# Order of magnitude

In maths, what is meant by Order of magnitude, symbol O .

jeff
Orders of magnitude indicate the size of something in powers of ten within a factor of ten. For example;

By "X exceeds Y by n orders of magnitude" is meant that X is at least 10^n but less than 10^(n+1) times greater than Y.

By "X is within n orders of magnitude of Y" is meant X is less than 10^(n+1) but greater than 10^-(n+1) times Y.

Last edited:
If you see an expression like

Y(t)=1+t+t^2+O(t^3)

The O means that there are terms to the third power and higher that are drop.

JMD

jeff