Is super-accuracy matters?

[Garth Wilson]

(10-13-2023 03:36 PM)johnb Wrote:  

(10-13-2023 03:21 PM)KeithB Wrote:  I think the super-accuracy in scientific calculators came about because it was the one real advantage they had over slide rules - other than addition of course 8^).

Not the only big advantage. Don't forget programmability!

Programmability is what got me into calculators, first the TI-58c, then the TI-59, then the HP-41cx.

Quote:When doing the same set of calculations over and over again (chemistry or astronomy class, anyone?), programmability was invaluable simply because it avoided mistakes such as step omissions. Not to mention how much it speeded up the tedium in the first place.

There were iterative processes I wanted to do that I wouldn't live long enough to do on a slide rule.  The calculator could do ten steps per second, plus conditional branching!  Oooooooo!   I had programs I would let run for as much as 24 hours, which means close to a million instructions executed, with no mistakes.  I was in good practice with the slide rule though, so for single operations, the calculator was not significantly faster.

Quote:Having said that, prior to programmable calculators, accuracy (and just plain nerdy niftiness!) was a big point! I remember as a kid, just being amazed that I could multiply 1234 x 5678 and instead of getting ~ 7x10¹², it would (more or less promptly) flash "7,006,652."

Er... make that 7.01x10^6   (not 10^12)

Quote:"Wow, I've finally gotten good enough at eyeballing this cursor to get 2-3 significant digits, and this new clicky LED machine gives me EIGHT?"

You should always be able to get three digits on the C, CF, CI, CIF, D, and DF scales, and usually four if the first digit is a 1 or maybe even a 2.  That's not to say the 4th digit will always be correct, but it will make your answer more accurate than not using it at all, for example 1.237 where perhaps it should have been 1.236.  On other scales you may get more.  For example, on the LL1 scale for natural logs, you can read off 1.01014.  The scale goes from 1.01 at the left end (for slightly below e^.01) to 1.105 at the right end (for slightly below e^.1).  The next scale up is LL2 which goes from there to e, then LL3 which goes from e to e^10 or about 20,000 (and each little mark is 1000, meaning there's very little precision left at the right end).  However, I've never seen an online video where the operator knew how to roll his fingers to microadjust the slide or even the cursor for greatest precision.  There's a way to quickly do it to the limits of good human visual acuity.