3.1: Numbers with Decimal Place Value
Julie goes to the gas station with her father. She notices that the gas pump says 2.076 gallons, but she doesn't know how to say the number. What is the number written in words?
In this concept, you will learn about decimals.
Decimal and Place Values
There are a couple of ways to write a part of a whole. One of the ways is to write it is as a decimal. A decimal is a part of a whole.
An example of a decimal is 4.56. Notice that there is a point in the middle of the number. The point is called the decimal point. The decimal point divides 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.
Another example of a decimal is 0.43. This decimal has 0 whole parts and .43 parts of a whole.
This decimal has two decimal places. Each digit after the decimal is in a different place. These places are called place values.
To express a decimal using place value you need to use a place value chart.
Here is a place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


. 
Notice that the words after the decimal point each has a 'ths' in it. The 'ths' lets you know that you are working with a part of a whole.
You can take the decimal 0.43 and write it in the place value chart. Take the last example and write it in the place value chart. Above each number is a word. That word gives you 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 you know to read the entire number as hundredths.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  4  3 
To better understand what whole the decimal is a part of, you can use a hundreds grid. Notice that the number in the last example was 0.43 or 43 hundredths. The hundredths tells you that this is “out of one hundred.” Here is a picture of a hundreds grid.
Now show 43 hundredths of the hundreds grid. To do that, shade 43 squares. Each square is one part of one hundred.
If you look at a place value chart, you can see that there are other decimal names besides hundredths. You can also have tenths. An example of tenths is 0.5.
Here is a number that is fivetenths. You can create a picture of fivetenths using a grid of ten units. If you want to show 0.5 in this box, shade five boxes of the ten.
You can make pictures of tenths, hundredths, thousandths and tenthousandths.
Examples
Example 1
Earlier, you were given a problem about Julie and the number of gallons on the gas pump.
If there are 2.076 gallons, what is the number of gallons written in words?
First, place the number in a place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


2  .  0  7  6 
Next, write the name of the place value above the 6.
thousandths
Then, write the number in words.
two and seventysix thousandths
The answer is two and seventysix thousandths.
Example 2
Write the number as a decimal using the grid.
First, identify the type of grid.
hundreds grid
Next, count the shaded squares.
57
Then, write the decimal.
0.57
The answer is 0.57.
Example 3
Write the number as a decimal using the grid.
Fist, identify the type of grid.
hundreds grid
Next, count the shaded squares.
12
Then, write the decimal.
0.12
The answer is 0.12.
Example 4
Write the number as a decimal using the grid.
First, identify the type of grid.
hundreds grid
Next, count the shaded squares.
25
Then, write the decimal.
0.25
The answer is 0.25.
Example 5
Write the number in words and as a decimal using the grid.
First, identify the type of grid.
hundreds grid
Next, count the shaded squares.
80
Then, write the decimal.
0.80
The answer is 0.80.
Review
Look at each hundreds grid and write a decimal to represent the shaded portion of the grid.
Identify the place value of each of the digits in the following decimals.
 \begin{align*}.32\end{align*}
 \begin{align*}.43\end{align*}
 \begin{align*}.125\end{align*}
 \begin{align*}.6\end{align*}
 \begin{align*}.789\end{align*}
 \begin{align*}.209\end{align*}
 \begin{align*}.1\end{align*}
 \begin{align*}.009\end{align*}
 \begin{align*}.08\end{align*}
 \begin{align*}.003\end{align*}
Review (Answers)
To see the Review answers, open this PDF file and look for section 3.1.
Resources
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
In this concept, you will learn to express numbers using decimal place value.
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