Decomposing Three-Digit Numbers by Place Value
This Grade 4 Eureka Math skill teaches students to decompose three-digit numbers by place value using the formula abc = (a × 100) + (b × 10) + (c × 1). Place value disks on a chart make each digit visible: 423 is shown as 4 hundreds disks, 2 tens disks, and 3 ones disks. Understanding this decomposition is the foundation for multi-digit addition, subtraction, and multiplication, because each operation works digit by digit according to place value.
Key Concepts
A three digit number can be decomposed into its place values: $abc = (a \times 100) + (b \times 10) + (c \times 1)$. This is represented on a place value chart by placing $a$ disks in the hundreds column, $b$ disks in the tens column, and $c$ disks in the ones column.
Common Questions
How do you decompose a three-digit number by place value?
Identify the hundreds, tens, and ones digits separately. Multiply each digit by its place value: hundreds digit × 100, tens digit × 10, ones digit × 1, then write the sum.
What does 423 look like decomposed?
423 = (4 × 100) + (2 × 10) + (3 × 1) = 400 + 20 + 3.
What are place value disks?
Place value disks are circular counters used in Eureka Math. Each disk represents one unit of a specific place value: hundreds, tens, or ones.
How would you represent 580 with place value disks?
Place 5 disks in the hundreds column, 8 disks in the tens column, and 0 disks in the ones column.
Why is decomposing by place value important in Grade 4?
It underpins the standard algorithms for addition, subtraction, and multiplication by clarifying how regrouping works within the base-10 system.