Fun with Numbers - Expanded Form

Definition of Expanded Form: Expanded form is a way of writing a number to show the value of each digit. It is expressed as a sum of the place values of its digits. For example, the number $254$ is broken down into its parts based on where the digits sit.

Place Value Chart: To understand expanded form, imagine a table with three columns: Hundreds (H), Tens (T), and Ones (O). For a number like $382$, you would place $3$ in the H column, $8$ in the T column, and $2$ in the O column. This visual helps you see that $3$ actually represents $300$.

Value of Digits: The position of a digit determines its actual value. In a 3-digit number, the first digit from the left is multiplied by $100$, the second by $10$, and the third by $1$. Visualizing base-10 blocks, a 'hundred' is a large square flat, a 'ten' is a long rod, and a 'one' is a small cube.

Writing the Sum: To write the expanded form, we connect the individual place values using the plus symbol ($+$). For example, for the number $671$, we identify the values as $600$, $70$, and $1$, then write them as $600 + 70 + 1$.

Zero as a Placeholder: When a number has a $0$ in a specific place, its value is $0$. In expanded form, we can either write the $0$ or skip it, though writing it helps maintain the place value structure. For $503$, the expanded form is $500 + 0 + 3$, showing there are no tens (an empty Tens column in our mental chart).

Standard Form: This is the normal way we write numbers, like $419$. Converting from expanded form ($400 + 10 + 9$) back to standard form ($419$) involves adding the values together or simply placing the digits in their correct H-T-O positions.