Place Value

Introduction

Numbers are used every day to count, measure, compare, and solve problems. Whether reading the population of a country, the distance to another city, or the price of an item, understanding place value allows us to interpret numbers correctly.

Our number system is based on ten digits and follows a base-ten pattern. The position of each digit determines its value. Learning place value is one of the most important foundations in mathematics because it helps us read, write, compare, estimate, and calculate with numbers of any size.

Digits and Numbers

A digit is one of the ten symbols used to write numbers.

The ten digits are:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Digits can be combined to form numbers.

For example:

• 7 is a one-digit number.
• 42 is a two-digit number.
• 583 is a three-digit number.
• 9,418 is a four-digit number.

Definition:
A digit is a single symbol (0–9) used to write numbers.

The Base-Ten Place Value System

Our number system is called the base-ten system because each place is worth ten times the place to its right.

For example:

• 10 ones = 1 ten
• 10 tens = 1 hundred
• 10 hundreds = 1 thousand
• 10 thousands = 1 ten thousand

This repeating pattern continues for larger numbers.

Notice how the value of each digit changes depending on its position in the number.

Place Value Chart

Place	Value
Millions	1,000,000
Hundred Thousands	100,000
Ten Thousands	10,000
Thousands	1,000
Hundreds	100
Tens	10
Ones	1

Each move to the left makes the value 10 times larger.

Each move to the right makes the value 10 times smaller.

The Value of a Digit

A digit's value depends on where it appears in the number.

Consider the number:

4,582

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

Although the digit 5 is always the same symbol, its value changes depending on its position.

What is the value of the digit 7 in 57,321?

The 7 is in the thousands place.

Value:

7,000

Reading and Writing Numbers

Large numbers are separated into groups of three digits called periods.

For example:

5,472,318

can be divided into:

Period	Digits
Millions	5
Thousands	472
Ones	318

The number is read as:

Five million, four hundred and seventy-two thousand, three hundred and eighteen.

Understanding Periods

A period is a group of three digits.

Common periods include:

Period	Example
Ones	583
Thousands	24,583
Millions	7,024,583
Billions	4,007,024,583

Grouping digits into periods makes large numbers much easier to read.

 Write the following number in words: 8,105,046

Eight million, one hundred and five thousand, and forty-six.

Expanded Form

Expanded form shows the value of each digit separately.

Example:

6,483

Expanded form:

6,000 + 400 + 80 + 3

Expanded form helps us understand the contribution of each digit.

Write 43,207 in expanded form.

40,000 + 3,000 + 200 + 7

(The tens digit is 0, so it is not written.)

Representing Large Numbers

Place value helps us understand and compare large numbers.

Examples include:

• Population of Singapore: about 6 million people.
• Distance from Earth to the Moon: about 384,400 kilometres.
• A large stadium may hold 60,000 spectators.

Knowing place value helps us interpret the size and meaning of these numbers.

Comparing Numbers Using Place Value

To compare two numbers:

1. Compare the number of digits.
2. If they have the same number of digits, compare the leftmost digit.
3. Continue comparing each digit until they differ.

Example:

Compare:

482,715

479,999

Since:

482 thousand > 479 thousand,

482,715 is greater than 479,999.

Which number is greater?  3,456,781  OR  3,465,781?

Compare from left to right.

The millions are equal.

The hundred thousands are equal.

The ten thousands differ:

6 > 5

Therefore:

3,465,781 is greater.

Thinking a digit always has the same value.

Read numbers one period at a time.

Confusing the digit with its value.

Example:

In 8,531, the digit is 5, but its value is 500.

A zero means there is no value in that place.

Real-World Connection

Place value is used everywhere. Banks record balances that may reach millions of pounds or dollars, scientists work with very large and very small numbers, and governments use place value when reporting populations and national budgets. Understanding place value helps people read financial statements, maps, measurements, and statistical data accurately.

Did You Know?

The modern base-ten number system, including the use of zero as a place holder, developed from ideas originating in ancient India. It was later spread throughout the world by Arab mathematicians and eventually became the number system used almost everywhere today.

Key Terms

• Digit — one of the ten symbols (0–9) used to write numbers.
• Place value — the value of a digit determined by its position in a number.
• Base-ten system — a number system in which each place is worth ten times the place to its right.
• Expanded form — writing a number as the sum of the value of each digit.
• Period — a group of three digits in a large number.
• Ones, Tens, Hundreds — the first three place values in the base-ten system.

Key Takeaways

• Our number system uses ten digits and is based on the base-ten place value system.
• The value of a digit depends on its position within a number.
• Large numbers are organised into periods such as ones, thousands, and millions.
• Numbers can be written in standard form, word form, and expanded form.
• Understanding place value helps us read, write, compare, and interpret large numbers accurately.
• Place value is a fundamental mathematical concept used in everyday life, science, engineering, and finance.