Lesson 5: Multiplying Decimals

Property

To multiply two decimals, we move both decimal places to the right so that both numbers are whole numbers.
Now multiply those whole numbers.
Finally, move the decimal point to the left a number of spaces equal to the sum of the moves to the right of the decimal places in the original two numbers.

Examples

• To multiply $4.5 \times 0.5$: First, calculate $45 \times 5 = 225$. The original numbers have two decimal places in total (one in $4.5$, one in $0.5$), so the answer is $2.25$.

• To multiply $1.25 \times 3$: Calculate $125 \times 3 = 375$. The original numbers have two total decimal places (in $1.25$), so the answer is $3.75$.

Property

Base ten blocks can model decimal multiplication by arranging blocks in rectangular arrays, where the area represents the product.
On hundredths grids, decimal multiplication is shown by creating overlapping shaded regions where the intersection area equals the product: $0.3 \times 0.4$ creates a $3 \times 4$ rectangle covering $12$ squares out of $100$.

Examples

Property

When multiplying a decimal by a whole number, multiply as if both numbers were whole numbers, then place the decimal point in the product so it has the same number of decimal places as the original decimal factor.