Moving the Point

Why does moving the decimal point work when you multiply decimals?


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)