$T: [0,1)\to [0,1), x\mapsto 10x-\lfloor 10x\rfloor$

Question

Consider $T: [0,1)\to [0,1), x\mapsto 10x-\lfloor 10x\rfloor$.

Is that the same as $$ 10x (mod 1)? $$ or in which sense is that multiplication with 10 mod 1?

Answer 1

It is exactly the same. It is also just move the decimal one position right and erase what comes to the left.