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Memorizing the prefixes is helpful, but not necessary. Most answers are fine in SI units. However, knowing the prefixes will help you check your answer. For example, for wavelength, you would expect to have your length to be in nanometers.
I know for a fact that we will have to know the conversions between micro (10^-6 m), nano (10^-9 m), and picometers (10^-12 m) because of their relation to wavelength. First it is important to realize that the conversions for these three measurements decrease by 1000 (10^-3) beginning with 10^-6. A mnemonic device that I use to help me memorize the order that the measurements go in (because i often confuse nano and micro) is that the measurements' names occur in alphabetical order, M, N, and P. If you can relate the first letters of each measurement to the order of the alphabet, it should make it easier to memorize the order of the measurements as well as their conversions.
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