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Break down numbers by place value in multiple forms
Expanded form is a way of writing numbers that shows the value of each digit based on its place in the number. It breaks down a number into the sum of each digit multiplied by its place value, helping students understand the concept of place value and number composition.
Shows the actual value of each place added together
345 = 300 + 40 + 5
Best for: Elementary students learning place value
Shows each digit multiplied by its place value
345 = (3 × 100) + (4 × 10) + (5 × 1)
Best for: Understanding the relationship between digits and place values
Uses powers of 10 to show place values
345 = (3 × 10²) + (4 × 10¹) + (5 × 10⁰)
Best for: Advanced students and connection to scientific notation
Decimals can also be written in expanded form using negative powers of 10:
Example: 3.45
Place Value Understanding: Reinforces the concept that position determines value
Number Sense: Helps visualize the magnitude of different digits
Foundation for Algebra: Prepares students for polynomial notation and algebra
Mental Math: Makes it easier to add and subtract multi-digit numbers mentally
The expanded form of 1,234 is: 1,000 + 200 + 30 + 4 (addition form), or (1 × 1,000) + (2 × 100) + (3 × 10) + (4 × 1) (multiplication form), or (1 × 10³) + (2 × 10²) + (3 × 10¹) + (4 × 10⁰) (exponential form).
Zeros are typically omitted in expanded form since they contribute no value. For example, 305 = 300 + 5, not 300 + 0 + 5. However, in some contexts (especially when teaching), all place values may be shown: 300 + 0 + 5.
Expanded form shows the mathematical breakdown (300 + 40 + 5), while word form spells out the number in words (three hundred forty-five). Expanded form focuses on place value mathematics, while word form focuses on reading and writing numbers.
0.25 in expanded form is 0.2 + 0.05 (addition), or (2 × 0.1) + (5 × 0.01) (multiplication), or (2 × 10⁻¹) + (5 × 10⁻²) (exponential). The key is understanding that decimal places represent tenths, hundredths, etc.
No, they're opposites. Standard form is the normal way we write numbers (345), while expanded form breaks them down by place value (300 + 40 + 5). Standard form is compact; expanded form is detailed.
Exponential notation (using 10⁰, 10¹, 10², etc.) connects place value to powers of 10, which is fundamental in mathematics. It bridges elementary place value concepts to advanced topics like scientific notation and helps students understand the base-10 number system.