Question

The thickness of a metal sheet is measured to be 326 mm. Express its order of magnitude in mm.
(A) ${10^0}$
(B) ${10^0}$
(C) ${10^2}$
(D) ${10^3}$

Answer 1

Hint Order of magnitude is the approximation of scale of a value. It can be calculated by using the following steps:
(i) Each quantity involved in the formula has to be expressed in terms of one significant figure i.e. a x ${10^b}$ where “a” is an integer whose range is from 1 to 10 and b can be 0, positive or negative.
(ii) Final result is also expressed in terms of$a \times {10^b}$.
(iii) If$a < 5$, the order of magnitude is ${10^b}$.
(iv) If $a < 5$, the order of magnitude is ${10^{b + 1}}$.

Complete step by step solution
Here, the thickness of the metal sheet is 326mm.
Converting it in the form of $a{\text{ }} \times {\text{ }}{10^b}$
$3.26 \times {10^2}$mm
$= {\text{ }}3 \times {10^2}$mm
If we compare the standard form with the above result, we can say $a = 3$(which is less than 5) and$b = 2$.

$\therefore$ Order of magnitude = ${10^2}$ (Option C)

Note We use order of magnitude to compare two values. For example: Say we have two commodities A and B whose prices are ₹100 and ₹10,00,000 respectively. When we are comparing these two values its more convenient to compare it in terms of multiple, like A is what multiple of B. In this example B is 10,000 times more than A or A is ${10^4}$ more than A which is simpler than saying B is 9,99,900 more than A. We can also consider the example where we are comparing the price of a budget Xiaomi phone and an I-phone. Here, also it's simpler to compare it in terms of multiple.