Multiplying Decimals

Hey, guys! Welcome to this Mometrix video on multiplying decimals.

Multiplying decimals may seem like a daunting challenge, but in this video, we’ll show you the techniques you need to decimate this decimal dilemma.

Place Value

In order to understand decimals, you first have to understand place value. Every number has a value based on its place relative to the other numbers.

Let’s look at the number 1,762. Based on place value, the number to the far left has the largest value. In this case, the number farthest to the left is in the “thousands” place.

The second number farthest to the left, our 7, is in the “hundreds” place.

The third number, 6, is in the “tens” place.

And then our last number here, which is farthest to the right, is in the “ones” place.

Here’s another way to think of this:

Thousands place: \(1\times 1,000=1,000\)
Hundreds place: \(7\times 100=700\)
Tens place: \(6\times 10=60\)
Ones place: \(2\times 1=2\)

Total: \(1,762\)

So what we see when we do that, is we should be able to multiply whatever number is in a specific place value, we should be able to take that number and multiply it times its place value. So, in this case, it’s in the thousands place, so we should be able to multiply it by a thousand, multiply 7 by 100, 6 by 10, and then 2 by 1. And so again, we’re multiplying every number by its place value. And then when we add it all up, we should get the total, which is equal to our number.

So now, any number behind our last number, so in this case 2, is called the “tenths” place. And this is where decimals come into play.

Let’s look at 1,762.8. The .8 behind the number 2 equals \(\frac{8}{10}\) of one whole.

So that was a review of numbers and their place value. Let’s take a look at how to actually multiply decimals.

Multiplying Decimals

You multiply decimals just like you would normal whole numbers. The trick is understanding how and when to move the decimal point so you get the right answer.

We’ll use this equation to show how it’s done:

\(45.18\times 0.5\)

Remember place value. That means 45 and 18 hundredths multiplied by 0.5, or five-tenths. So let’s figure this out.

In solving the problem, pretend (for just a moment) that the decimal point isn’t there. That would give you this equation:

\(4,518\times 5\)

You don’t need the 0 since it doesn’t add anything to the equation. If we solve this equation, we get:

But we’re not done. We have to figure out where to place the decimal. Here’s how you do that.

Go back to the original equation and count how many numbers are behind each decimal point. In this case, there are three. Two here (45.18) and one here (0.5).

We’re almost done. Now that we know there are three numbers behind the decimals, we go back to our answer and place the decimal three places from the last number. So the first answer we got was 22,590. But remember, we have to move our decimal point three places to the left because we had 3 places behind our decimal points here. So when we do that, our decimal point ends up right after our 22.

So our final answer is 22.59.

So that’s our look at multiplying decimals. As you can see, the concept seems much harder than it actually is. If you understand place value and how to move the decimals in the right place, you’ll do just fine.

I hope this video was helpful! See you guys next time!

Frequently Asked Questions

Multiplying Decimals Practice Questions