Numbers in Expanded Form
Jen Kershaw, M.ed
Kimberly Hopkins
Jen Kershaw
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Printed: June 19, 2016
AUTHORS
Jen Kershaw, M.ed
Kimberly Hopkins
Jen Kershaw
www.ck12.org
Chapter 1. Numbers in Expanded Form
C HAPTER
1 Numbers in Expanded Form
In this concept, you will learn how to write a decimal in expanded form.
Kailey is learning how to write numbers in expanded form. Her teacher gives her a quarter and asks her to write the
numerical value of the quarter. Kailey writes $0.25. Her teacher tells her that she’s right, then asks her to write the
value in expanded form. How can Kailey write the value in expanded form?
In this concept, you will learn how to write a decimal in expanded form.
Decimals in Expanded Form
You can stretch out a decimal to see how much value each digit of the decimal is worth. This is called expanded
form. Let’s look at a whole number first then use this information with decimals.
265
You can break this apart to say that you have two hundreds, six tens and five ones. Look at a place value chart to
make sense of it.
TABLE 1.1:
Hundred
Tens
Ones
2
6
5
Tenths
Hundredths Thousandths Ten
Thousandths
.
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
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This uses words, now let’s write this as a number.
200 + 60 + 5
This is the expanded form.
You can work on decimals in expanded form in the same way. First, look at a decimal and put it into a place value
chart to learn the value of each digit. Let’s look at 0.483.
TABLE 1.2:
Hundred
Tens
Ones
Tenths
.
4
Hundredths Thousandths Ten
Thousandths
8
3
Now you can see the value of each digit.
4 = four tenths
8 = eight hundredths
3 = 3 thousandths
Translate the words to numbers.
Four tenths = 0.4
Eight hundredths = 0.08
Three thousandths = 0.003
The zeros after the decimal are needed to mark each place and make sure that the digit has the correct value. Without
the zeros 0.08 would be 8 tenths rather than 8 hundredths.
Now, let’s write this out in expanded form.
0.483 becomes 0.4 + 0.08 + 0.003 = 0.483.
Examples
Example 1
Earlier, you were given a problem about Kailey and the quarter.
What is the value of the quarter written in expanded form?
First, write the number in the place value chart.
TABLE 1.3:
Hundred
Tens
Ones
Tenths
.
Next, write the value of each number.
2 = two tenths
5 = five hundredths
Then, write the number in expanded form.
0.2 + 0.05
2
2
Hundredths Thousandths Ten
Thousandths
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Chapter 1. Numbers in Expanded Form
The answer is 0.2 + 0.05.
Example 2
Write 0.456 in expanded form.
First, write the number in the place value chart.
TABLE 1.4:
Hundred
Tens
Ones
Tenths
.
4
Hundredths Thousandths Ten
Thousandths
5
6
Next, write the value of each number.
4 = four tenths
5 = five hundredths
6 = six thousandths
Then, write the number in expanded form.
0.4 + 0.05 + 0.006
The answer is 0.4 + 0.05 + 0.006.
Example 3
Write 0.567 in expanded form.
First, write the number in the place value chart.
TABLE 1.5:
Hundred
Tens
Ones
Tenths
.
5
Hundredths Thousandths Ten
Thousandths
6
7
Next, write the value of each number.
5 = five tenths
6 = six hundredths
7 = seven thousandths
Then, write the number in expanded form.
0.5 + 0.06 + 0.007
The answer is 0.5 + 0.06 + 0.007.
Example 4
Write 0.345 in expanded form.
First, write the number in the place value chart.
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TABLE 1.6:
Hundred
Tens
Ones
Tenths
.
3
Hundredths Thousandths Ten
Thousandths
4
5
Next, write the value of each number.
3 = three tenths
4 = four hundredths
5 = five thousandths
Then, write the number in expanded form.
0.3 + 0.04 + 0.005
The answer is 0.3 + 0.04 + 0.005.
Example 5
Write 0.99 in expanded form.
First, write the number in the place value chart.
TABLE 1.7:
Hundred
Tens
Ones
Tenths
.
Next, write the value of each number.
9 = nine tenths
9 = nine hundredths
Then, write the number in expanded form.
0.9 + 0.09
The answer is 0.9 + 0.09.
Review
Write each decimal in expanded form.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
4
.5
.7
.11
.05
.62
.78
.345
.98
.231
.986
9
Hundredths Thousandths Ten
Thousandths
9
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11.
12.
13.
14.
15.
Chapter 1. Numbers in Expanded Form
.33
.821
.4321
.8739
.9327
Review (Answers)
To see the Review answers, open this PDF file and look for section 3.2.
Resources
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