Uganda NCDC Lesson Plans

Expanded Form of Numbers
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P6 Mathematics - Term I

Topic 2: Whole Numbers

Lesson 2: Expanded Form of Numbers

Duration: 45 minutes

Learning Objectives

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

Review: Place Values

Quick! Name the seven place values:

M HTh TTh Th H T O
Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones

Review: Value of Each Digit

In the number 3,456,789:

Digit Place Value Value
3 Millions 3,000,000
4 Hundred Thousands 400,000
5 Ten Thousands 50,000
6 Thousands 6,000
7 Hundreds 700
8 Tens 80
9 Ones 9

What is Expanded Form?

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!

Expanded Form

Expanded form shows the value of each digit added together.

Two Ways to Write a 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!

Let's Practice: Step by Step

Write 2,345,678 in expanded form

Digit Place Value
2 M 2,000,000
3 HTh 300,000
4 TTh 40,000
5 Th 5,000
6 H 600
7 T 70
8 O 8

Answer

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 About Zeros?

Write 5,030,402 in expanded form

Digit Place Value
5 M 5,000,000
0 HTh 0
3 TTh 30,000
0 Th 0
4 H 400
0 T 0
2 O 2

Zeros in Expanded Form

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 these numbers in expanded form:

  1. 1,234,567

  2. 8,006,050

  3. 4,500,003

Work in your exercise book!

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 → Standard

Now let's go the other way!

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

Step by Step

Put each value in the place value chart:

M HTh TTh Th H T O
4 2 5 3 6 7 1

Answer: 4,253,671

Missing Place Values

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

Which places are missing?

  • Hundred Thousands → 0
  • Thousands → 0
  • Tens → 0
M HTh TTh Th H T O
7 0 5 0 2 0 6

Answer: 7,050,206

Important Rule!

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:

  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 = ?

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

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 is Expanded Form Useful?

  • 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

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

Answer 1

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

Question 2:
Write in standard form:

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

Answer 2

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

M HTh TTh Th H T O
9 0 0 8 0 7 3

= 9,008,073

Quick Quiz

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

What digit is in the thousands place?

Answer 3

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

M HTh TTh Th H T O
5 2 4 0 0 0 6

The thousands place has a 0!

Summary

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

  • 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

Homework

  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

Tomorrow: Numbers in Words and Figures

We will practice:

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

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

Great Work Today!

You learned:

  • ✅ How to write numbers in expanded form
  • ✅ How to convert expanded form to standard form
  • ✅ How to handle zeros in expanded form
  • ✅ Why expanded form is useful

Expanded form shows the building blocks of numbers!

Credits

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/