Chapter 5.2, Problem 5P

When we multiply $0.48\times 3.9,$ we first multiply as if the decimal points were not there:

   $\begin{array}{l}3.9\\ \frac{\times .48}{\begin{array}{l}312\\ \frac{1560}{1872}\end{array}}\end{array}$

Then we place a decimal point in 1872 to get the correct answer. Explain clearly why it makes sense to put the decimal point where we do.