Place Value

Introduction

Numbers can be written in different ways depending on the situation. You might see a number written using digits, written in words, or broken apart to show the value of each digit.

These different forms all represent the same number, but each one helps us understand numbers in a different way.

Learning to convert between these forms is an important skill because it strengthens your understanding of place value and helps you read, write, and compare large numbers.

Standard Form

Standard form is the way numbers are normally written using digits.

Examples:

• 7
• 45
• 382
• 6,194
• 425,018

Standard form is the quickest and most common way to write numbers.

Examples:

Standard Form
19
357
8,204
91,560

Word Form

Word form writes a number using words instead of digits.

Examples:

Standard Form	Word Form
15	fifteen
82	eighty-two
306	three hundred six
2,519	two thousand five hundred nineteen
45,830	forty-five thousand eight hundred thirty

Notice:

• Hyphens are used in numbers like twenty-one and sixty-eight.
• In most mathematics textbooks, the word "and" is not used in whole numbers. (It is often reserved for decimals.)

Example:

• 325 → three hundred twenty-five

rather than

• three hundred and twenty-five

Expanded Form

Expanded form shows the value of each digit according to its place value.

For example:

425

becomes

400 + 20 + 5

Each digit is written as its actual value.

Understanding Expanded Form

Consider the number:

4,582

Each digit has a different place value.

Digit	Place Value	Value
4	Thousands	4,000
5	Hundreds	500
8	Tens	80
2	Ones	2

Expanded form:

4,000 + 500 + 80 + 2

More Examples

Standard Form	Expanded Form
326	300 + 20 + 6
1,408	1,000 + 400 + 8
5,672	5,000 + 600 + 70 + 2
82,451	80,000 + 2,000 + 400 + 50 + 1

Notice that place values with a zero are usually omitted.

Example:

7,045

Expanded form:

7,000 + 40 + 5

The hundreds place is zero, so it is not included.

Converting Between Forms

Let's look at how to convert between the different forms.

Standard → Word

4,218

↓

Four thousand two hundred eighteen

Standard → Expanded

4,218

↓

4,000 + 200 + 10 + 8

Word → Standard

Seven thousand fifty-three

↓

7,053

Expanded → Standard

9,000 + 500 + 40 + 6

↓

9,546

Why Expanded Form is Useful

Expanded form helps us:

• understand place value
• compare numbers
• perform calculations
• estimate answers
• identify the value of each digit

For example:

6,482

Expanded form:

6,000 + 400 + 80 + 2

We can immediately see that:

• the digit 6 represents 6,000
• the digit 4 represents 400
• the digit 8 represents 80
• the digit 2 represents 2

Common Mistakes

Be careful not to confuse the value of a digit with the digit itself.

Example:

In the number 5,321

The digit 3 does not represent three.

It represents:

300

Another common mistake is forgetting place values containing zeros.

Example:

2,006

Expanded form:

2,000 + 6

Not:

2 + 6

Real-World Applications

Writing numbers in different forms is useful in many everyday situations.

Examples include:

• Writing cheques
• Reading prices
• Recording population figures
• Understanding bank statements
• Completing government forms
• Reading scientific data
• Interpreting statistics

Understanding expanded form also helps when learning addition, subtraction, multiplication, and division.

Worked Examples

Example 1

Write 3,504 in word form.

Answer:

Three thousand five hundred four

Example 2

Write 6,721 in expanded form.

Answer:

6,000 + 700 + 20 + 1

Example 3

Write:

Eight thousand ninety-six

in standard form.

Answer:

8,096

Example 4

Write:

9,000 + 300 + 50 + 7

in standard form.

Answer:

9,357

Example 5

What is the value of the digit 8 in 48,271?

Answer:

8,000

Did You Know?

The Hindu-Arabic number system that we use today was developed over many centuries and is based on place value. This system made calculations much easier than older numeral systems, such as Roman numerals, and became the standard numbering system used around the world.

Key Terms

Term	Definition
Standard Form	Writing a number using digits.
Word Form	Writing a number using words.
Expanded Form	Writing a number as the sum of the value of each digit.
Place Value	The value of a digit based on its position in a number.
Digit	Any of the symbols 0–9 used to write numbers.

Key Takeaways

• Standard form uses digits to write numbers.
• Word form uses words to describe numbers.
• Expanded form shows the value of each digit according to its place value.
• You should be able to convert easily between standard, word, and expanded forms.
• Expanded form helps explain how our base-ten place value system works.
• Understanding different number forms strengthens place value skills and prepares you for more advanced mathematics.