Hey guys, and 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.
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:
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 1000, multiply 7 by 100, 6 by 10, and then 2 by 1.
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.
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 point 8 behind the number 2 equals 8/10 of 1 whole.
That was a review of numbers and their place value, let’s take a look at how to actually multiply 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:
Remember place value.
That means 45 and 18 hundredths multiplied by point 5, or 5/10, so let’s figure this out.
In solving this problem, pretend (just for a moment) that the decimal point isn’t there.
That would give you this equation:
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 3 (2 here, and then 1 here).
We’re almost done.
Now that we know there are 3 numbers behind the decimals, we go back to our answer
and place the decimal 3 places from the last number.
The first number we got was 22,590,
but remember, we have to move our decimal point 3 places to the left
because we had 3 numbers behind our decimal point here. When we do that,
our decimal point ends up right after our 22, so our final answer is 22.59.
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 that this video was helpful!
See you guys next time!