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Multiplying and Dividing Decimals

Skip to Dividing Decimals

Multiplying is possibly one the very thing calculations to do with decimals. As long as you can multiply other numbers and can count, you'll find multiplying decimals a piece of cake!
Let's dive right in:
Solve: 4.75 x 3.02

We like to rewrite those as:

Step 1: Multiply the numbers. At this point, we do not care about the decimals. As with multiplying non-decimals, be sure to include placeholders!

We end up with an answer of: 143450

Step 2: Put the decimal point back in. How do you know where? Easy! Count up all the numbers that are after a decimal point in the original problem. In 4.75, there are 2 numbers after the decimal point (7 and 5), and in 3.02 there are also 2 numbers after the decimal point (0 and 2.)That's 4 total numbers after a decimal point. Now, starting from the RIGHT, count over that many numbers in our answer from step 1.

So we end up with 14.3450 or 14.345.

Note: Unlike addition and subtraction, the decimal points do not have to align in order to keep the place values!

Here are some more examples: (Answers Below)

Example 1
Example 2

As always, be sure to count the number of numbers after the decimal. There are multiple ways to do certain problems - such was with Example 1, you could change 3.20 to "3.2" and perform calculations like that. However, if you use the ending 0 in your multiplication, then you need to count it when you're adding the decimal point back in!


Example 1
Example 2

Dividing decimals just needs an one extra step before and after actually dividing the number. Oddly enough, that step requires multiplication. (Very easy multiplication, too!) Consider this problem:
21.23 / 3.1

Off hand, it would be difficult to determine how many times 3.1 can go into 21.23. But we don't have to do that! Instead of dealing with the decimals, we are going to get rid of them! We'll do this by find the most number of decimal places in the numbers, and multiplying both numbers by a factor of 10. So, 21.23 has two decimal places (the 2 and the 3), whereas 3.1 only has one decimal place (the 1.) We'll use the 2 decimal places to multiply the number by. Since there are two decimal places, we will multiply each number by 100. (Number of zeros and number of decimal places are the same.) This is easy, as all we have to do is move the decimal places over.

After performing the multiplication of 100, we then have: 2123 / 310. This is easily done:

As you can see, we are not quite done, but we can continue doing normal division in order to find the answer to this problem!

And our final answer will depend on how precise we want the answer; here is one answer: 6.8483870967741935483870967741935. Of course, it is very unlikely that you would need that length and precision in an answer! Another reasonable (and correct) answer is 6.85.

And it's just that simple!

Find another math lesson at the Math Lesson and Tutorial Center!

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