Order of Magnitude

The order of magnitude of a physical quantity is that power of 10 which is closest to its magnitude. It gives an idea about how big or how small a given physical quantity is.

To determine the order of magnitude of a number N, we first express it as

N = n × 10^x.

If 0.5 < n ≤ 5, then x will be the order of magnitude of N.

Few examples are illustrated in table given below:

Table: Order of magnitude

Measure number N	Expressed in nearest power of 10	Order of magnitude
8	0.8 × 101	1
49	4.9 × 101	1
52	0.52 × 102	2
555	0.555 × 103	3
999	0.999 × 103	3
1001	1001×io3	3
753000	0.753 × 106	6
0.135	1.35 × 10-1	-1
0.05	5 × 10-2	-2
0.99	0.99 × 100	0

Question:

Write the order of magnitude of the following measurements:

(i) 25,710,000 m (ii) 0.00000521 kg.

Solution:

We first express each number in terms of nearest power of 10.

(i) 25,710,000 m =2.571 × 10⁷ m

As 0.5 < 2.571 < 5

∴ Order of magnitude = 7.

(ii) 0.00000521 kg = 0.521 × 10^-5kg

As 0.5 < 0.521 < 5 ∴ Order of magnitude = -5.

Question:

Write the order of magnitude of the following:

(i) 8

(ii) 49

(iii) 52

(iv) 999

(v) 1001

(vi) 753000

(vii) 0.05

(viii) 0.99.

Ans: 1, 1, 2, 3, 3, 6, – 2, 0

Table: Orders of Magnitude of length

S. No.	Size of object or distance	Length (m)
1.	Radius of a proton	10-15
2.	Size of atomic nucleus	10-14
3.	Size of hydrogen atom	10-10
4.	Size of typical virus	10-8
5.	Wavelength of light	10-7
6.	Size of red blood corpuscle	10-5
7.	Thickness of a paper	10-4
8.	Height of a person	100
9.	Height of Mount Everest	104
10.	Radius of the earth	107
11.	Distance of the moon from the earth	108
12.	Radius of the sun	109
13.	Distance of the sun from the earth	1011
14.	Distance of Pluto from the earth	1013
15.	Size of Milkway	1021
16.	Distance to Andromeda galaxy	1022
17.	Distance to the boundary of observable universe	1026