Numbers up to 10,000 - Place Value and Face Value

Introduction to 4-Digit Numbers: A 4-digit number consists of four places: Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). The smallest 4-digit number is $1,000$ and the largest is $9,999$. Visually, you can imagine these numbers represented by blocks: a large cube for $1,000$, a flat square for $100$, a rod for $10$, and a small cube for $1$.

Face Value: The face value of a digit is the digit itself, regardless of its position in a number. For example, in the number $5,821$, the face value of $8$ is simply $8$. It is the visual identity of the digit on the page.

Place Value: The place value of a digit depends on its position in the number. In a place value chart, moving from right to left, the values of the places are $1$ (Ones), $10$ (Tens), $100$ (Hundreds), and $1,000$ (Thousands). For example, in $4,732$, the digit $7$ is in the Hundreds place, so its place value is $7 \times 100 = 700$.

Expanded Form: Writing a number as the sum of the place values of its digits is called expanded form. It helps visualize the 'weight' of each digit. For example, the number $6,305$ is written as $6,000 + 300 + 0 + 5$.

Standard Form: This is the normal way of writing numbers using digits. To convert expanded form to standard form, we place each digit in its respective column. For instance, $2,000 + 900 + 40 + 8$ becomes $2,948$. If a place is missing (like no 'Tens'), we must use $0$ as a placeholder.

Successor and Predecessor: The successor is the number that comes just after a given number ($Number + 1$). The predecessor is the number that comes just before a given number ($Number - 1$). On a horizontal number line, the predecessor is always to the left and the successor is always to the right of the given number.

Comparing Numbers: To compare two 4-digit numbers, start by comparing the digits in the Thousands place. If they are the same, move to the Hundreds, then Tens, and finally Ones. We use symbols like $>$ (greater than), $<$ (less than), or $=$ (equal to). For example, $5,432 > 5,429$ because at the Tens place, $3 > 2$.