On Thursday, March 7, 2002 at 1:42:12 PM UTC-5, JAXAshby wrote:

And exactly what is the specific mathematical meaning that is important
in engineering for the term "... on the order of..." ?

An "order of magnitude" is a power of ten. three orders of magnitude is 10^3.
Therefore, therefore"... on the order of 8% to 10% ..." makes no sense.

There is more to it, however. Three orders of magnitude (for instance) actually (unless specifically stated as precise) means that something is probably about 1,000 times greater, but there is a finite probability that it is only about 100 times greater and a finite probability of it being 10,000 times greater. There is more to the nuance, but that's more or less it.

"An [meaning "one"] order of magnitude" means roughly probably greater than twice and probably less than 100 times and most likely around 10 times.

Unless stated to be exactly "one order of magnitude", but this is slightly misusing the term.

Anyone who has actually studied engineering -- or any of the hard sciences --
knew this before they had studied even a week at school.

no, 3 orders of magnitude is not necessarily 10³, it is always x³ with the value of x depending on the context.

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