### Theory:

"The digits are multiplied without using the decimals. Then the decimal point separates as many decimal digits as there are in the multipliers together."
 $\begin{array}{l}\underset{¯}{\begin{array}{l}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}2.5\\ \phantom{\rule{0.147em}{0ex}}×1.6\end{array}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}150\phantom{\rule{0.147em}{0ex}}\\ \underset{¯}{\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}25\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}4.00\end{array}$ First, multiply by articles as integers:$\left(25\cdot 16=400\right)$ Then point separated the last $$2$$ digits ($$00$$).$2.5×1.6=4.\overline{)00}=4$ $\begin{array}{l}\underset{¯}{\begin{array}{l}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}2.75\\ ×\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}0.16\end{array}}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}1650\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}275\\ \overline{\phantom{\rule{0.147em}{0ex}}0.4400}\end{array}$ First, multiply by articles as integers:$\left(275\cdot 16=4400\right)$  Then point separated the last $$4$$ digits ($$4400$$).$2.75×0.16=0.44\overline{)00}=0.44$

$0.01111×55.5=0.616605$

First, multiply the digits as integers.

$\left(1111×555=616605\right)$

Then the point separated the last $$6$$ digits ($$616605$$).

$\begin{array}{l}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}0.01111\\ \underset{¯}{\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}×\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}55.5}\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}5555\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}5555\\ \phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}5555\\ \overline{0.616605}\end{array}$