Result of number with decimal point modulo $10$.

Question

This is a very simple question, very trivial to many, but I have to resolve this doubt!
I have done the division $2.2/10$ by hand, and the result is $0.22$, without any remainder:

But why if I do with calculator, I obtain this: $$2.2 \mod 10 = 2.2$$ why it is not equal to $0$, instead?

Answer 1

You can define modulo for real variables like this: $\quad {a \bmod b=a-\lfloor \frac ab\rfloor\times b}$

Here $\frac ab=0.22$ whose integer part is $0$, so basically for $0\le x<10$ then $x\bmod 10=x$.