Expanded Notation
Expanded notation writes a number as the sum of each digit multiplied by its place value. In Grade 6 Saxon Math Course 1, the number 47,382 in expanded notation is 40,000 + 7,000 + 300 + 80 + 2, or equivalently 4 × 10,000 + 7 × 1,000 + 3 × 100 + 8 × 10 + 2 × 1. This decomposition makes the value of each digit explicit and deepens place-value understanding. Expanded notation also works with decimals: 3.47 = 3 + 0.4 + 0.07 = 3 × 1 + 4 × 0.1 + 7 × 0.01.
Key Concepts
New Concept Expanded notation breaks a number into a sum, revealing the true value of each digit based on its place in the number.
To write a number in expanded notation , we write each nonzero digit times its place value.
For instance, the number 8,430 is written as: $$ (8 \times 1000) + (4 \times 100) + (3 \times 10) $$ What’s next This is your starting point. Next, you'll walk through examples converting numbers between standard and expanded forms and apply this skill to compare values.
Common Questions
Write 47,382 in expanded notation.
40,000 + 7,000 + 300 + 80 + 2, or 4×10,000 + 7×1,000 + 3×100 + 8×10 + 2×1.
Write 3.47 in expanded notation.
3 + 0.4 + 0.07, or 3×1 + 4×0.1 + 7×0.01.
What does expanded notation show that standard form does not?
It shows the exact place-value contribution of each digit, making the value of each numeral explicit.
How do you write expanded notation for a number with a zero digit?
The zero digit contributes 0 × its place value = 0, so that term is omitted. Example: 3,045 = 3,000 + 40 + 5.
How does expanded notation connect to addition?
A number in expanded notation is literally written as a sum of its place-value components, reinforcing that place-value addition underlies the standard algorithm.