Expanded Notation
Expanded notation expresses a number by writing each non-zero digit multiplied by its place value, then adding them together. For 5,280, expanded notation is (5 times 1000) + (2 times 100) + (8 times 10). In Grade 7 Saxon Math Course 2, Chapter 1, expanded notation reinforces the meaning of place value and connects to exponent notation (10^3 = 1000), preparing students for scientific notation and polynomial expressions. It is also a bridge to understanding how the decimal system works structurally.
Key Concepts
Property We write a number in expanded notation by writing each nonzero digit times its place value.
Examples $5280$ in expanded notation is $(5 \times 1000) + (2 \times 100) + (8 \times 10)$. $25,000$ in expanded notation is $(2 \times 10,000) + (5 \times 1000)$. $750,000$ in expanded notation is $(7 \times 100,000) + (5 \times 10,000)$.
Explanation Expanded notation is like taking a number apart to see its secret formula! You take each digit, multiply it by its personal place value (like thousands or hundreds), and then add all those pieces together. It's a fantastic way to show the true power and value hiding behind each digit in a number.
Common Questions
What is expanded notation in math?
Expanded notation writes each non-zero digit of a number as that digit times its place value. For example, 4,275 = (4 times 1000) + (2 times 100) + (7 times 10) + (5 times 1).
How do you write a number in expanded notation?
Identify each non-zero digit and its place value, then write the product of each digit and its place value separated by plus signs. For 25,000: (2 times 10,000) + (5 times 1,000).
How is expanded notation different from standard form?
Standard form is the regular way to write a number, like 3,400. Expanded notation shows the value of each digit separately: (3 times 1,000) + (4 times 100).
How does expanded notation connect to exponents?
Each place value is a power of 10. Ones = 10^0, tens = 10^1, hundreds = 10^2, and so on. Expanded notation can be written as (3 times 10^3) + (4 times 10^2) to show this connection.
When do 7th graders learn expanded notation?
Saxon Math, Course 2, Chapter 1 covers expanded notation as part of the Grade 7 place value and number sense unit.
Do you write zeros in expanded notation?
No. Only non-zero digits are written in expanded notation because multiplying any digit by its place value and getting zero contributes nothing to the sum.