Order of magnitude

Definition

An order of magnitude is a class in a system of classification determined by size, typically measured in powers of ten. It is used to compare quantities by their relative scale.

5 Must Know Facts For Your Next Test

1. An order of magnitude represents a factor of ten change in quantity.
2. When comparing two quantities, if one is about ten times larger than the other, they differ by one order of magnitude.
3. In physics, orders of magnitude are commonly used to simplify and understand the vast range of physical quantities.
4. Orders of magnitude can be applied to both very large numbers (e.g., distance between stars) and very small numbers (e.g., atomic sizes).
5. $10^2$ and $10^3$ differ by one order of magnitude because $10^3 = 10 \times 10^2$.

Review Questions

• What does an order of magnitude represent in terms of numerical change?
• How many orders of magnitude difference are there between $10^4$ and $10^7$?
• Why are orders of magnitude useful in the study and understanding of physical quantities?

Related terms

Scientific Notation:

A way to express very large or very small numbers using powers of ten. For example, $1.23 \times 10^6$.

Scale: The relative size or extent of something, often used to compare different physical quantities or phenomena.

Logarithm: The exponent that indicates the power to which a base number is raised to produce a given number. For example, if $b^y = x$, then $\log_b(x) = y$.