Question

If a typical molecule has `10^(25)` parts and someone wanted to artificially build them at a rate of a million parts per second, how long would it take to complete just one molecule? What is this problem called and why?

Answer 1

It would take 10¹¹ (a hundred billion) years to complete one molecule.

This is a problem on unit conversions, because you have to convert one unit to another in a series of steps until you get to the final answer.

You can set it up as a string calculation.

`1 cancel("molecule") × (10^25 cancel("parts"))/(1 cancel("molecule")) × (1 cancel("s"))/(10^6 cancel("parts")) × (1 cancel("min"))/(60 cancel("s")) × (1 cancel("h"))/(60 cancel("min")) × (1 cancel("day"))/(24 cancel("h")) × "1 yr"/(365.24 cancel("days")) = 10^11"yr"`

Note: The answer can be expressed only to an order of magnitude, because that is all you gave for the number of parts. If you need more precision, you will have to recalculate.