Calculate the Product: 0.1 × 0.5 Decimal Multiplication

To solve this problem, we'll multiply the decimal numbers $0.1$ and $0.5$, following these steps:

• Step 1: Treat each number as if it were a whole number and multiply: $1 \times 5 = 5$.
• Step 2: Count the decimal places in both factors. The number $0.1$ has one decimal place, and $0.5$ also has one decimal place.
• Step 3: The total number of decimal places in the product should be the sum of the decimal places in the factors, which is $1 + 1 = 2$.
• Step 4: Place the decimal point in the product $5$, resulting in $0.05$, to ensure it has two decimal places.

Therefore, the product of $0.1$ and $0.5$ is $0.05$.