The product of $0.5$ and $0.4$ is $0.2$.

To understand how we arrive at this result, let’s break it down step by step. When multiplying decimals, you can initially ignore the decimal points and multiply the numbers as if they were whole numbers. In this case, you would multiply $5$ by $4$, which gives you $20$.

Next, it’s important to consider the decimal places in the original numbers. The number $0.5$ has one decimal place, and $0.4$ also has one decimal place. When you multiply these two numbers, the total number of decimal places in the product should equal the sum of the decimal places in the factors. Therefore, $1$ decimal place (from $0.5$) plus $1$ decimal place (from $0.4$) equals $2$ decimal places.

Now, take the product you obtained from multiplying the whole numbers, which is $20$, and place the decimal point so that there are two decimal places. This results in $0.20$, which can be simplified to $0.2$.

Hence, the product of $0.5$ and $0.4$ is indeed $0.2$. This method ensures that you accurately account for the decimal places, which is essential for obtaining the correct answer.