Grade 4
The Human Knowledge Project
Unit 5 — Place Value and Large Numbers
Welcome to Grade 4 Mathematics!
As numbers become larger, understanding place value becomes even more important.
Place value helps us read, write, compare, estimate, and calculate with confidence.
Today you will strengthen your understanding of our base-ten number system.
Understanding Place Value
Each digit has a value based on its position.
For example:
482,731
| Digit | Place | Value |
|-------|--------|---------|
| 4 | Hundred Thousands | 400,000 |
| 8 | Ten Thousands | 80,000 |
| 2 | Thousands | 2,000 |
| 7 | Hundreds | 700 |
| 3 | Tens | 30 |
| 1 | Ones | 1 |
Moving one place to the left makes a digit worth ten times more.
Moving one place to the right makes it worth one-tenth as much.
Reading and Writing Large Numbers
Large numbers are easier to read when separated into periods.
Example:
5,248,916
Read as:
Five million, two hundred forty-eight thousand, nine hundred sixteen.
Practice reading numbers aloud to become more comfortable with them.
Expanded Form
Expanded form shows the value of each digit.
Example:
348,205
Expanded form:
300,000
+ 40,000
+ 8,000
+ 200
+ 5
Expanded form helps us understand how numbers are built.
Comparing Numbers
To compare numbers:
- Compare the greatest place value first.
- If those digits are equal, move to the next place.
Example:
562,413
and
561,982
Both begin with:
562 thousand
Since:
562,413 > 561,982
the first number is larger.
Use the symbols:
- >
- <
- =
to compare numbers correctly.
Rounding Numbers
Rounding gives an estimate that is easier to work with.
Example:
67,482
Rounded to the nearest thousand:
67,000
Rounded to the nearest ten thousand:
70,000
Always look at the digit immediately to the right of the place you are rounding.
Estimating
Estimation helps us judge whether answers are reasonable.
Example:
398 + 605
Estimate:
400 + 600 = 1,000
The exact answer should be close to 1,000.
Good mathematicians estimate before solving.
Activity
Write five large numbers.
For each number:
- read it aloud
- write it in expanded form
- round it to the nearest thousand
- compare it with another number
Explain your reasoning.
Practice
Answer these questions.
What determines a digit's value?
How do you read 4,608,315?
Write 507,042 in expanded form.
Which is greater?
829,451 or 829,145?
Why is estimation useful?
Review
Today you learned:
- place value determines a digit's value
- large numbers are organized into periods
- expanded form shows each digit's value
- numbers can be compared systematically
- rounding produces useful estimates
- estimation helps check answers
Understanding place value is the foundation for all work with larger numbers.
Looking Ahead
Next we will use place value to add, subtract, multiply, and divide larger numbers accurately and efficiently.