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Why is 1000 micrometer not a correct representation of a prefix?

I ask because I recently took an entrance exam with a multiple-choice question which went along the lines of

which of the following is not a correct representation for prefixes: (A) 1mm, (B) 10km, (C) 1000 micrometer, (D) Both A and B.

and the stated answer was (C), but I don't know why.

Is it because when we write it in scientific form, it produces a double prefix which is not possible?

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  • $\begingroup$ Was "micrometer" written as you wrote it or in symbols, µm? $\endgroup$ Oct 20, 2020 at 12:39
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    $\begingroup$ Reminds me of 5000 mAh batteries haha $\endgroup$ Oct 20, 2020 at 14:14
  • $\begingroup$ µm was written. $\endgroup$ Oct 20, 2020 at 19:32

4 Answers 4

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which of the following is not a correct representation for prefixes: (A) 1mm, (B) 10km, (C) 1000 micrometer, (D) Both A and B.

The question is about prefixes and has nothing to do with the numbers. The three prefixes here are “m” for milli, “k” for kilo, and “micro” for micro. The proper representation of micro is “$\mu$”, not “micro”.

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  • $\begingroup$ My bad, it was µm not micro. I couldn't find the symbol :/ $\endgroup$ Oct 20, 2020 at 19:32
  • $\begingroup$ In that case, the question as you have stated and corrected it makes no sense because all three prefixes are correctly represented. $\endgroup$
    – G. Smith
    Oct 20, 2020 at 19:51
  • $\begingroup$ The symbol $\mu$ is written \mu in MathJax. Other Greek letters are similar. $\endgroup$
    – G. Smith
    Oct 20, 2020 at 19:53
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It is more a matter of convention.

For example, it is quite conventional to speak about pressures of 1000 hPa. There are historical reasons for that.

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Writing $1000\:\mu \rm m$ is not wrong as such, in the sense that there are plenty of contexts in which it can be used, or might even be the best representation for that length. (As a rule, the best notation is the one that adds the most clarity to the text.)

Presumably, your exam has singled out that notation because the length can also be expressed as $\rm 1\: mm$, which is definitely simpler (and, if (if!) you are using significant figures to express uncertainties, allows you to distinguish between $\rm 1\: mm$ and $\rm 1.000\: mm$, though it's also important to note that significant figures are a fairly coarse tool, and if you really care about uncertainties then you handle them explicitly).

The distinction is stronger in engineering notation, which does force you to incorporate the rough size of the number (i.e. to within a factor of 1000) into the SI prefix. However, in general, the preference for $\rm 1\: mm$ over $1000\:\mu \rm m$ is only a matter of choice of convention.

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  • $\begingroup$ Thank you :D (for editing the post and answering) $\endgroup$ Oct 20, 2020 at 19:33
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1000 micrometers is one millimeter

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  • $\begingroup$ So, we try to simplify the expression as much as possible to produce the highest order prefix? $\endgroup$ Oct 20, 2020 at 8:37
  • $\begingroup$ I mean it could also have been 0.000001 kilometer. Does that mean we follow the scientific notation rule which states there should only be 1 non-zero digit before the decimal point? $\endgroup$ Oct 20, 2020 at 8:47
  • $\begingroup$ no rule. you can write "1000 micrometers". it's not conventional, but there's nothing wrong about it. $\endgroup$
    – Rd Basha
    Oct 20, 2020 at 11:00
  • $\begingroup$ Ah, thanks! Also, if you don't mind, could you tell me why 9800 mm has 4 significant figures and not 2 (since trailing zeros aren't considered significant)? (i can't ask any more questions :/) $\endgroup$ Oct 20, 2020 at 11:05
  • $\begingroup$ 9800 mm is ambiguous. The trailing zeros might or might not be significant. You'd need to write 9800 mm (4 sigfigs) or 9800 (2 sigfigs) or some such. This is rather messy and it's often better to signal the number of sig figs by writing $9.800\times 10^3$ mm or $9.8\times 10^3$ mm, or better still, just 9.800 m or 9.8 m. $\endgroup$ Oct 20, 2020 at 12:12

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