# Numbers in Expanded Form

## Expand given numbers by value of place up to the ten-thousandths.

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Numbers 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.

Hundred Tens Ones Tenths Hundredths Thousandths

Ten

Thousandths

2 6 5 .

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, 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.

Hundred Tens Ones Tenths Hundredths Thousandths

Ten

Thousandths

. 4 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.

Hundred Tens Ones Tenths Hundredths Thousandths

Ten

Thousandths

. 2 5

Next, write the value of each number.

2 = two tenths

5 = five hundredths

Then, write the number in expanded form.

0.2 + 0.05

The answer is 0.2 + 0.05.

#### Example 2

Write 0.456 in expanded form.

First, write the number in the place value chart.

Hundred Tens Ones Tenths Hundredths Thousandths

Ten

Thousandths

. 4 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.

Hundred Tens Ones Tenths Hundredths Thousandths

Ten

Thousandths

. 5 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.

Hundred Tens Ones Tenths Hundredths Thousandths

Ten

Thousandths

. 3 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.

Hundred Tens Ones Tenths Hundredths Thousandths

Ten

Thousandths

. 9 9

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. .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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### Vocabulary Language: English

TermDefinition
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 one-tenth. 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, ...