Vtyjkyuk

I was trying really large number multiplication.

Stuff like 123456789123456789 x 2

Now, if you do this, the long-form multiplication way on a paper and pen, You'd get some answer, that .. trivially you'd know 100% is correct... I would imagine you can't go wrong multiplying that on your own.. even in your head..

Now, when you'd try to do that on say a calc app on Windows/Linux/Google/Duckduckgo.. or even Excel / LibreOffice calc (I tried all of them).. You'd get an answer that is slightly different..

The 3 least-significant digits are 000 .. instead of the actual digits.

The question was, why is there a difference. What is the computer not being able to handle.

As it turned out, some of these apps, simply used the default multiplication algorithms provided by the OS which meant, it used code that truncates or gives a closest estimate.

Packages such as wolfram alpha and others ... that are specifically designed to handle computation, are doing it just fine.

In a rush, I had asked this question, I should have gone to wolfram alpha before bothering elite mathematicians on the stack-exchange.. and I am sorry for that :)

Back when we used handheld calculators they typically could only store $8, 10$ or $12$ decimal digits. The apps on many computers have maintained that limitation. Before that we had slide rules and could only operate with about three digits. Your multiply demands $18$ decimal digits. A computer that uses $64$ bit integers will get this right. There are many software packages that use arbitrary precision integers and they will get this right as well. A computer that uses $32$ bit integers can only do this by converting to floating point and will not have enough precision to get all the places correct. This is not math, this is computing. All of these computing devices make compromises in the interest of doing useful work. They do useful work. The user must understand the limitations and find ways around them if they are a problem. There is a whole field called numerical analysis which finds clever ways to avoid the problems.

That is because of register width limitation. If you want to manipulate numbers that don't fit into registers, you need to use different techniques.

This depends on what computer and programme you use. Any supercomputer will get the right answer. Plus, you may have made an error in your pen & paper calculation.