b061b060-96ad-4b59-b894-002b763aa26b 20 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Lab demo about numerical result

Example 1

radius Hydrogen Atom radiusH 251012 -^* m * :

diameter Hydrogen Atom diameterH 501012 -^* :

calculAccuracy 11015 -^(* :

The 32 bits floating point can measure the thickness of a sheet of 50000 atoms [H]

diameterH calculAccuracy / 50000

Example 2

C(x) = Cπ segment coefficient

x C 1 π / 12 x * - acos 12 x * - (4 x * 2 x * (2^- sqrt * - (* :

x C

1 C 0.999999999999999

111 C / - 11015 -^* -

Example 3

Accuracy of

5.6 Zeta 1.02338 ≡

5610 / Zeta 1.023375479227029991089041788103 ≡

Accuracy of

[....]

... Smath

1.023375479227029991089041788103 1.02337547922703

Example 4

1 x / x 12 int 0.693147180559949

1 x / x 12 int Adaptive ≡ Exact to 15 D ≡

2 ln 0.693147180559945

RelativeError 12 ln 1 x / x 12 int / - : 1.000000000000000 1.000000000000000 1015^* / -

1.000000000000000 1.000000000000000 1015^* / 11015 -^*

Example 5

How accurate exp(1) ?

1 exp 2.71828182845905

How accurate exp(1.0) ?

1.0 exp unknown ≡

How accurate ?

2 sqrt (2 ln^1.27153712971414

22 ln 2 /^1.27153712971414

How accurate ?

0.123456789 0.123456789^0.772398384

You can't have more decimals than those specified

How accurate ?

2 sqrt (0.123456789^1.043715416

How accurate ?

3 sqrt (0.123^1.070

π 2^9.86960440108936

π 2^9.86960440108935862 ≡ Kalkulator 2.27 ≡