LESSON: Decimal Place Value
READ: Express Numbers Given in Words or Hundredths Grids Using Decimal Place Value
Express Numbers Given in Words or Hundredths Grids Using Decimal Place Value
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.
Example
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 is 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.
Example
.43
This decimal has two decimal places. Each digit after the decimal is in a different place. We call these places place value. 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 in the hundredths place so that lets us know that this is hundredths.
Tens  Ones  
Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  4  3  

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.
Example
.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.