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 10n – 1

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

So
For 3 × 1034 we can say it’s order of magnitude is 1034 – 1 = 1033
For 7 × 1034 we can say it’s order of magnitude is 1034 + 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.

QuantityOrder of magnitude
Radius of Proton10-15 m
Radius of Atom10-10 m
Radius of Earth107 m
Distance between Sun, Earth1011 m
Mass of Electron10-30 kg
Mass of Proton10-27 kg
Mass of Sun1030 kg
Period of micro waves10-10 s

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