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Suppose you're stuck on a desert island with no internet, no books, and an evil genius
who will only let you off if you can tell him how much a million dollars weighs.
Luckily, you're a physicist, so you can weigh a million dollars with your mind!
Here's how it goes: we approximate.
We don't know how much a dollar weighs, but we do know how big it is… more or less.
A dollar is about 15 cm long and 5 cm wide… now how thick is it?
We don't know that either, but money is made out of paper, and we do know that those 'Harry
Potter' books were around 800 pages long, or 400 sheets of paper.
And I think they were about 5 cm thick… so that gives 80 sheets per cm.
Now we can find the volume of a dollar: 15 cm long times 5cm wide times one 80th of a
cm high is 0.9 cubic centimeters.
We still don't know how much paper weighs, though.
But we do know that a cubic centimeter of water weighs a gram.
And money's a liquid asset, right?
So we'll say a cubic centimeter of dollars weighs a gram.
Multiply 0.9 by a million and we're done!
A million dollars weighs 900 kilograms, or two thousand pounds.
So why are approximations important in physics?
Well, you don't want to attempt a two-month calculation without a ballpark estimate of
what you're calculating.
And sometimes approximations like ours can be pretty accurate: case in point, according
to the US treasury, a million dollars is a ton of money.