P6 Mathematics - Term I

Topic 2: Whole Numbers

Lesson 2: Expanded Form of Numbers

Duration: 45 minutes

Today's Learning Objectives for Expanded Form

By the end of this lesson, you will be able to:

• Write numbers in expanded form
• Convert from expanded form to standard form
• Explain the relationship between position and value

Quick Review of the Seven Place Values

Quick! Name the seven place values:

Review: The Value of Each Digit

In the number 3,456,789:

What Happens When We Add the Values?

If we add all the values together:

3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9

= 3,456,789

This is called EXPANDED FORM!

A Picture of Expanded Form

Expanded form shows the value of each digit added together.

Two Ways to Write the Same Number

Standard Form: 3,456,789
(The normal way)

Expanded Form:
3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9

Both represent the same number!

Writing a Number in Expanded Form

Write 2,345,678 in expanded form

The Answer in Expanded Form

2,345,678 in expanded form:

2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8

✓ Check: Does it add up to 2,345,678? Yes!

What Happens with Zero Digits?

Write 5,030,402 in expanded form

Skipping the Zero Values Entirely

5,030,402 in expanded form:

5,000,000 + 30,000 + 400 + 2

We skip the zeros!
(Because 0 + anything = same number)

Your Turn: Write in Expanded Form

Write these numbers in expanded form:

1. 1,234,567
2. 8,006,050
3. 4,500,003

Work in your exercise book!

Checking Your Expanded Form Answers

1,234,567:
1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7

8,006,050:
8,000,000 + 6,000 + 50

4,500,003:
4,000,000 + 500,000 + 3

Converting Back: Expanded to Standard Form

Now let's go the other way!

4,000,000 + 200,000 + 50,000 + 3,000 + 600 + 70 + 1 = ?

Building the Standard Form Step by Step

Put each value in the place value chart:

Answer: 4,253,671

What If Some Place Values Are Missing?

7,000,000 + 50,000 + 200 + 6 = ?

Missing places (HTh, Th, T) are all 0.

Answer: 7,050,206

An Important Rule to Remember

When converting to standard form:

Fill in ZEROS for missing places!

A seven-digit number MUST have exactly 7 digits.

Your Turn: Convert to Standard Form

Convert to standard form:

1. 3,000,000 + 500,000 + 40,000 + 2,000 + 100 + 60 + 5 = ?

2. 6,000,000 + 80,000 + 9 = ?

3. 1,000,000 + 1,000 + 1 = ?

Checking Your Standard Form Answers

1. 3,000,000 + 500,000 + 40,000 + 2,000 + 100 + 60 + 5
= 3,542,165

2. 6,000,000 + 80,000 + 9
= 6,080,009

3. 1,000,000 + 1,000 + 1
= 1,001,001

Partner Practice: Test Each Other

Partner A: Write a 7-digit number in expanded form

Partner B: Convert it to standard form

Then switch roles! Check each other's work.

Why Expanded Form Is Worth Learning

• Helps us understand the VALUE of each digit
• Shows how numbers are built from place values
• Helps with mental math
• Makes addition and subtraction easier

Quick Quiz: Write in Expanded Form

Question 1:
Write 6,789,012 in expanded form.

Answer: The Expanded Form of 6,789,012

6,789,012 =

6,000,000 + 700,000 + 80,000 + 9,000 + 10 + 2

(Note: The hundreds place is 0, so we skip it)

Quick Quiz: Write in Standard Form

Question 2:
Write in standard form:

9,000,000 + 8,000 + 70 + 3 = ?

Answer: The Full Standard Form

9,000,000 + 8,000 + 70 + 3

= 9,008,073

Quick Quiz: Find a Missing Digit

Question 3:
A number in expanded form is:
5,000,000 + 200,000 + 40,000 + 6

What digit is in the thousands place?

Answer: The Thousands Place Is Zero

5,000,000 + 200,000 + 40,000 + 6

The thousands place has a 0!

Summary: Standard and Expanded Form

Standard Form: The normal way to write a number

• Example: 3,456,789

Expanded Form: Sum of place values

• Example: 3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9

Remember: Skip zeros in expanded form!

Key Vocabulary from Today's Lesson

• Standard form - Normal way to write a number
• Expanded form - Number as sum of place values
• Compose - Put parts together to make a number
• Decompose - Break a number into its parts

Tonight's Homework on Expanded Form

1. Write in expanded form: 4,567,890; 2,003,456; 7,800,007

2. Write in standard form:

   • 1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7
   • 6,000,000 + 400,000 + 5,000 + 30 + 2

Time: 20-25 minutes

Next Lesson Preview: Words and Figures

Tomorrow: Numbers in Words and Figures

We will practice:

• Reading large numbers aloud
• Writing numbers from words to figures and back

Example: 3,456,789 = "Three million, four hundred fifty-six thousand, seven hundred eighty-nine"

Great Work Today on Expanded Form!

You learned:

• How to write numbers in expanded form
• How to convert expanded form to standard form
• How to handle zeros in expanded form

Expanded form shows the building blocks of numbers!

Lesson Credits and Curriculum Source

Created: November 30, 2025
Based on: NCDC P6 Mathematics Curriculum - Topic 2: Whole Numbers

Source: National Curriculum Development Centre (NCDC), Uganda

Available from: https://ncdc.go.ug/