key term - Order of magnitude

Definition

An order of magnitude is a class in a system for expressing the scale or size of a value, typically measured as powers of 10. It helps compare quantities on a logarithmic scale.

5 Must Know Facts For Your Next Test

1. An increase by one order of magnitude means the quantity has increased tenfold.
2. Orders of magnitude are commonly used to express exponential growth or decay in real-world phenomena.
3. Logarithmic scales, which use orders of magnitude, simplify comparisons between vastly different values.
4. In scientific notation, an order of magnitude can be represented by the exponent in powers of 10 (e.g., $10^3$ is three orders of magnitude).
5. Understanding orders of magnitude is crucial for interpreting and creating exponential and logarithmic models.

Review Questions

Related terms

Exponential Growth:

A process that increases quantity over time at a rate proportional to its current value, often modeled with functions like $y = ae^{bx}$.

Logarithm:

The inverse function to exponentiation, indicating the power to which a base number must be raised to obtain another number (e.g., $\log_b(a)$).

Scientific Notation:

A method for representing very large or very small numbers through powers of ten, such as $1.23 \times 10^4$.