Definition:Expanded Number

Definition

Let $x$ be a number expressed in base $b$ for some $b \in \Z_{>1}$.

Let $x$ be written as a sum of multiples of powers of $b$.

Then $x$ is said to be expressed as an expanded number.

Also known as

An expanded number is also said to be expressed in expanded form.

Examples

Example: $163$

The number expressed as $163$ in decimal notation is expressed in expanded form as:

$1 \times 10^2 + 6 \times 10^1 + 3 \times 10^0$

or more compactly as:

$1 \times 10^2 + 6 \times 10 + 3$

Also see

• Results about expanded numbers can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): expanded number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): expanded number