Assistance with algebra word problem

(Question)

Suppose you multiply a decimal that has 2 digits to the right of its decimal point by a decimal that has 3 digits to the right of its decimal point. Explain why you put the decimal point 2+3 places from the end of the product calculated without the decimal points.

Re: Assistance with algebra word problem

A number of the form A.** is the same as $\displaystyle A**\times 10^{-2}$ and a number of the form B.*** is the same as $\displaystyle B***\times 10^{-3}$.

The product lf the two numbers is $\displaystyle (A**)(B***)\times 10^{-5}$.