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How Do You Multiply Decimals?

Here is an example of how to multiply two decimals: $$13.75 \times 5.5=75.625$$

How many places past the decimal point in your answer? As many as necessary. Don't worry about rounding for now.

Let's do another example to practice.

Step One: Forget About Decimal Points and Multiply Normally

Here's a reminder on how to multiply integers. The section itself is on how to multiply two-digit numbers, but the techniques may be helpful to you. $$\begin{align} 17929\\ \times \quad \phantom{ } 24\\ \hline 430296 \end{align}$$

Step Two: Insert Decimal Point

Remember: $$\begin{align} # \text{decimal places in first number }&\

• \quad # \text{ decimal points in second number }&\ \hline # \text{ decimal places in final answer}& \end{align}$$

There are $3$ decimal places in $17.929$ and $2$ decimal places in $0.24.$ Thus, there will be $3+2=5$ decimal places in our final answer.

Now all we have to do is put the decimal point in the correct spot in $430{,}296$ so that it will have $5$ decimal places. $$4.30296$$

(Videos) Multiplying Decimals

by PatrickJMT

Patrick JMT has some great videos with a ton of examples that cover decimal multiplication.

$\large{\text{Summary}}$

He starts off with $0.02\times6.3$. We want to set up the problem as if the decimals weren't there. $$\begin{align} &0\color{lightgray}{.}02\\ \times\quad&\,\,\,6\color{lightgray}{.}3\\ \hline &\,\,\,006\\ +\quad&012\text{x}\\ \hline &0126 \end{align}$$

Now, we want to count the decimal places in each number. $0.002$ has $2$ decimal places and $6.3$ has $1$ decimal place. Together, there's a total of $3$ decimal places. Starting from the ones place, move the decimal $3$ places in the final product. $$\begin{align} &\,\,\,0.02\\ \times\quad&\,\,\,\,\,\,6.3\\ \hline &\,\,\,\,\,006\\ +\quad&\,\,012\text{x}\\ \hline &0.126 \end{align}$$

The final video, Patrick looks at a decimal word problem.

If the average yearly rainfall in Lakeview is $23.15$ inches, how much rainfall can we expect in $4.5$ years?

We can rewrite this question as: $23.15\times4.5$. $$\begin{align} &\,\,\,\,\,\,23.15\\ \times\quad&\,\,\,\,\,\,\,\,\,\,\,\,4.5\\ \hline &\,\,\,\,\,11575\\ +\quad&\,\,\,\,\,9260\text{x}\\ \hline &104.175 \end{align}$$ We can expect $104.175$ inches of rainfall over $4.5$ years.

(Videos) Multiplying Decimal Numbers

by mathman1024

This video by mathman1024 shows you how to multiply decimals. There is a video with more examples later in the explanation.

$\large{\text{Summary}}$

Multiplying decimals is super easy. You just multiply the numbers together regardless of where the decimal is. Then once you have your final product, you move the decimal to the left the number of decimal places the two numbers have combined.

Let's do an example so you can see: $(0.4)(0.09)$.

It doesn't matter which number you put on the top or bottom. I chose this way because I like to put the number with less digits on the bottom.

You multiply through like you normally do. When you get to the end, you have to count up the decimal places in the numbers above. The first, $0.09$, has two decimal places. The second, $0.4$, has one decimal place. If we add these together, we get three decimal places. So we have to move the decimal place in our answer over to the left three decimal places. $$(0.4)(0.09)=0.036$$

Try these next ones on your own and then watch the video to see the answers!

1. $(2.1)(1.9)$
2. $(3.5)(2.77)$

Here's another video with another example. Try this on your own and then watch the video to see the answer!

1. $(7.15)(0.28)$