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Order-of-magnitude calculations

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1) If the entire population of the United States forms a human chain by holding hands, how many times can such a chain be wrapped around the earth's equator?
Round your answer to the nearest integer.

2) How many times does your heart beat during your lifetime?
Round the answer to the nearest power of 10 and then express your answer as the order of magnitude. For instance, if your estimated answer is 3times10^5, enter 5. If your estimated answer is 8.7times10^5, you should enter 6 (rounding up to the next power of 10)

3) Legend has it that, many centuries ago, Archimedes jumped out of his bathtub and ran across town naked screaming "Eureka!" after he solved an especially difficult problem. Though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinking contains some water molecules that were in Archimedes' bathwater that day, because water doesn't get created or destroyed on a large scale. It follows the water cycle, which includes rain, evaporation, flowing of rivers into the ocean, and so on. In the more than two thousand years since his discovery, the water molecules from Archimedes' bathwater have been through this cycle enough times that they are probably about evenly distributed throughout all the water on the earth. When you buy a can of soda, about how many molecules from that famous bathtub of Archimedes are there in that can?

Round the answer to the nearest power of 10 and then express your answer as the order of magnitude. For instance, if your estimated answer is 3times10^5, enter 5. If your estimated answer is 8.7times10^5, you should enter 6 (rounding up to the next power of 10).

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Solution Summary

This solution performs order-of-magnitude calculations

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To answer these questions you need to make a few assumptions, and get some rough data.

For question number 1 you need the population of the United States ~ 300 million (but I am a Canadian). Then you will have to measure the apporximate length of a persons arm breadth, I would assume 1.5 meters (but again I am Canadian) or 5 feet. Then you need to find the circumference of the world (http://geography.about.com/library/faq/blqzcircumference.htm) and I will assume 40, 000 km (I am Canadian) or 25, 000 miles.

Now I will muliply the population by the breadth and get a number 450 million meters. ...

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