3.4: Combinations of Decimal Money Amounts
Julie and her friend Jose are working at an ice cream stand for the summer. They are excited because in addition to making some money for the summer, they also get to eat an ice cream cone every day. On the first day on the job, Julie is handed a cash register drawer that is filled with money. This is the drawer that she can collect money from sales in as well as make change for customers. Julie needs to count the amount of money in her drawer to be sure that it is accurate. Her boss Mr. Maguire tells her that her drawer should have sixtyfive dollars and seventyfive cents in it. He hands her a data sheet that she needs to write that money amount in on. Julie looks at the bills in her drawer and begins to count. She finds 220 dollar bills, 2ten dollar bills, 1five dollar bill and 2 quarters, 2 dimes and 1 nickel.
Now it is your turn to help.
In this Concept, you will learn all about decimals. One of the most common places that we see decimals is when we are working with money. Your work with decimals and place value will help Julie count her bills and change accurately.
Guidance
How can we apply what we have learned about decimals in a real world way?
Money is a way that we use decimals every day.
Let’s think about change.
Coins are cents. If we have 50 pennies, then we have 50 cents. It takes 100 pennies to make one dollar or one whole. Coins are parts of one dollar. We can represent coins in decimals.
Let’s start with pennies.
A penny is one cent or it is one out of 100. When we have a collection of pennies, we have so many cents out of 100.
5 pennies is 5 cents.
How can we write 5 cents as a decimal?
To do this, we need to think about 5 out of 100. We can say that 5 cents is 5 hundredths of a dollar since there are 100 pennies in one dollar.
Let’s write 5 cents as a decimal using place value.
Hundred  Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  5 
The five is in the hundredths box because five cents is five one hundredths of a dollar. We need to add a zero in the tenths box to fill the gap.
Hundred  Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  0  5 
Now we have converted 5 cents to a decimal.
How can we write 75 cents as a decimal?
First, think about what part of a dollar 75 cents is. Seventyfive cents is seventyfive out of 100. Now, we can put this into our place value chart.
Hundred  Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  7  5 
Now we have written it as a decimal.
What about when we have dollars and cents?
Suppose we have twelve dollars and fourteen cents. A dollar is a whole number amount. Dollars are found to the left of the decimal point. Cents are parts of a dollar. They are found to the right of the decimal point. How much money do we have? There is one ten and the two ones gives us twelve dollars. Then we have some change. One dime and four pennies is equal to fourteen cents.
Here are the numbers:
12 wholes
14 parts
Let’s put them in our place value chart.
Hundred  Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


1  2  .  1  4 
There is our money amount. Our answer is $12.14.
Notice that we added a dollar sign into the answer to let everyone know that we are talking about money.
Now let's practice.
Example A
Write three dollars and fifteen cents as a decimal.
Solution: $3.15
Example B
Write eighty  nine cents as a decimal.
Solution: .89
Example C
Write fifteen dollars and twenty  five cents as a decimal.
Solution: $15.25
Remember Julie and her cash drawer? Now that we know about decimals and money we are ready to help Julie with her ice cream shop dilemma.
Julie and her friend Jose are working at an ice cream stand for the summer. They are excited because in addition to making some money for the summer, they also get to eat an ice cream cone every day. On the first day on the job, Julie is handed a cash register drawer that is filled with money. This is the drawer that she can collect money from sales in as well as make change for customers. Julie needs to count the amount of money in her drawer to be sure that it is accurate.
Her boss Mr. Maguire tells her that her drawer should have sixtyfive dollars and seventyfive cents in it.
He hands her a data sheet that she needs to write that money amount in on. Julie looks at the bills in her drawer and begins to count. She finds 220 dollar bills, 2ten dollar bills, 1five dollar bill and 2 quarters, 2 dimes and 1 nickel.
First, let’s underline all of the important information. Now, let’s count the money she has in the drawer.
How many whole dollars are there?
There are 2 Twenty Dollar bills = $40 plus 2 Ten Dollar bills = $20 plus 1 Five Dollar bill = $5.
The total then is $40 + $20 + $5 = $65.
How many cents are there?
There are 2 Quarters at $25. each = $.50 plus 2 Dimes at $.10 each = $.20 plus 1 Nickel at $.05 = $.05
The total then is $.50 + $.20 + $.05 = $.75
Our next step is to write the wholes and parts in the place value chart. Then we will have this written as a money amount.
Hundred  Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


6  5  .  7  5 
Great work!! Julie has $65.75 in her drawer. That is the correct amount. She is ready to get to work.
Vocabulary
Here are the vocabulary words that are found in this concept.
 Whole number
 a number that represents a whole quantity
 Decimal
 a part of a whole
 Decimal point
 the point in a decimal that divides parts and wholes
 Expanded form
 writing out a decimal the long way to represent the value of each place value in a number
Guided Practice
Here is one for you to try on your own.
Maggie found a ten dollar bill, two five dollar bills, three quarters and two pennies in her wallet. How much money did she find? Write this amount as a decimal.
Answer
First, let's add the dollar amounts. We can write these amounts as decimals.
\begin{align*}10.00 + 5.00 + 5.00 = 20.00\end{align*}
Next we can add the change.
\begin{align*}.75 + .02 = .77\end{align*}
Now we can combine the amounts.
\begin{align*}20.00 + .77 = $20.77\end{align*}
This is our final answer.
Video Review
Here is a video for review.
Khan Academy: Decimal Place Value 2
http://www.teachertube.com/viewVideo.php?title=Money_Fractions_and_Decimals&video_id=59116&vpkey=4badb7d45d – This video is a short story and features two students learning about money with fractions and decimals.
Practice
Directions: Write the following money amounts as decimals.
1. Ten dollars and fifty cents
2. Five dollar bills, two quarters and three pennies
3. A twenty dollar bill, a ten dollar bill and three dimes
4. Fifteen nickels and two quarters
5. Six dollar bills, three quarters and a nickel
6. A dime and fifteen pennies
7. Two dollars, ten dimes and two quarters
8. Three quarters, five nickels and ten pennies
9. Sixteen dollar bills, two quarters, a nickel and ten pennies
10. A ten dollar bill, a five dollar bill, one quarter, three nickels, a dime and ten pennies
11. A ten dollar bill, a quarter, a dime, five nickels and fifteen pennies
12. A five dollar bill, two quarters, two dimes, a nickel and two pennies
13. Two dollar bills, a quarter and five pennies
14. Three dollar bills, a twenty dollar bill, two quarters and five dimes
15. A dollar, three quarters, two dimes, five nickels and two pennies
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Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of onetenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Decimal point
A decimal point is a period that separates the complete units from the fractional parts in a decimal number.Expanded Form
Expanded form refers to a base and an exponent written as repeated multiplication.Whole Numbers
The whole numbers are all positive counting numbers and zero. The whole numbers are 0, 1, 2, 3, ...Image Attributions
Here you'll learn how to write combinations of decimal money amounts.