Question 1064312: the distance between earth and the moon is about 400000 km. take a piece of cardboard that is 1mm thick. how many times would you have to fold the same piece of cardboard over and over again, doubling the thickness with each fold to make it reach a thickness equal to this distance?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 400,000 km is equal to 4 * 10^5 km.
1 km is equal to 1 * 10^6 mm.
400,000 km is therefore equal to 4 * 10^5 * 10^6 mm.
that means 400,000 km is equal to 4 * 10^11 mm.
how many times do you have to double 1 mm to make it equal to 4 * 10^11 mm?
basic formula would be f = p * (1 + r)^n
f is the future value = 4 * 10^11 mm.
p is the present value = 1 mm.
(1 + r) has to be equal to 2.
formula becomes 4 * 10^11 = 1 * 2^n
simplify to get 4 * 10^11 = 2^n
take the log of both sides of this equation to get:
log(4 * 10^11) = log(2^n) which becomes log(4 * 10^11) = n * log(2)
solve for n to get n = log(4 * 10^11) / log(2).
you get n = 38.54120904 times.
you would have to fold it over and over again 38.54120904 times in order for it to reach the same thickness as the distance between the earth and he moon.
does this make sense?
let's try the same formula with something smaller.
assum you start with 1 mm and then double it 5 times.
what would you get?
you would get 1 * 2 * 2 * 2 * 2 * 2 = 32
let's use the same formula to see if we get the same answer.
f = 32
p = 1
1 + r = 2
formula of f = p * 2^n becomes 32 = 1 * 2^n which becomes 32 = 2^n
take the log of both sides of the equation to get log(32) = log(2^n) which becomes log(32) = n * log(2).
solve for n to get n = log(32)/log(2) = 5.
formula is good.
i checked with an online conversion calculator to confirm that 400,000 km is equal to 4 * 10^11 mm.
the calculator confirmed this is correct.
i believe this is your answer.
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