Fun with Numbers - Place Value and Face Value

Digits are the building blocks of numbers ($0, 1, 2, 3, 4, 5, 6, 7, 8, 9$). In a 3-digit number like $456$, there are three positions. A 4-digit number like $2,456$ extends this to four positions, reaching into the thousands.

Face Value is the actual value of the digit itself, which never changes regardless of its position. For example, in the number $7,842$, the face value of the digit $8$ is simply $8$. You can imagine the 'face' of the number looking the same no matter where it stands.

Place Value is the value a digit has because of its position in a number. In the number $5,321$, the digit $3$ is in the 'Hundreds' place, so its place value is $300$. As a digit moves to the left, its value increases ten times for every step.

The Place Value Chart is a visual grid used to organize numbers into columns: Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). For the number $6,713$, we visualize $6$ in the $Th$ column, $7$ in the $H$ column, $1$ in the $T$ column, and $3$ in the $O$ column.

Expanded Form is a way of writing a number as a sum of the place values of each digit. For example, the number $4,529$ is visualized as being pulled apart into $4,000 + 500 + 20 + 9$. This shows exactly what each digit is worth.

Standard Form (or Short Form) is the common way we write numbers by putting digits together in their correct places. For instance, if we have $7,000 + 300 + 5$, we combine them into the standard form $7,305$. Note how the $0$ acts as a placeholder for the missing tens.

The digit $0$ is a special placeholder. Its Face Value is always $0$, and its Place Value is also always $0$, no matter which column ($Th, H, T,$ or $O$) it occupies in the place value chart.

Successor and Predecessor are terms used for the numbers that come immediately after and before a given number. The Successor is $Number + 1$ (the next number), while the Predecessor is $Number - 1$ (the previous number).