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Our chemistry professor said that "mg for mass, g/m3 for density, ms for time are all SI units".

I want to make sure now, even if we added a prefix to the unit, will it still be an SI unit?

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    $\begingroup$ Have a look here. $\endgroup$ – airhuff Sep 30 '17 at 8:53
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Yes, when prefixes are used with coherent SI units, the resulting units are still SI units; however, they are no longer coherent.

The metre per second, symbol m/s, is the coherent SI unit of speed. The kilometre per second, km/s, the centimetre per second, cm/s, and the millimetre per second, mm/s, are also SI units, but they are not coherent SI units.

BIPM: The International System of Units (SI)

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    $\begingroup$ Worth mentioning the exception to the rule: kg is the base unit of mass, not grams. See also unc.edu/~rowlett/units/cgsmks.html: the CGS system (centimeter, gram, second) used to be the base units (with force in dynes for example), but now almost everyone uses MKS (with force in Newtons). $\endgroup$ – Peter Cordes Sep 30 '17 at 15:52
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    $\begingroup$ The main advantage of Metric/SI is that everything makes sense and is so easy to work with. Which is why it infuriates me that the base unit of mass is kg. WHY? Why would you ruin an otherwise perfect system? Like, in a system all about logical unit choices, you go and do that. Sigh. $\endgroup$ – Bassinator Sep 30 '17 at 19:03

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