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Multiplying Decimals

Multiplying decimal numbers is very similar to multiplying 2 digit by 2 digit (or 2 digit by 3 digit, etc) numbers, but you have to remember a couple key points. First, start out as you would with a normal multiplication problem. For example, let’s say your problem looks like this:

You would start out multiplying the 4 by the 5, then the 4 by the 3, like this:

Now, you’re ready to complete the very last step—inserting the decimal place. In order to do this, you have to count how many digits are behind each decimal, and add them together for a grand total. For example, in this problem there is one digit behind the decimal in the top number, and one digit behind the decimal of the bottom number. You would add these together, 1 + 1 = 2, so your grand total would be 2. Now, starting at the end of your answer, you are going to count two digits to the left, and that is where you will place your decimal. This is shown in red in the diagram below.

Thus, your final answer is 1.40 The most important part of this process is the last step—figuring out where the decimal should go. Therefore, it’s extremely important that you remember this step! Your answer won’t be correct without the decimal, so be sure you put it in the right place.

Examples of Multiplying Decimals

Now, let’s try a harder one. Here’s the problem:

Now, try working it out on your own. After you have your answer, look below to check your answer with ours.

Solution:

Last step--add in the decimal!

And now, we’ll try one super advanced problem—just to make sure you see how it works:

Ready? Copy this down on a piece of paper and test it out—then compare your work with ours!

Solution:

Last step--count the decimal places. In this problem, there are five of them. Now, place the decimal in the answer, like this:

Thus, your final answer is 1516.01942. Congrats! You made it through multiplying decimals.

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