HP 40gs, error in calculator?

[Dieter]

(11-01-2017 07:31 PM)Skipjack Wrote:  Hi, finally back with HP again after 15 yrs with TI and Casio. Got My HP 40gs today which I bought on Ebay. Been testning it out, and when punching in 1/9 and then multiplying answer with 9 again it displays 0.99999999.

I thought this was a common flaw on cheaper calculators. All my other machines (some 20+ of them) will return to "1".

If other calculators return "1" they are either wrong or they are doing things behind your back.

The 12-digit value for 1/9 is 0,11111 11111 11. This is what your HP returns.
9 x 0,11111 11111 11 is 0,99999 99999 99. That's what your HP returns as well.

Imagine you manually enter 0,11111 11111 11. Now multiply this with 9. What result would you expect?

So your calculator is perfectly OK. If it would return 9 x 0,11111 11111 11 = 1 it would be simply wrong.

Some calculators use hidden digits. For instance, they use 12 digits but they only display 10. In this case the displayed rounded 10-digit value of the above calculation is 1,0000 00000. And that's what you see then. Subtract 1 from this and you should get –1E–12. If you don't your calculator applies some "result cosmetics". That's not what a decent calculator should do.

So your 40gs is perfectly OK. It calculates 1/9 correctly, and it calculates 9 x 0,11111 11111 11 correctly. Remember: 0,111... is not 1/9. It's just the first 12 digits of this. Just as any displayed result is just the first digits of the true result.

The same is true for (√2)², e^(ln 3) etc. etc. Also sin(pi) will not return zero in radians mode. Simply because the calculator does not evaluate sin(pi) but sin(3,14159265359)=–2,067...E–13.

Dieter