On page 7 (4th & 5th ed) of Moons & Planets, Problem 3 reads as follows:
Meteorites of pure nickel iron (which can probably be seen in a museum near you) testify that some asteroidal fragments are pure metal. Suppose the economic value of iron is of the order of ten cents per kilogram. Calculate the economic value of a 1-km-diameter asteroid of iron.
Do this problem. I do not really care right now about whether you want to stake a claim on an asteroid. I want you to see how valuable it is to ESTIMATE answers to problems where the data are somewhat uncertain, and where you have to dig out other pieces of information because you don't have quite enough.
For example, a "1-km-diameter asteroid". Is it a sphere? Approximately so- you don't have much choice. But really now, most asteroids are shaped more like potatoes, and you know how THEY vary! And how much stuff is in a 1-km-diameter sphere, anyway? This is usually called the volume and you probably learned about the volume of a sphere long ago.
Now, how much mass is there in a given volume of iron? That is usually called the density, and people have been measuring the densities of things for a long time- at least since the days of Archimedes. So you can look up the density of iron somewhere, or you can measure it yourself, or you can guess if you have some related experience to draw on. You don't need to know it to more that ONE significant figure, considering all the other approximations and estimates involved here. TRY IT!
Of course, I want you to hand in a sheet of paper with your work shown so I can follow your thinking, not just a scrap that says "ten trillion dollars" or whatever number you come up with.
The rules for collaboration for this and other homework problems are these: You work in groups and figure out things together and argue about the problem all you want (in fact, I encourage you to work on homework in groups), but you take away no notes, so you go back and work out the problem on your own and hand it in. After all, if you can't do that, then you really don't understand it (and who knows? It might be on the exam later!) Fair enough? Yes!!