Place value allows us to represent large numbers using just ten digits. A digit’s value depends on its position, such as ones, tens, or hundreds. In this lesson, you will learn how place value works and how numbers are built from different digit positions.
Our number system is called 'base-ten' because it is built on groups of ten. Every time you move one position to the left in a number, the value of the place becomes ten times larger. This exponential growth allows us to represent massive quantities very efficiently.
A single digit on its own represents 'ones'. Once you collect ten of those ones, they bundle together to form a single 'ten'. When you collect ten of those bundles, they form a 'hundred'. This pattern continues forever, creating a consistent structure for all mathematics.
Understanding this scaling effect is the secret to mental math and estimation. It helps you realize that a 5 in the hundreds place is vastly more significant than a 9 in the ones place.
| Ones | Tens | Hundreds | Thousands |
|---|---|---|---|
| 1 | 10 | 100 | 1,000 |
| × 10 → | × 10 → | × 10 → |
Each place to the left is ten times greater than the one to its right.
100
We usually write numbers in standard form, like 352. While this is concise, it hides the 'true' value of the digits. Expanded form pulls the number apart to show the addition of each place value's total.
To write a number in expanded form, you look at each digit and multiply it by its place value. For the number 352, the 3 represents , the 5 represents , and the 2 represents . Adding them together gives you the full picture of the number's composition.
Using expanded form makes addition and subtraction much clearer because you can work with the hundreds, tens, and ones separately before combining them again.
4
hundreds7
tens9
onesExpanded form shows the sum of each digit's actual value.
479
Zero is perhaps the most important invention in the history of number systems. In place value, zero acts as a placeholder to keep other digits in their correct positions. Without zero, we could not tell the difference between 52 and 502.
In the number 502, the zero tells us that there are 'no tens' in this specific value. However, the zero is still doing the heavy lifting of pushing the 5 into the hundreds place. If the zero were missing, the 5 would slide into the tens place, and the number would change entirely.
Always be careful when writing numbers with zeros in the middle. Skipping a zero changes the scale of the entire number.
| Number | Hundreds | Tens | Ones |
|---|---|---|---|
| 502 | 5 | 0 | 2 |
| 52 | — | 5 | 2 |
Zero holds a place open so other digits stay in their correct positions.
Break down the number into its place value components and write it in expanded form.
The value of each digit and the expanded expression
Our system uses 10 digits (0-9) to represent all numbers.
A digit's value is found by multiplying the digit by its place (1, 10, 100, etc.).
Expanded form expresses a number as the sum of its parts.
Zero is a critical placeholder that maintains the value of larger digits.
Place value turns a simple list of symbols into a powerful tool for measuring the universe.
Use a place value chart to visualize columns for hundreds, tens, and ones.
Practice reading numbers aloud to hear the place values (e.g., 'four hundred' implies ).
Try writing your own age or house number in expanded form.
In the number , what is the value of the digit ?
Write the expanded form of .
What number is formed by hundreds, tens, and ones?
If you have the digits and , what is the largest three-digit number you can create using each digit once?
How do you value this lesson?