Multiplying Decimals by Decimals

Multiplying two decimals might look tricky at first, but it is actually very similar to multiplying regular whole numbers. The only extra step is figuring out where to put the decimal point in your final answer.

The 3-Step Rule

To multiply a decimal by a decimal, follow these three simple steps:

1. Ignore the decimal points and multiply: Treat both numbers as if they were whole numbers.
2. Count the decimal places: Look at your original problem. Count the total number of digits to the right of the decimal point in both numbers combined.
3. Place the decimal point: Take your whole-number answer from Step 1. Starting from the far right, move the decimal point to the left by the total number of places you counted in Step 2.

Example Problems

Let's walk through a few examples to see how the 3-step rule works in practice.

Example 1: $2.4 \times 0.35$

Step 1: Multiply as whole numbers. Ignore the decimals and multiply $24 \times 35$. $24 \times 35 = 840$

Step 2: Count the decimal places.

• $2.4$ has 1 decimal place.
• $0.35$ has 2 decimal places.
• Total decimal places = $1 + 2 = 3$.

Step 3: Place the decimal point. Start at the right of $840$ and move the decimal point 3 places to the left: $0.840$. You can drop the trailing zero to get your final answer: $2.4 \times 0.35 = 0.84$

Example 2: $0.06 \times 0.3$

Step 1: Multiply as whole numbers. Ignore the decimals and zeros in front. Just multiply $6 \times 3$. $6 \times 3 = 18$

Step 2: Count the decimal places.

• $0.06$ has 2 decimal places.
• $0.3$ has 1 decimal place.
• Total decimal places = $2 + 1 = 3$.

Step 3: Place the decimal point. Move the decimal point 3 places to the left in the number $18$. Since $18$ only has two digits, you need to add a zero as a placeholder: $0.018$. $0.06 \times 0.3 = 0.018$

Example 3: $1.25 \times 3.6$

Step 1: Multiply as whole numbers. Multiply $125 \times 36$. $125 \times 36 = 4500$

Step 2: Count the decimal places.

• $1.25$ has 2 decimal places.
• $3.6$ has 1 decimal place.
• Total decimal places = $2 + 1 = 3$.

Step 3: Place the decimal point. Move the decimal point 3 places to the left in $4500$, which gives you $4.500$. Drop the extra zeros at the end. $1.25 \times 3.6 = 4.5$

Quick Tips

• Always count, don't just drop down: Unlike adding or subtracting decimals, you do not line up the decimal points when multiplying. Just count the total places!
• Use zeros as placeholders: If your product doesn't have enough digits when you are moving the decimal point left, add zeros in front of the number to fill the gaps.