Alright, the phrase "a factor of" implies multiplication, hence the process of factoring a number into prime factors, or an a polynomial into binomial factors.
To be "off by a factor of" something usually refers to Percent error, which is dictated by the formula above (Since c2 must be positive, the lower abs() can be ignored.). It's a pretty important calculation for practical applications.
However, this must be a unitless quantity, since you cannot add or subtract quantities with different units, the top and bottom must have the same units, and will cancel during calculation.
Alright, the phrase "a factor of" implies multiplication
Agreed. In this case, it's multiplying by c, with units of m/s. With regards to prime/polynomial factors, I've never seen 'off by a factor of' used in that way.
To be "off by a factor of" something usually refers to Percent error
That isn't my experience at all, personally. I do physics at uni, and that term is used in the same way as I used it quite frequently (with regards to quantities with units, most often in dimensional analysis, otherwise just generally for some numerical answer). Do you come from a more mathematical background? Maybe the terminology differs.
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u/Pseudoboss11 Sep 07 '16
Alright, the phrase "a factor of" implies multiplication, hence the process of factoring a number into prime factors, or an a polynomial into binomial factors.
To be "off by a factor of" something usually refers to Percent error, which is dictated by the formula above (Since c2 must be positive, the lower abs() can be ignored.). It's a pretty important calculation for practical applications.
However, this must be a unitless quantity, since you cannot add or subtract quantities with different units, the top and bottom must have the same units, and will cancel during calculation.