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Why were the SI unit prefixes, i.e.

\begin{align} \mathrm{giga} && 10^9 \\ \mathrm{mega} && 10^6 \\ \mathrm{kilo} && 10^3 \\ \mathrm{milli} && 10^{-3} \\ \mathrm{micro} && 10^{-6} \\ \mathrm{nano} && 10^{-9} \end{align}

chosen to be a multiple power of 3?

Edit: Although this question stemmed from a physics based discussion, I'm not sure which stack exchange would be better suited for this question.

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    $\begingroup$ Related: The origin of femto, atto and zepto SI prefixes. $\endgroup$ – Emilio Pisanty Sep 7 '17 at 13:49
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    $\begingroup$ Didn't the SI merely copy the previous "metric system" in using blocks of 3 like this? $\endgroup$ – Gerald Edgar Oct 4 '17 at 13:15
  • $\begingroup$ It's not really true that they're all powers of 1000. We have centi-, hecto-, deci-, etc. However, most of these have fallen out of use except for special cases like the hectare and centimeter. $\endgroup$ – Ben Crowell Oct 8 '17 at 2:30
  • $\begingroup$ Many time ago, I did read in some part it is related to the human brain being able to perceive scale factor up to three order of magnitude, but cannot find the source :-( $\endgroup$ – juanrga Nov 20 '17 at 17:17
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I'd have to say because the SI prefixes correspond to the standard number grouping, i.e.:

  • kilo = thousand
  • mega = million
  • giga = billion
  • tera = trillion

Here's the complete list:
SI Prefixes
Not to mention, an SI prefix for every ten-fold increase would be hugely cumbersome. Can you imagine a prefix for 10,000, 100,000, 10,000,000; 100,000,000...?

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Because of a tradition that goes back to ancient Greece. The greek alphabet was also used to denote numerals with just a little tweaking. Three archaic letters were used to have a total of 27 signs, so the first nine leters were 1..9, the next nine 10,20..90 and the last 100 to 900. This is known as the Miletsian system. It is obvious that after 999 some kind of loop should be implemented but there was not a universally agreed way to do it. Apparently the archaic latter 'sampi' was often used as a factor for thousands and is this usage is called 'numeric sampi' (there was some confusion as it could also be just 900).

For refs and details see the wikipedia article Sampi

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