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.