Number System - Place Value and Face Value

Face Value: The face value of a digit in a number is the value of the digit itself. It never changes, regardless of where it is placed in the number. For example, in $8,452$, the face value of $4$ is simply $4$.

Place Value: The place value is the value represented by a digit in a number on the basis of its position. Imagine a chart where columns are arranged from right to left as Ones ($O$), Tens ($T$), Hundreds ($H$), Thousands ($Th$), and Ten-Thousands ($T-Th$). As you move one place to the left, the value becomes $10$ times greater.

Indian Place Value System: In this system, we use periods like Ones, Thousands, and Lakhs to read large numbers easily. The Ones period has three places ($H, T, O$), while the Thousands period has two ($T-Th, Th$). Visually, we use commas to separate these periods, such as $54,321$.

Calculating Place Value: To find the place value of a digit, multiply the Face Value of the digit by the value of the position it occupies. The formula is $Place Value = Face Value \times Value of the Position$.

The Zero Property: The digit $0$ is unique because its face value is $0$ and its place value is also always $0$, no matter which position (Ones, Tens, or Thousands) it occupies in a number.

Expanded Form: This is a way to write a number as the sum of the place values of its digits. For example, the number $6,345$ can be visualized as being broken down into $6000 + 300 + 40 + 5$.

Successive Place Values: Each place in the place value chart is $10$ times the value of the place to its immediate right. For instance, $1 \text{ Ten} = 10 \times 1 \text{ One}$ and $1 \text{ Hundred} = 10 \times 1 \text{ Ten}$.