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Help to settle a bet

6 Answers
Mathematically, how wide would a 2 inch New York Times newspaper be if I were able to fold it in half 100 times?
G

If this was actually possible, then you would solve it using an exponential equation. Since each time you fold in half the thickness is twice as much, you have 2 times 2^100.

so it is 2.5353012 × 10^30 inches thick, 2.112751 × 10^29 feet, 4.00142235 × 10^25 miles

this comes out to about 6.8 trillion light years to travel across

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D

Well... There is no real answer to this question.

First of all, folding a piece of paper more than eight times in half is impossible. Give it a try, I bet you can't do it. Even if you had the machinery to go further, at some point it would fail as well, probably around the 10th or 11th folding. Either that or the paper will fall apart due to too much force applied.

Considering that you asked how thick it would be if you were technically able to, I'm going to try heading in this direction as well. Folding a 2 inch thick paper in half once will leave you with more or less 4 inches. So if you were able to fold it a hundred times, you would have to double it's thickness a hundred times, which leaves us with the equation:

2 inch thickness * (2) ^times folded (in this case 100) = 2.535 * 10^30

Realistically, however, there's air and ink caught in between those pages which adds up to the full amount as well. It's hard to tell how much but it's probably above the estimate, assuming you actually were able to fold it that many times.

Hope this has answered your question. Have a great day and I hope you won the bet!

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S

You can solve this quickly by using an exponential function. Their general form is y = ab^x, where a is the starting quantity, b is rate of growth or decay, and x, the exponent, represents how many times you multiply by your growth rate. In this context I'll use "W" for width instead of "y."

W = 2(.5)^100 . . . "B" is .5 because you keep folding the paper in half.
W = 1.578 x 10^(-30)

In words, that's 1.578 "times ten to the negative thirtieth." Which is to say, that's a very, very narrow newspaper. I hope you're on the winning side of the bet.

Edit: Thanks to Dancel57 I just realized you might have meant 2 inches thick. In which case the same formula would apply with a different growth rate. An increase of 100% is decimally 1. So you add 1 to 1 and your growth rate is 2.

T (for thickness) = 2(2)^100
T = 2.54 x 10^30

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S

Okay, so after a trillion comes quadrillion, quintillion, sextillion, and septillion. One septillion is a 1 followed by 24 zeroes.

I divided the number up above by 12 to convert from inches to feet, then I divided it by 5280 to convert from feet to miles. The answer comes out to 4.00 x 10^25. So if a 4 with 24 zeroes after it is 4 septillion, then a 4 with 25 zeroes after it must be 40 septillion. Now, if you were to travel at a speed 60 mph, that means you could travel its length in 667 sextillion hours. Bon voyage.

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S

Your correct; I did mean thickness. As a layperson these equations are to abstract. Give it to me in distance. If I were able to travel along it's length, how much time would have elapsed at the end?
you can leave out air, ink, fingerprints, dust , and any other variables.

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I don't have time to travel at 60 miles an hour. Can you put it in light years; I'm in a hurry!

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