When multiplying a decimal number by another decimal number, it always helps to be reminded what they'd look like in fraction form.
Sample Problem
Just like with addition and subtraction, converting decimals to fractions and back again is pretty inefficient. Thankfully, we can get around that. Just plow right through those "detour" signs.
In the example 0.8 × 0.4, we multiplied two decimals with one decimal place each. When we wrote the numbers as fractions, we were multiplying two fractions that each had 10 in the denominator. The product of those fractions gave us a denominator of 100, so the corresponding decimal had two decimal places. Once again, we're just counting zeros. Better than counting crows.
Suppose a, b, and c are three decimal numbers. How do you figure out the number of decimal places in the product of a × b × c? Just add the number of decimal places in a to the number of decimal places in b to the number of decimal places in c. Yeah, unfortunately you'll need to know how to multiply three numbers together. Curse those three-dimensional shapes.