Introduction

When working with large numbers, writing them as a sum of place values is sometimes helpful.

Let's write the following number as a sum of hundreds, tens, and ones:

{\color{purple}{6}}{\color{blue}{2}}{\color{red}{4}}

We start by writing down the place values.

Hundreds Tens Ones
{\color{purple}{6}} {\color{blue}{2}} {\color{red}{4}}

Next, we interpret each place value as a number:

  • {\color{purple}{6}} hundreds is {\color{purple}{6}}00

  • {\color{blue}{2}} tens is {\color{blue}{2}}0

  • {\color{red}{4}} ones is {\color{red}{4}}

Therefore, we can write 624 as a sum of hundreds, tens, and ones as follows:

{\color{purple}{6}}{\color{blue}{2}}{\color{red}{4}} = {\color{purple}{6}}00 + {\color{blue}{2}}0 + {\color{red}{4}}

Note the following:

  • The way we usually write numbers is called standard form. In the example above, 624 is a number written in standard form.

  • When a number is written as a sum of its place values, we say it's in expanded form. In the example above, 600+20+4 is a number written in expanded form.

FLAG
Example: Writing Numbers in Expanded Form

Express 4,385 in expanded form.

EXPLANATION

We need to convert the given number from standard form to expanded form.

Let's start by writing down the place values.

Thousands Hundreds Tens Ones
4 3 8 5

From the table:

  • 4 thousands is 4,000

  • 3 hundreds is 300

  • 8 tens is 80

  • 5 ones is 5

Therefore,

4,385 = 4,000 + 300 + 80 + 5.

FLAG
Practice: Writing Numbers in Expanded Form

Which expanded form is equivalent to the number $7, 392 ?$

a
 $7,000 + 300 + 90$
b
 $700,000 + 30,000 + 9,000 + 200$
c
 $700,000 + 3,000 + 900 + 2$
d
 $7,000 + 300 + 90 + 2$
e
 $70,000 + 3,000 + 900 + 20$
Practice: Writing Numbers in Expanded Form

$68,633=$

a
 $60,000 + 8,000 + 600 + 30 + 3$
b
 $80,000 + 6,000 + 600 + 30 + 3$
c
 $6,000 + 600 + 80 + 30 + 3$
d
 $600,000 + 80,000 + 6000 + 30 + 3$
e
 $6,000 + 800 + 60 + 3$
Converting a Number Containing Zeros to Expanded Form

Let's write the following number in expanded form:

8,{\color{blue}0}94

Notice that this number has a {\color{blue}0} in the hundreds place.

To write this number in expanded form, we write down the place values.

Thousands Hundreds Tens Ones
8 \color{blue}0 9 4

Next, we interpret each place value as a number:

  • 8 thousands is 8,000

  • \color{blue}0 hundreds is {\color{blue}0}

  • 9 tens is 90

  • 4 ones is 4

Therefore, we get 8,094 = 8,000 + {\color{blue}0} + 90 + 4.

Since adding \color{blue}0 to a number doesn't change it, we can remove this zero. So, our final answer is

8,094 = 8,000 + 90 + 4.

FLAG
Example: Writing Numbers Containing Zeros in Expanded Form

Write 900,010 in expanded form.

EXPLANATION

We need to convert the given number from standard form to expanded form.

Let's start by writing down the place values.

Hundred-Thousands Ten-Thousands Thousands Hundreds Tens Ones
9 0 0 0 1 0

From the table:

  • 9 hundred-thousands is 900,000

  • 0 ten-thousands is 0

  • 0 thousands is 0

  • 0 hundreds is 0

  • 1 ten is 10

  • 0 ones is 0

Therefore,

\begin{align*} 900,010 &=\\[3pt] 900,000+0 + 0 + 0 +10+ 0&=\\[3pt] 900,000+10&. \end{align*}

FLAG
Practice: Writing Numbers Containing Zeros in Expanded Form

Which expanded form is equivalent to the number $8,603?$

a
 $8,000 + 600 + 3$
b
 $80,000 + 6,000 + 30$
c
 $800 + 60 + 3$
d
 $8,000 + 600 + 30$
e
 $800 + 30 + 6$
Practice: Writing Numbers Containing Zeros in Expanded Form

$240,405=$

a
 $200,000+400,000 + 40 + 5$
b
 $200,000+400 + 40+ 5$
c
 $200,000+40,000 + 400 + 5$
d
 $2,000,000+40,000 + 4000 + 5$
e
 $2,000,000+400,000 + 40 + 5$
Example: Determining Missing Parts of an Expanded Form

What is the missing number in the following equality?

150,210 = 100,000 + 50,000 + \underline{\phantom{{}^{55555555555}}} + 10.

EXPLANATION

Let's start by writing down the place values.

Hundred-Thousands Ten-Thousands Thousands Hundreds Tens Ones
1 5 0 2 1 0

From the table:

  • 1 hundred-thousand is 100,000

  • 5 ten-thousands is 50,000

  • 0 thousands is 0

  • 2 hundreds is \color{blue}200

  • 1 ten is 10

  • 0 ones is 0

As a result,

150,210 = 100,000 + 50,000 + \bbox[2pt,Gainsboro]{\color{blue}200} + 10

Therefore, the missing number is 200.

FLAG
Practice: Determining Missing Parts of an Expanded Form

$2,361 = 2,000 + 300 \: +$

a
b
c
d
e
Practice: Determining Missing Parts of an Expanded Form

$504,534 = 500,000 \:+$

a
b
c
d
e
Practice: Determining Missing Parts of an Expanded Form

$1,097,401 = 1,000,000 +\:\:$

a
b
c
d
e
Flag Content
Did you notice an error, or do you simply believe that something could be improved? Please explain below.
SUBMIT
CANCEL