Numbers up to 10,000 - Expanded Form and Standard Form

A 4-digit number is made up of four places: Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). Imagine a place value chart where the leftmost column is the Thousands house and the rightmost is the Ones house.

The Face Value of a digit is the digit itself, regardless of its position. For example, in $4,582$, the face value of $5$ is simply $5$.

The Place Value of a digit depends on its position in the number. It is calculated by multiplying the digit by its position's value ($1, 10, 100, \text{ or } 1000$). In $4,582$, the place value of $5$ is $5 \times 100 = 500$.

Standard Form is the short way of writing a number using digits. In this form, we use commas to separate the thousands period from the rest, such as $7,314$.

Expanded Form is a way to write a number as the sum of the place values of its digits. It shows how much each digit is worth. For example, $6,235$ becomes $6,000 + 200 + 30 + 5$.

Zero ($0$) acts as a placeholder in both standard and expanded forms. If a place has a value of zero, like in $2,045$, we write $0$ in the hundreds place to keep the other digits in their correct positions.

Numbers can be visualized using Base-10 blocks: a large 3D cube represents $1,000$ units, a flat square represents $100$ units, a vertical rod represents $10$ units, and a small single cube represents $1$ unit.