Multiplying Decimals by Whole Numbers

Multiplying a decimal by a whole number is just like regular multiplication, with one extra step at the end. You don't need to line up the decimal points!

The 3-Step Rule

1. Ignore the decimal point for a moment and multiply the numbers as if they were both whole numbers.
2. Count the decimal places in the original decimal number (how many digits are to the right of the decimal point).
3. Place the decimal point in your answer so it has the exact same number of decimal places. Count from right to left.

Step-by-Step Examples

Example 1: $3.45 \times 6$

• Step 1: Multiply as whole numbers: $345 \times 6 = 2070$.
• Step 2: Look at $3.45$. It has 2 decimal places.
• Step 3: Place the decimal point in $2070$ so it has 2 decimal places. Count two spots from the right: $20.70$.

$3.45 \times 6 = 20.7$

(Note: $20.70$ is the same as $20.7$)

Example 2: $0.75 \times 24$

• Step 1: Multiply $75 \times 24 = 1800$.
• Step 2: The number $0.75$ has 2 decimal places.
• Step 3: Place the decimal point in $1800$ to give it 2 decimal places: $18.00$.

$0.75 \times 24 = 18$

Example 3: $12.6 \times 15$

• Step 1: Multiply $126 \times 15 = 1890$.
• Step 2: The number $12.6$ has 1 decimal place.
• Step 3: Place the decimal point in $1890$ to give it 1 decimal place: $189.0$.

$12.6 \times 15 = 189$