Multiplying Decimal Numbers
When multiplying decimal numbers, multiply the digits as if they were whole numbers, then count the total number of decimal places in all factors and place the decimal point that many places from the right in the product. For 0.35 x 0.2, multiply 35 x 2 = 70, then place the decimal three places from the right (2 + 1) to get 0.070 = 0.07. This method is covered in Chapter 4 of Saxon Math Course 2 and is a critical 7th grade math operation used in area calculations, money problems, and scientific measurements.
Key Concepts
Property When we multiply decimal numbers, the product has as many decimal places as there are in all the factors combined.
Examples $0.35 \times 0.2 \rightarrow \begin{array}{rl} 0.35 & \text{(2 places)} \\ \times \quad 0.2 & \text{(1 place)} \\ \hline 0.070 & \text{(3 places) simplifies to 0.07} \end{array}$ $(0.04)^2 = 0.04 \times 0.04 = 0.0016$ $15 \times 2.54 \rightarrow \begin{array}{r} 2.54 \\ \times \quad 15 \\ \hline 1270 \\ 254\phantom{0} \\ \hline 38.10 \end{array}$.
Explanation Don't worry about lining up the decimals here. Just multiply the numbers as if they were whole numbers. Afterward, count the total decimal places in your original factors. Your final answer must have that same total number of decimal places. It's a simple counting trick!
Common Questions
How do you multiply decimals?
Multiply the numbers ignoring the decimal points. Then count the total decimal places in both factors and place the decimal point that many places from the right in the answer.
How many decimal places does the product have?
The product has as many decimal places as all the factors combined. If one factor has 2 decimal places and another has 1, the product has 3 decimal places.
What is 0.04 squared?
0.04 x 0.04: multiply 4 x 4 = 16, then place the decimal 4 places from the right (2 + 2) to get 0.0016.
Why do you count decimal places when multiplying?
Each decimal place represents a division by 10. If you have 2 + 1 = 3 total decimal places, the true product is the whole-number product divided by 10^3 = 1000.
What are common mistakes when multiplying decimals?
Students often miscount decimal places or forget to add trailing zeros when the product needs more decimal places than the digits provide.
Is multiplying decimals taught in 7th grade?
Yes. Saxon Math Course 2 covers decimal multiplication in Chapter 4, reinforcing place-value understanding through practice with various factor types.