Forbin

Well, I guess it depends on what year and what the student was studying. I was 13 in 1975, knew I wanted to be a scientist or engineer of some kind, and was taking algebra and learning to program in FORTRAN IV in a special program. So, yeah, I absolutely knew the terms "mantissa" and "exponent". The derelicts who hung out in the smoking area who were taking remedial math probably did not.

@user1271772, for example: 1.42e12 x 7.89e-6. Nowadays I'd just plug those into my calculator and get 11,208,800. But in the old days with no calculators and computers being rarely available even to engineers, it was faster to use log tables. log(1.42e12) = 12.15229, and log(7.89e-6) = -5.10292. Add those together and get 7.04937. Take the antilog and get (roughly) 1.12e7. (You can stop shivering uncontrollably now.)

@user1271772, what he means is that log(a x b) = log(a) + log(b). If you want to quickly estimate the product "a x b" when either may be very large or very small, and if you don't have a calculator, then you can look up log(a) and log(b) in a book filled just with tables of logarithms (and other functions). You look up log(a) and log(b), add them together, then look up the antilog of the result. This was actually faster and somewhat less error prone than methodically working out products involving values of vastly differing sizes.