Casio FX-602P vs fx-4000P, different results

[Nigel (UK)]

Both calculators evaluate results to 12 significant figures: \(\sqrt{2}\approx 1.414\,213\,562\,37\). Squaring this number gives 2, to 10 significant figures. This is what is displayed on the FX-602P.

However, pressing the EXE key on the FX-4000P rounds the result to 10 significant figures: \(\sqrt{2}\approx 1.414\,213\,562\). Squaring this rounded number gives \(1.999\,999\,999\), to 10 significant figures.

The rounding happens, I guess, because registers on the FX-4000P only store 10 significant figures. Pressing EXE stores the displayed number into the Ans register, hence the rounding. There is no Ans register on the FX-602P, and in any case the FX-602P's registers store all 12 digits of a calculated result.

Typing \((\sqrt{2})^2\) EXE on the FX-4000P gives an answer of 2, as the rounding doesn't occur until the calculation is complete.

Incidentally, the answer on the FX-602P is not exactly correct. Squaring \(1.414\,213\,562\,37\) gives \(1.999\,999\,999\,99\), rounded to 12 significant figures. The FX-602P rounds the answer to 2, exactly. Quite a lot of Casio calculators do this - personally, I disapprove!

Nigel (UK)