Mathematics Essentials Q1

Express Numbers in Expanded Form Given Decimal 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.

Example

265

If we read this number we can read it as two hundred and sixty-five. We can break apart this to say that we have two hundreds, six tens and five ones. 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	.

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 can look at a decimal and put it into a place value chart to learn the value of each digit.

Example

.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 value 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 wouldn’t be 8 hundredths it would be 8 tenths.

Now, we can write this out in expanded form.

.483

.4 + .08 + .003 = .483

This is our answer in expanded form.