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# Decimal Multiplication

## Multiply decimals like whole numbers, then place the decimal point.

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Decimal Multiplication

[Figure1]

### Introduction

Have you ever seen a dinosaur exhibit?

When the students in Mrs. Williams’s class arrive at the Science Museum, Jenna is very excited to learn that there is a dinosaur exhibit. In fact, it is a famous dinosaur exhibit. A set of dinosaur bones from a stegosaurus has been reconstructed and is on display. Jenna can’t wait to get to see it. She has a feeling that this is going to be her favorite part of the museum. Several other students are equally excited, so Mrs. Williams and the chaperones decide to go to the exhibit first and the split up into groups. When Jenna walks in, she is delighted. There before her eyes is a huge skeleton of a stegosaurus. After visiting the exhibit for a while, the students begin to move on. Mrs. Williams sees Jenna hesitate before leaving the exhibit. She walks over to her.

“Imagine, that dinosaur is about 5 and a half times as long as you are!” Mrs. Williams smiles. The students exit the exhibit hall, but Jenna pauses at the door. She has to think about this. In all of her excitement she forgot to find the information that actually says how long the stegosaurus actually is. Mrs. Williams’s words stay with her, “the dinosaur is 512\begin{align*}5 \frac{1}{2}\end{align*} times as long as you are.” Jenna knows that she is 434\begin{align*}4 \frac{3}{4}\end{align*} feet tall. If the dinosaur is 512\begin{align*}5 \frac{1}{2}\end{align*} times as long as she is, how long is the dinosaur? While Mrs. Williams and the chaperones start to split up the students, Jenna begins working some quick math on the back of her museum map.

She writes down the following figures.

5.50 ×\begin{align*}\times\end{align*} 4.75 =\begin{align*}=\end{align*} ______

If Jenna multiplies these numbers correctly, she will be able to figure out how long the stegosaurus is.

How long is he?

In this Concept you will learn all about multiplying decimals. When finished, you will know the length of the stegosaurus.

### Guided Learning

Sometimes, you will want to multiply two decimals without using a hundreds grid. You will want to use a method that is more efficient.

How can we multiply two decimals without using a hundreds grid?

One of the ways is to work on the equation just like we did when we multiplied decimals and whole numbers together.

First, we ignored the decimal point and multiplied just like it was two whole numbers that we were multiplying.

Second, we counted our decimal places and inserted the decimal into the product when we had finished multiplying.

We can approach two decimal multiplication in the same way.

2.3 ×\begin{align*}\times\end{align*} .42 = ______

To work on this problem, let’s start by writing it vertically instead of horizontally. Then we multiply.

Take a look at this problem.

2.3×.4246+  920926\begin{align*}2.3 \\ \underline{\times \quad .42} \\ 46 \\ \underline{+ \ \ 920} \\ 926\end{align*}

Now that we have finished the other steps, our final step is to put the decimal point in the correct spot. To do this, we need to count the decimal places in each number from right to left. The first number has one decimal place.

2.3

The second number has two decimal places.

.42

This is a total of three decimal places that need to be placed into the product.

How can we confirm our answer by using estimation?

When we multiply two decimals, sometimes we can use estimation to check our work.

3.8 ×\begin{align*}\times\end{align*} 3.3 =\begin{align*}=\end{align*} ______

We can start by rounding each decimal to the nearest whole number.

3.8 rounds to 4.

3.3 rounds to 3.

Next, we multiply 4 ×\begin{align*}\times\end{align*} 3 =\begin{align*}=\end{align*} 12.

Now let’s figure out our actual answer and see if our estimate is reasonable.

3.8× 3.3114+114012.54\begin{align*}3.8 \\ \underline{\times \quad \ 3.3} \\ 114 \\ \underline{+ \quad 1140} \\ 12.54\end{align*}

We can see that our estimate is reasonable because 12.54 is very close to 12.

Now it is your turn. Multiply the following decimals.

#### Example A

4.2 ×\begin{align*}\times\end{align*} 3.8 =\begin{align*}=\end{align*} _____

Solution: ______

#### Example B

2.1 ×\begin{align*}\times\end{align*} 1.5 =\begin{align*}=\end{align*} _____

Solution: _____

#### Example C

7.6 ×\begin{align*}\times\end{align*} 2.5 =\begin{align*}=\end{align*} _____

Solution: _____

Now that you have learned all about multiplying decimals, let’s help Jenna figure out the height of the stegosaurus. Here is the problem once again.

When the students in Mrs. Williams’s class arrive at the Science Museum, Jenna is very excited to learn that there is a dinosaur exhibit. In fact, it is a famous dinosaur exhibit. A set of dinosaur bones from a stegosaurus has been reconstructed and is on display. Jenna can’t wait to get to see it. She has a feeling that this is going to be her favorite part of the museum. Several other students are equally excited, so Mrs. Williams and the chaperones decide to go to the exhibit first and the split up into groups. When Jenna walks in she is delighted. There before her eyes is a huge skeleton of a stegosaurus. After visiting the exhibit for a while, the students begin to move on. Mrs. Williams sees Jenna hesitate before leaving the exhibit. She walks over to her. “Imagine, that dinosaur is about 5 and a half times as long as you are!” Mrs. Williams smiles.

The students exit the exhibit hall, but Jenna pauses at the door. She has to think about this. In all of her excitement she forgot to find the information that actually says how tall the stegosaurus actually is.

Mrs. Williams’s words stay with her, “the dinosaur is 512\begin{align*}5 \frac{1}{2}\end{align*} times as long as you are.”

Jenna knows that she is 434\begin{align*}4 \frac{3}{4}\end{align*} feet tall. If the dinosaur is 512\begin{align*}5 \frac{1}{2}\end{align*} times as long as she is, how long is the dinosaur?

While Mrs. Williams and the chaperones start to split up the students, Jenna begins working some quick math on the back of her museum map.

She writes down the following figures.

5.50 ×\begin{align*}\times\end{align*} 4.75 =\begin{align*}=\end{align*} ______

Let’s work on figuring out the height of the triceratops.

First, let’s estimate the product.

5.50 rounds up to 6.

4.75 rounds up to 5.

×\begin{align*}\times\end{align*} 5 is 30 feet tall.

The stegosaurus is approximately 30 feet long.

Now let’s figure out its actual height.

5.50×  4.75275038500+  220000261250\begin{align*}5.50 \\ \underline{\times \quad \ \ 4.75} \\ 2750 \\ 38500 \\ \underline{+ \ \ 220000} \\ 261250\end{align*}

Next, we add in the decimal point.

The stegosaurus is 26.13 feet long. He is a little longer than 23 feet.

Wow! That is one big dinosaur!!

Here is one for you to try on your own.

.134 ×\begin{align*}\times\end{align*} .567 =\begin{align*}=\end{align*} ______

This problem is going to have several steps to it because we are multiplying decimals that are in the thousandths place. That is alright though. We can do the same thing that we did with larger decimals. We can multiply the numbers as if they were whole numbers and then insert the decimal point at the end into the final product.

Let’s start by rewriting the problem vertically instead of horizontally.

.134× .5679388040+  6700075978\begin{align*}.134 \\ \underline{\times \quad \ .567} \\ 938 \\ 8040 \\ \underline{ + \ \ 67000} \\ 75978\end{align*}

Wow! There are a lot of digits in that number-now we need to put the decimal point into the product. There are three decimal places in the first number .134. There are three decimal places in the second number .567.

We need to count six decimal places from right to left in the product.

When this happens, we can add a zero in front of the digits to create the sixth place.

### Video Review

Here are videos for review.

### Practice Set

Directions: Multiply the following decimals.

1. 3.4 ×\begin{align*}\times\end{align*} .21 =\begin{align*}=\end{align*} ______

2. 2.7 ×\begin{align*}\times\end{align*} 4.5 =\begin{align*}=\end{align*} ______

3. .55 ×\begin{align*}\times\end{align*} .39 =\begin{align*}=\end{align*} ______

4. 1.7 ×\begin{align*}\times\end{align*} 8.2 =\begin{align*}=\end{align*} ______

5. 6.5 ×\begin{align*}\times\end{align*} 6.7 =\begin{align*}=\end{align*} ______

6. .23 ×\begin{align*}\times\end{align*} .28 =\begin{align*}=\end{align*} ______

7. 3.21 ×\begin{align*}\times\end{align*} .5 =\begin{align*}=\end{align*} ______

8. .2 ×\begin{align*}\times\end{align*} .66 =\begin{align*}=\end{align*} ______

9. .73 ×\begin{align*}\times\end{align*} .8 =\begin{align*}=\end{align*} ______

10. 5.43 ×\begin{align*}\times\end{align*} 3.21 =\begin{align*}=\end{align*} ______

11. 3.03 ×\begin{align*}\times\end{align*} .93 =\begin{align*}=\end{align*} ______

12. .97 \begin{align*}\times\end{align*} .8 \begin{align*}=\end{align*} ______

13. .215 \begin{align*}\times\end{align*} .5 \begin{align*}=\end{align*} ______

14. 14.3 \begin{align*}\times\end{align*} .4 \begin{align*}=\end{align*} ______

15. 17.7 \begin{align*}\times\end{align*} .8 \begin{align*}=\end{align*} ______

16. 29.3 \begin{align*}\times\end{align*} .56 \begin{align*}=\end{align*} ______

17. 12.7 \begin{align*}\times\end{align*} .9 \begin{align*}=\end{align*} ______

18. 52.4 \begin{align*}\times\end{align*} .59 \begin{align*}=\end{align*} ______

19. 22.1 \begin{align*}\times\end{align*} .4 \begin{align*}=\end{align*} ______

20. 34.03 \begin{align*}\times\end{align*} .28 \begin{align*}=\end{align*} ______

21.

Eric uses four 15.7 oz
cans of beef broth when he makes
his delicious barley soup. How many
total ounces of beef broth does he
use?

22.

Sarah works on a ranch in
the mountains. It takes her 1.75 hours to
drive to the nearest town and back. She usually
goes to town for supplies three times a week.

How much time does Sarah
spend driving if she takes 12 trips to
town each month?

23.

Tim wants to buy 24 heavy duty screws
from the local home improvement store. Each
screw costs $0.02. How much will Tim pay for the bolts? 24. Cathy is making costumes for this year’s fall production. The pattern she is using calls for 3.125 yards of fabric for each costume. How many yards of fabric will she need to make 12 costumes? 25. The family is going to the aquatic center for the afternoon. It costs$8.00  to get a pool pass that includes the slides. It costs \$6.50 to get a pool pass that doesn't include the slides. Three people want slide passes. Four people want passes without slides. How much will it cost the family to spend an afternoon at the aquatic center?

### Review

• We multiply two decimals without using a hundreds grid.
• One of the ways is to work on the equation just like we did when we multiplied decimals and whole numbers together.
• Ignore the decimal point and multiply just like it was two whole numbers.
• Count the decimal places and insert the decimal into the product.

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