## Decimals

**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.

### Division with Decimals

Another type of division you’ll encounter is division with decimals in both the divisor and the dividend. It might look something like this:

In this situation, you move the decimal place the number of spaces in the divisor until the decimal is at the end of the number; you move the decimal the same number of spaces in the dividend: this does NOT necessarily mean the decimal will land at the end of the dividend. Here’s an example:

Your new problem looks like this (note the change in decimal places in both the divisor and dividend):

Now you continue to work the problem out, remembering to bring your decimal up into your quotient at the appropriate time (it will be in red in the diagram).

Thus, your final answer is simply 16.

Let’s try one more example of moving the decimal over in order to solve the problem.

becomes

After the decimals are moved, it looks like this:

After you move the decimals, continue the problem, like this:

Thus, your final answer is 6.25.

Source: https://www.wyzant.com/resources/lessons/math/elementary_math/long_division/division_with_decimals

### Helpful Links:

1. Decimal Competency Packet https://www.northshore.edu/cas/pdf/decimals_comp_packet.pdf

2. Multiplying and Dividing Packet https://www.mathlearningcenter.org/sites/default/files/pdfs/SecB5SUP-A11_MultDivDecimals.pdf

### PDF/Worksheet Links:

1. Decimals Worksheet http://www.mathematicshed.com/uploads/1/2/5/7/12572836/decimals.pdf

2. Add, Subtract, Multiply, and Divide Decimals http://www.commoncoresheets.com/Math/Decimals/Add,%20Subtract,%20Multiply%20and%20Divide%20Decimals/English/All.pdf

3. Fractions and Decimals https://cdn.kutasoftware.com/Worksheets/PreAlg/Fractions%20and%20Decimals.pdf

4. Dividing Decimals http://www.tlsbooks.com/dividingdecimals.pdf

5. Adding and Subtracting Decimals http://getintoenergy.com/gie-math-program/AddingSubtractingDecimals-Quiz.pdf

6. Multiplying Decimals http://getintoenergy.com/gie-math-program/MultiplyingDecimals-Quiz.pdf

7. Multiplying Decimals Word Problems http://classroom.dickinsonisd.org/users/1691/docs/Practice/Mult_Div/Multiplying%20Decimals%20Word%20Problems.pdf

8. Comparing Decimals http://www.beaconlearningcenter.com/documents/731_01.pdf

9. Percentages to Fractions and Decimals http://teachingimage.com/percentages-worksheets/changing-percentages-into-fractions-and-decimals.pdf

10. Addition and Subtraction of Decimals http://static.3plearning.com/Worksheets_USA/Worksheets_fl_USA/G5_add_and_sub_of_decimals_worksheets_FL_USA.pdf

### Video Links:

1. Decimals https://youtu.be/tEJ_P7HyuFE

2. Ordering Decimals https://youtu.be/tRsUo5D3WSU

3. Adding and Subtracting Decimals https://youtu.be/72lQDdUBAZA

4. Changing a Number from Standard Form to Scientific Notation https://youtu.be/PGAfVihasAE

5. Converting Decimals to Fractions and Percentages https://youtu.be/wHQYU5-EduY

6. Converting Decimals to Improper Fractions and Mixed Numbers https://youtu.be/-sygkMilJKY

7. Dividing Decimals https://youtu.be/rcJx7u4bC5w

8. Multiplying Decimals https://youtu.be/m3fUb6mscFs

9. Scientific Notation https://youtu.be/Csfueab3GAc