Expanded Form
Grade 4 students learn expanded form in Saxon Math Intermediate 4 Chapter 2, writing numbers as the sum of their place values. The number 365 = 300 + 60 + 5; the number 482 = 400 + 80 + 2; the number 907 = 900 + 7 (the zero in tens place is omitted since 0 + anything = anything). For 3,458 in expanded form: 3,000 + 400 + 50 + 8. The critical pitfall: zeros indicate a missing place value—603 is 600 + 3, not 60 + 3, because the 6 is in the hundreds place, not the tens place.
Key Concepts
Property Expanded form shows a number as the sum of its place values. For example, the number 365, meaning "3 hundreds, 6 tens, and 5 ones," is written as $300 + 60 + 5$.
Examples The expanded form of 482 is $400 + 80 + 2$. For a number with a zero like 603, we write $600 + 3$. A two digit number like 94 becomes $90 + 4$.
Explanation Think of this as deconstructing a number into its LEGO building blocks—hundreds, tens, and ones—to see its true value. It’s like number anatomy, showing what it's made of!
Common Questions
What is expanded form?
Expanded form shows a number as a sum of the values of each of its digits based on their place positions. For example, 482 = 400 + 80 + 2, showing the contribution of each digit separately.
How do you write 907 in expanded form?
9 is in the hundreds place (value = 900); 0 is in the tens place (value = 0); 7 is in the ones place (value = 7). Expanded form: 900 + 7. The zero term is usually omitted since adding 0 changes nothing.
How do you write 3,458 in expanded form?
3 (thousands) = 3,000; 4 (hundreds) = 400; 5 (tens) = 50; 8 (ones) = 8. Expanded form: 3,000 + 400 + 50 + 8.
What is the most common mistake when writing numbers with zeros in expanded form?
Assigning the wrong place value to a digit near a zero. In 603, the 6 is in the hundreds place (not tens), so its value is 600. Writing 60 + 3 is wrong—always check each digit's actual place value position.
How does expanded form strengthen understanding of place value?
Expanded form makes explicit that a digit like 5 in 528 is not just 5—it is 500. Seeing the full expanded sum reinforces that each digit's contribution depends entirely on its position in the number.
How does expanded form connect to addition?
Expanded form decomposes a number into addends organized by place value. This mirrors the column-by-column addition process and helps students understand why adding hundreds to hundreds and tens to tens always produces the correct sum.