Why calculators aren't mathematicians, and how you can get a calculator to be wrong.
Calculators aren't mathematicians.
They're tools. And if you don't know how to use the tool right, you'll use it wrong.
Story time.
In one of my sophomore circuits classes, we had to find the value of a capacitor on a test. Every single student got the answer wrong. We all asked for an explanation why we were wrong. The instructor did the problem on the board, in front of the class.
He got the wrong answer, too. The thing about it? ALL of us got different wrong answers.
Turns out, we were doing equations that started with reasonable whole numbers close to zero, and the answer was less than thousandths of microFarads (1x10^-9, the answer was at 1x10^-12).
*Extremely* small numbers... so small that all the calculators, even the same model from the same manufacturer, got different answers because of the inherent imprecision at that distance from zero. You actually have to know *how* a calculator works to understand the why. Numbers expressed as binary digits lose precision when you put 9 zeros in front of it.
These were expensive scientific calculators, too. Things you don't buy in a Staples (this was pre-internet, too, so programs that could do the things we were asking were expensive, too).
The answer was so imprecise that so long as the number was "whatever" x 10^-12, we were actually right, because it was impossible to overcome the inherent unreliability of a fundamental way binary numbers are stored. So we all got credit.
Now. Tell me more about how this online calculator got the "right" answer.
Because calculators don't actually KNOW things.
So sure, you got 9. And it's STILL the wrong answer, because the calculator doesn't know that what you put in isn't explicitly written. Humans can and do.