Numbers up to 10,000 - Successor and Predecessor

Definition of Successor: The successor of a number is the value that comes immediately after it. On a horizontal number line, the successor is always one step to the right of the given number.

Calculating Successor: To find the successor of any number up to $10,000$, you add $1$ to the value in the ones place. For example, the successor of $4,562$ is $4,563$. Visualize this as adding one single unit block to a base-ten block representation.

Definition of Predecessor: The predecessor of a number is the value that comes just before it. On a number line, the predecessor is located exactly one unit to the left of the given number.

Calculating Predecessor: To find the predecessor, you subtract $1$ from the given number. If you have a collection of $3,000$ beads and remove one, the remaining $2,999$ beads represent the predecessor.

The 9-to-0 Successor Rule: When a number ends in $9$, the successor involves a carry-over to the next place value. For example, the successor of $1,299$ is $1,300$. This is like a car odometer where $9$ rolls over to $0$ and the next digit increases.

The 0-to-9 Predecessor Rule: When a number ends in $0$, finding the predecessor requires regrouping across place values. For instance, the predecessor of $5,000$ is $4,999$. Imagine an abacus where you must take a bead from the thousands rod to populate the hundreds, tens, and ones rods.

Boundary Numbers: The largest 4-digit number is $9,999$. Its successor is $10,000$, which is the smallest 5-digit number. This marks the transition from four place-value columns (Th, H, T, O) to five columns (T-Th, Th, H, T, O).

Identity of Zero: In the set of whole numbers, the number $0$ has a successor ($1$), but it does not have a predecessor that is a whole number.