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Numbers in Expanded Form

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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 Numbers with Decimal Place Value 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 sixty-five. 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.

.483

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.

.483

.4 + .08 + .003 = .483

This is our answer in expanded form.

Now let's practice. Write each number in expanded form.

Example A

567

Solution: 500 + 60 + 7

Example B

.345

Solution: .3 + .04 + .005

Example C

.99

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.

.6 + .07 = .67

This is our answer.

Vocabulary

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.

.4562

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.

.4 + .05 + .006 + .0002 = .4562

This is our answer.

Video 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

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