3.1: Numbers with Decimal Place Value
Have you ever wanted a summer job? Have you ever had a summer job?
Julie wants a job for the summer vacation. Most of her friends have already found a place to work, and Julie isn't sure that she is going to get one.
Just when Julie was ready to give up hope, she saw a sign for an ice cream stand. It looked like the perfect job. Julie put in an application and waited for the phone to ring.
While she was waiting, she decided to work on her math homework.
"Decimals," said Julie with a sigh.
The first problem that she saw showed the following decimal.
\begin{align*}.67\end{align*}
What does this mean? This Concept is all about decimals and place value. By the end of the Concept, you will understand how to put the pieces together to understand this decimal better.
Guidance
Up until this time in mathematics, we have been working mainly with whole numbers. A whole number represents a whole quantity. There aren’t any parts when we work with a whole number.
When we have a part of a whole, we can write it in a couple of different ways.
One of the ways that we write it is as a decimal.
A decimal is a part of a whole.
4.56
This decimal has parts and wholes in it. Notice that there is a point in the middle of the number.
This is called the decimal point.
The decimal point helps us to divide the number between wholes and parts. To the right of the decimal point are the parts of the whole and to the left of the decimal point is the whole number.
We can have numbers with parts and wholes in them, and we can have numbers that are just decimals.
.43
This decimal has two decimal places. Each digit after the decimal is in a different place. We call these places place values. When you were working with whole numbers you used place value too, but this is a new place value system that includes decimals.
How can we express a decimal using place value?
To express a decimal using place value we need to use a place value chart. This gives us an idea about the worth of the decimal.
Here is a place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


. 
Notice that if we take the last example and write it in the place value chart above each number is a word. That word gives us the value of that digit according to its place in the chart. This number is fortythree hundredths. The three is the last number, and is in the hundredths place so that lets us know to read the entire number as hundredths.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  4  3 
Hmmm. Think about that, the word above each digit has a name with a THS in it. The THS lets us know that we are working with a part of a whole.
What whole is this decimal a part of?
To better understand what whole the decimal is a part of, we can use a picture. We call these grids or hundreds grids. Notice that the number in the last example was .43 or 43 hundredths. The hundredths lets us know that this is “out of one hundred.” Here is a picture of a hundreds grid.
Now we want to show 43 hundredths of the hundreds grid. To do that, we shade 43 squares. Each square is one part of one hundred.
What about tenths?
If you look at a place value chart, you can see that there are other decimal names besides hundredths. We can also have tenths.
.5
Here is a number that is fivetenths. We can create a picture of fivetenths using a grid of ten units.
If we want to show .5 in this box, we can see that tenths means 5 out of 10. We shade five boxes of the ten.
We can make pictures of tenths, hundredths, thousandths and tenthousands. Tenthousandths, whew! Think about how tiny those boxes would be.
Now let's practice. Write each number in words and as a decimal using each grid.
Example A
Solution: .12
Example B
Solution: .25
Example C
Solution: .80
Now let's think about Julie and the decimals. Here is the original situation from the beginning of the Concept.
Julie wants a job for the summer vacation. Most of her friends have already found a place to work, and Julie isn't sure that she is going to get one. Have you ever wanted a job? Have you ever had one?
Just when Julie was ready to give up hope, she saw a sign for an ice cream stand. It looked like the perfect job. Julie put in an application and waited for the phone to ring.
While she was waiting, she decided to work on her math homework.
"Decimals," said Julie with a sigh.
The first problem that she saw showed the following decimal.
\begin{align*}.67\end{align*}
If you think about this Concept, this decimal has two places represented. It has a tenths place and a hundredths place represented. The six is the in the tenths place and the seven is in the hundredths place. In a later Concept, you will look at how these places help when we work with money.
Vocabulary
Here are the vocabulary words used 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
Guided Practice
Here is one for you to try on your own.
How would you represent 57 hundredths on the following grid?
Answer
First, this isn't an ordinary grid, it is a hundreds grid. We can represent 57 hundredths by filling in 57 of the squares on this grid. Then we could write the following decimal.
\begin{align*}.57\end{align*}
Video Review
Here is a video for review.
James Sousa, Write a Number in Decimal Notation from Words
Practice
Directions: Look at each hundreds grid and write a decimal to represent the shaded portion of the grid.
1.
2.
3.
4.
5.
Directions: Identify the place value of each of the digits in the following decimals.
6. \begin{align*}.32\end{align*}
7. \begin{align*}.43\end{align*}
8. \begin{align*}.125\end{align*}
9. \begin{align*}.6\end{align*}
10. \begin{align*}.789\end{align*}
11. \begin{align*}.209\end{align*}
12. \begin{align*}.1\end{align*}
13. \begin{align*}.009\end{align*}
14. \begin{align*}.08\end{align*}
15. \begin{align*}.003\end{align*}
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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.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 to express numbers using decimal place value.