gap and is only made up of the sheets.

Then the calculation can be done by typing this into google:

2^50*(5cm/500) in km

Breaking this down:

(5cm/500) = 0.1mm gives you the thickness of the paper (bit of an assumption, but not too much of a stretch)
If you fold a paper once, you will get 2 times the thickness (again neglecting some real world stuff). If you fold it twice you get 2x2 times the thickness (blah blah). And in general, if you fold in $n$ times you get $2^n$ times the thickness.


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