Lesson 4: Decimal Multiplication Algorithms and Decimal Placement

Property

How to multiply decimal numbers:
Step 1. Write the numbers in vertical format, lining up the numbers on the right.
Step 2. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
Step 3. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.

Examples

Property

To multiply decimals, first multiply the numbers as if they were whole numbers. The total number of decimal places in the product is the sum of the number of decimal places in the factors being multiplied.

Examples

• To solve $0.3 \times 0.07$: First, find the product of the whole numbers, $3 \times 7 = 21$. The factors have one and two decimal places, respectively, for a total of three ($1+2=3$). So, the product is $0.021$.
• To solve $1.2 \times 0.5$: First, find the product of the whole numbers, $12 \times 5 = 60$. Each factor has one decimal place, for a total of two ($1+1=2$). So, the product is $0.60$ or $0.6$.

Explanation

This rule works because multiplying by decimals is like multiplying by fractions with denominators of 10, 100, etc. When you multiply the numbers, you are also multiplying their place values. Counting the decimal places is a shortcut for determining the correct place value of the final product. This method allows you to use whole number multiplication skills and then correctly place the decimal point.