*Rayna Cummings*Show bio

Rayna has taught Elementary Education for 12 years (in both 1st, 2nd, and 3rd grades) and holds a M.Ed in Early Childhood Education from The Ohio State University

Lesson Transcript

Instructor:
*Rayna Cummings*
Show bio

Rayna has taught Elementary Education for 12 years (in both 1st, 2nd, and 3rd grades) and holds a M.Ed in Early Childhood Education from The Ohio State University

While multiplying by decimals may sound difficult, it's actually no different than multiplying whole numbers. In this lesson, you'll learn about the extra step used when multiplying decimals by 10, 100 and even 1000!
Updated: 05/26/2020

Money is great, right? If you have enough in your piggy bank, you can buy that awesome toy you've been saving up for. But did you know that money is also great for teaching how to work with decimals? For example, you just broke open that piggy bank and found four quarters. A quarter equals $0.25 cents, so four quarters would equal 4 x $0.25 or $1.00? You just multiplied decimals!

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While multiplying decimals may sound tricky, it really isn't. You can multiply decimals just the way you multiply whole numbers. When you have your **product**, or the result of multiplying two numbers, you'll have to deal with the decimal. Let's take a look at the steps for multiplying and dealing with decimals.

Step 1: Multiply the numbers as if the decimal point isn't there.

Step 2: Add the decimal point to the answer.

- You can determine where to place the decimal point by counting the total number of decimal places in the
**factors**, or numbers being multiplied. Count the number of decimal places by moving backwards, from right to left, from the end of each factor.

Let's take a look at a couple of examples:

Did you notice how we ignored the decimal point when multiplying? Then we counted the total number of decimal places in the factors and placed the decimal point in the answer, moving backwards from the end of the answer.

You may already know that when multiplying a number by 10, 100, or even 1,000, the easiest way to do that is to count the number of zeros and add that figure to the original number. For example, 6 x 100 = 600. Here, we just added the two zeros from the 100 to the 6.

Multiplying decimals by 10, 100, and 1,000 is just as easy. But this time, instead of adding zeros to the original number, we're going to move the decimal point to the right (which makes the number larger) the same number of spaces as there are zeros. For example, when multiplying 4.5 x 10, we notice that there's one zero in 10, so we move the decimal point in 4.5 one space to the right, making it 45. Checking our answer, we see that 4.5 x 10 = 45.

Let's look at another example: 2.2 x 1,000. There are three zeros in 1,000, so we need to move the decimal point in 2.2 three spaces to the right. As there aren't enough digits, we can only move to the right one space. No worries, we'll add two zeros to the end of 2.2. This gives us 2.200. Now we'll move the decimal point three spaces: 2,200. Checking this answer, we see that 2.2 x 1,000 = 2,200.

Here's some more examples:

Let's review. When multiplying decimals, ignore the decimal point until you have your **product**, or the result of multiplying two numbers. You can determine where to place the decimal by counting the total number of decimal places in the **factors**, or numbers being multiplied. Count the number of decimal places by moving backwards, from right to left, from the end of each factor.

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