4.11: Decimal Quotients Using Zero Placeholders
Remember how Mrs. Andersen had to give out change in the last Concept? Well, she isn't finished yet. Take a look.
When Mrs. Andersen got back to the bus, she found that the museum clerk had given her an additional 11 dollars in change. This 11 dollars would need to be distributed between the students. Since 22 students went on the trip, Mrs. Andersen would need to give some change to everyone.
"It's a good thing that she gave me a lot of change," Mrs. Andersen thought to herself.
How much of the 11 dollars should each of the 22 students receive?
You have been learning how to divide decimals. Now you are going to learn how to divide decimals when you need zero placeholders.
This Concept will teach you all that you need to know. Then you will be able to help Mrs. Anderson divide up the money.
Guidance
In our last Concept, you learned to divide a decimal by a whole number. Remember here that the divisor is the whole number which goes outside of the division box and the dividend is the decimal that goes inside of the division box.
The problems in the last Concept were evenly divisible by their divisors. This means that at the end there wasn’t a remainder.
How do we divide decimals by whole numbers when there is a remainder?
14.9 \begin{align*}\div\end{align*}
The first thing that we can do is to set up this problem in a division box. The five is the divisor and the 14.9 is the dividend.
\begin{align*}5 \overline{)14.9 \;}\end{align*}
Next we start our division. Five goes into fourteen twice, with four left over. Then we bring down the 9. Five goes into 49, 9 times with four left over. Before you learned about decimals, that 4 would just be a remainder.
\begin{align*}& \overset{2.9 \ \ } { \ 5 \overline{ ) {14.9}} \ {r \ 4} \;}\\ & \underline{ \ 10 \ \; \;}\\ & \quad \ 49\\ & \ \underline{ \ 45 \; \;}\\ & \quad \ \ \ 4 \end{align*}
However, when we work with decimals, we don’t want to have a remainder. We can use a zero as a placeholder.
Here, we can add a zero to the dividend and then see if we can finish the division. We add a zero and combine that with the four so we have 40. Five divides into forty eight times. Here is what that would look like.
\begin{align*}& \overset{ \quad 2.98}{5 \overline{ ) {14.90 \;}}}\\ & \underline{10 \ \ }\\ & \quad \ 49\\ & \ \ \underline{45 \ }\\ & \qquad 40 \\ & \ \ \ \ \underline{40 \ }\\ & \qquad \ \ 0 \end{align*}
Our final answer is 2.98.
When working with decimals, you always want to add zeros as placeholders so that you can be sure that the decimal is as accurate as it can be. Remember that a decimal shows a part of a whole. We can make that part as specific as necessary.
Try a few of these on your own. Be sure to add zero placeholders as needed.
Example A
13.95 \begin{align*}\div\end{align*}
Solution: 2.325
Example B
2.5 \begin{align*}\div\end{align*}
Solution: 1.25
Example C
1.66 \begin{align*}\div\end{align*}
Solution: .415
Now that you know how to work with zero placeholders, let's go back to Mrs. Andersen and the change. Here is the original problem once again.
When Mrs. Andersen got back to the bus, she found that the museum clerk had given her an additional 11 dollars in change. This 11 dollars would need to be distributed between the students. Since 22 students went on the trip, Mrs. Andersen would need to give some change to everyone.
"It's a good thing that she gave me a lot of change," Mrs. Andersen thought to herself.
How much of the 11 dollars should each of the 22 students receive?
To figure this out, we must first set up the math problem.
11 \begin{align*}\div\end{align*}
Now we divide 11 by 22.
\begin{align*}22 \overline{)11 \;}\end{align*}
\begin{align*}& \overset{ \quad .50}{22 \overline{ ) {11.00 \;}}}\\\end{align*}
You can see that we had to add a decimal point and two zeros.
Each student will receive .50 change.
Vocabulary
Here are the vocabulary words in this Concept.
 Divide
 to split up into groups evenly.
 Divisor
 a number that is doing the dividing. It is found outside of the division box.
 Dividend
 the number that is being divided. It is found inside the division box.
 Quotient
 the answer to a division problem
Guided Practice
Here is one for you to try on your own.
Divide the following numbers.
\begin{align*}3 \div 8\end{align*}
Answer
To divide 3 by 8, we have to add a decimal point and a zero right away. Here is how we can rewrite the problem.
\begin{align*}3.0 \div 8\end{align*}
Now we can divide. We'll need to add two more zeros.
Our final answer is .375</math>
Video Review
Here are videos for review.
Khan Academy Dividing Decimals 2
Practice
Directions: Divide each decimal by each whole number. Add zero placeholders when necessary.

\begin{align*}5 \overline{)17.5 \;}\end{align*}
5)17.5¯¯¯¯¯¯¯¯ 
\begin{align*}8 \overline{)20.8 \;}\end{align*}
8)20.8¯¯¯¯¯¯¯¯ 
\begin{align*}4 \overline{)12.8 \;}\end{align*}
4)12.8¯¯¯¯¯¯¯¯ 
\begin{align*}2 \overline{)11.2 \;}\end{align*}
2)11.2¯¯¯¯¯¯¯¯ 
\begin{align*}4 \overline{)14.4 \;}\end{align*}
4)14.4¯¯¯¯¯¯¯¯ 
\begin{align*}5 \overline{)27.5 \;}\end{align*}
5)27.5¯¯¯¯¯¯¯¯ 
\begin{align*}6 \overline{)13.8 \;}\end{align*}
6)13.8¯¯¯¯¯¯¯¯  \begin{align*}7 \overline{)16.8 \;}\end{align*}
 \begin{align*}7 \overline{)23.1 \;}\end{align*}
 \begin{align*}6 \overline{)54.6 \;}\end{align*}
 \begin{align*}8 \overline{)41.6 \;}\end{align*}
 \begin{align*}9 \overline{)86.4 \;}\end{align*}
 \begin{align*}10 \overline{)52 \;}\end{align*}
 \begin{align*}10 \overline{)67 \;}\end{align*}
 \begin{align*}11 \overline{)57.2 \;}\end{align*}
 \begin{align*}10 \overline{)96 \;}\end{align*}
 \begin{align*}8 \overline{)75.2 \;}\end{align*}
 \begin{align*}9 \overline{)32.4 \;}\end{align*}
 \begin{align*}12 \overline{)38.4 \;}\end{align*}
 \begin{align*}12 \overline{)78 \;}\end{align*}
Divide
To divide is split evenly into groups. The result of a division operation is a quotient.Dividend
In a division problem, the dividend is the number or expression that is being divided.divisor
In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression , 6 is the divisor and 152 is the dividend.Quotient
The quotient is the result after two amounts have been divided.Image Attributions
Description
Learning Objectives
Here you'll learn how to find decimal quotients using zero placeholders.