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Use the one that results in the most convenient number.

Since you don't know which one that is until you do the measurement, it's perfectly acceptable to perform the measurement in any unit, and then when you see what you have, you can convert it to any other unit that produces a more convenient number.

Example:

One morning after my shower, in order to weigh myself, I climb onto my postage scale, which is graduated in grams. My weight is equivalent to a mass of 86,636 grams.

This is an inconvenient number to remember, carry around on a little scrap of paper, and report to my doctor, so I want to convert it to a more convenient number. I'll convert it to milligrams.

1 gram = 1,000 milligrams.

86,636 grams = (86,636 x 1,000) = 86,636,000milligrams.

That's even worse ! I can't remember that, and if I write it down, chances are I'll make a mistake before I finish writing it. I'd better try something else. I'll try kilograms.

1,000 grams = 1 kilogram

86,636 grams = (86,636 / 1,000) = 86.636 which I'll round off to 86.6 kilograms.

Finally ! That's a number I can remember. Plus ... it's easy to write down, easy to say, easy to tell someone else, and easy for him to remember and write down. AND ... the error introduced by rounding it off is less than 0.05% of the real number that I read on the scale, which won't hurt anything.

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Q: How do you determine whether grams kilograms or milligrams should be used to measure the weight of an object?
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