Moving the Point

Why does moving the decimal point work when you multiply decimals? For example, if you multiply 2.7865 x 1.67, why does it work to put the decimal point 6 places (4 places + 2 places) from the end of the product? Connect this algorithm to multiplication of fractions.

(Source: Adapted from Mathematics for Elementary Teachers, Sybilla Beckman, 2nd ed., 2008)