3.2: Numbers in Expanded Form
Remember Julie and her decimal from the last Concept? She had the decimal .67 written in her notebook. In that Concept, you learned how to write identify the decimal digits according to place value.
Well, how could you write this decimal out the long way if you don't use words?
This is called expanded form, and it is the focus of this Concept. At the end of the Concept, you will know how to write any decimal in expanded form.
Guidance
In the last Concept, you learned how to express decimals in words using a place value chart and in pictures using grids with tens and hundreds in them. We can also stretch out a decimal to really see how much value each digit of the decimal is worth.
This is called expanded form.
What is expanded form?
Expanded form is when a number is stretched out. Let’s look at a whole number first and then use this information with decimals.
265
If we read this number we can read it as two hundred and sixtyfive. We can break this apart to say that we have two hundreds, six tens and five ones. HUH??? What does that mean? Let’s look at our place value chart to help us make sense of it.
Hundred  Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


2  6  5  . 
If you look at the chart you can see how we got those values for each digit. The two is in the hundreds place. The six is in the tens place and the five is in the ones place. Here it is in expanded form.
2 hundreds + 6 tens + 5 ones
This uses words, how can we write this as a number?
200 + 60 + 5
Think about this, two hundred is easy to understand. Six tens is sixty because six times 10 is sixty. Five ones are just that, five ones.
This is our number in expanded form.
How can we write decimals in expanded form?
We can work on decimals in expanded form in the same way. First, we look at a decimal and put it into a place value chart to learn the value of each digit.
\begin{align*}.483\end{align*}
Hundred  Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  4  8  3 
Now we can see the value of each digit.
4 = four tenths
8 = eight hundredths
3 = 3 thousandths
We have the values in words, now we need to write them as numbers.
Four tenths = .4
Eight hundredths = .08
Three thousandths = .003
What are the zeros doing in there when they aren’t in the original number?
The zeros are needed to help us mark each place. We are writing a number the long way, so we need the zeros to make sure that the digit has the correct value. If we didn’t put the zeros in there, then .8 would be 8 tenths rather than 8 hundredths. Now, we can write this out in expanded form.
\begin{align*}.483\end{align*}
.4 + .08 + .003 = .483
This is our answer in expanded form.
Now let's practice. Write each number in expanded form.
Example A
\begin{align*}567\end{align*}
Solution: 500 + 60 + 7
Example B
\begin{align*}.345\end{align*}
Solution: .3 + .04 + .005
Example C
\begin{align*}.99\end{align*}
Solution: .9 + .09
Now let's apply this to the decimal that was in Julie's homework. Here is the original problem once again.
Well, in the last Concept, Julie had the decimal .67 written in her notebook. In that Concept, you learned how to write identify the decimal digits according to place value.
Well, how could you write this decimal out the long way if you don't use words?
Now let's write out .67 in expanded form. We have the tenths place and the hundredths place represented.
\begin{align*}.6 + .07 = .67\end{align*}
This is our answer.
Vocabulary
Here are the vocabulary words 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.
Write the following decimal in expanded notation.
\begin{align*}.4562\end{align*}
Answer
We have four places represented in this decimal. We have tenths, hundredths, thousandths and ten  thousandths represented in the decimal. We have to represent each of these places in the expanded form too.
\begin{align*}.4 + .05 + .006 + .0002 = .4562\end{align*}
This is our answer.
Video Review
Here is a video for review.
Khan Academy Decimal Place Value
Practice
Directions: Write each decimal out in expanded form.
1. .5
2. .7
3. .11
4. .05
5. .62
6. .78
7. .345
8. .98
9. .231
10. .986
11. .33
12. .821
13. .4321
14. .8739
15. .9327
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 to express numbers in expanded form given decimal form.
Concept Nodes:
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, ...