Order of Magnitude

This article is for Class 11 students

In doing rough calculations or comparisons, we sometimes round off a number to one or even no significant figures.

A number rounded to nearest power of 10 is called order of magnitude.

For example – If height of an object is 8 × 10³ m, then we can say that order of magnitude of height of object is 10⁴ m.

Rules for figuring out order of magnitude
If a number is written in format A × 10ⁿ
where
A is some Real Number
n is some Natural Number

Then
If A < 5 then we say order of magnitude of A × 10ⁿ is 10^{n – 1}

If 5 <= A < 10 then we say order of magnitude of A × 10ⁿ is 10^{n + 1}

So
For 3 × 10³⁴ we can say it’s order of magnitude is 10^{34 – 1} = 10³³
For 7 × 10³⁴ we can say it’s order of magnitude is 10^{34 + 1} = 10³⁵

Do note that order of magnitude does not give exact value but usually its accurate to within a factor of 10.

Let’s now have a look at what are Advantages of order of magnitude.
1. It gives approximate value of physical quantity and can be assumed to be correct within a factor of 10.

2. For comparing two physical quantities, we need not know their actual values. Knowing their orders of magnitude is sufficient.

Below is a table containing orders of magnitude of some commonly used constants in Physics.