Order of magnitude

Definition

An order of magnitude is a class in a system of classification determined by size, each class being a factor of ten different from the next. In exponential and logarithmic models, it helps compare quantities and their scales.

5 Must Know Facts For Your Next Test

1. Orders of magnitude are often used to simplify complex numbers by expressing them as powers of ten.
2. A difference of one order of magnitude means one quantity is about ten times larger or smaller than another.
3. Logarithms are commonly used to calculate orders of magnitude; for instance, $\log_{10}(1000) = 3$ indicates an order of magnitude 3.
4. In exponential growth models, the concept helps in understanding how quickly quantities increase by factors of ten.
5. Scientific notation relies on orders of magnitude for expressing very large or very small numbers succinctly.

Review Questions

• What does a change in one order of magnitude represent in terms of multiplication?
• How would you express an order of magnitude difference using logarithms?
• Why are orders of magnitude important when dealing with exponential growth?

Related terms

Exponential Function: A mathematical function in which an independent variable appears as an exponent. It describes rapid growth or decay.

Logarithm: The inverse operation to exponentiation, indicating the power to which a base number must be raised to produce a given number.

Scientific Notation: A method for writing very large or very small numbers by representing them as a product of a number between 1 and 10 and a power of ten.