Expanded Notation
Learn to write numbers in expanded notation by multiplying each nonzero digit by its place value and connecting them with plus signs.
Key Concepts
Property To write a number in expanded notation , we write each nonzero digit times its place value.
Examples $27,000 = (2 \times 10,000) + (7 \times 1000)$ $1760 = (1 \times 1000) + (7 \times 100) + (6 \times 10)$ $8050 = (8 \times 1000) + (5 \times 10)$.
Explanation Think of this as showing a number's secret identity! You break the number down by multiplying each digit (except zero) by its place value, like thousands or hundreds. It's like writing out the full recipe for the number, showing all the valuable ingredients that add up to the final tasty total. We ignore zeros because they add no value.
Common Questions
What is expanded notation in math?
Expanded notation is a way of writing a number by multiplying each nonzero digit by its place value, then adding the results together with plus signs. For example, 1760 is written as (1 × 1000) + (7 × 100) + (6 × 10). It breaks a number down into its individual place value components.
Why do we skip zeros when writing expanded notation?
Zeros are skipped in expanded notation because multiplying zero by any place value equals zero, which adds no value to the number. For instance, 8050 is written as (8 × 1000) + (5 × 10), leaving out the zero in the hundreds and ones places. Including zeros would just add unnecessary terms that don't change the total.
How do you write 27,000 in expanded notation?
To write 27,000 in expanded notation, identify each nonzero digit and multiply it by its place value. The 2 is in the ten-thousands place and the 7 is in the thousands place, giving you (2 × 10,000) + (7 × 1000). The trailing zeros are nonzero digits have no value so they are omitted.
What grade level learns expanded notation in Saxon Math?
Expanded notation is taught in Grade 6 as part of Saxon Math Course 1, Chapter 4: Number, Operations, and Measurement. Students learn to decompose numbers by place value, reinforcing their understanding of ones, tens, hundreds, and thousands. This skill builds a strong foundation for understanding number structure and operations.