Why is $\,X\!\cdot\!10\%\!\cdot\!10\%\,$ not the same as $\,X\!\cdot\!20\%\,$?

Question

This confuses me a bit:

$X = 100$

Multiplying in two steps :

$100\cdot1.1 = 110$
$110\cdot1.1 = 121$

Directly multiplying by $1.2$ ($20\%$) :

$100\cdot1.2 = 120$

Answer 1

$x\cdot1.1\cdot1.1=x\cdot(1.1\cdot1.1)=x\cdot1.21\neq x\cdot 1.2$
multiplication is associative.
alternatively, in words: multiply the first $1.1$ get $1.1x$, multiply the second $1.1$ it is adding $10\%$ of $1.1x$ towards $1.1x$ but not $10\%$ of $x$ towards the $1.1x$, hence different.