Question

The length of a rod is $0.5 \times {10^2}\;{\rm{m}}$, the order of magnitude of the length of the rod is:
(A) ${10^3}\;{\rm{m}}$
(B) ${10^2}\;{\rm{m}}$
(C) ${10^1}\;{\rm{m}}$
(D) ${10^{ - 1}}$

Answer 1

To determine the correct option among the given options, we will use the concept of order of magnitude. We will determine the order of magnitude always in the power of 10 because it is known as the common logarithm of a positive number.

Complete step by step answer:
To know the amount of quantity of the matter, we determine the magnitude of the matter. The different types of unit are used to represent the quantity. To know the magnitude of the length of the rod meter is used. Another unit of length is km and mm. To know the magnitude of a very large object’s length, we will use km, and for the magnitude of a very small object’s length, we will use mm.
Order of magnitude comes in the power of ten, so, if the magnitude of the length is given to us, then we will find the order of the magnitude by rounding the number in a power of ten. But in question magnitude is already given in the power of ten. So, here to show the order of magnitude of the length we will write the magnitude in the power of ten i.e., ${10^2}\;{\rm{m}}$.
Therefore, if the length of the rod is $0.5 \times {10^2}\;{\rm{m}}$, then the order of magnitude of the length of the rod is ${10^2}\;{\rm{m}}$ and option (B) is correct.

Note: An order of magnitude calculation is a rough estimate designed to be accurate to within a factor of about 10. We determine the order of magnitude in the power of 10 so that we will get ideas and feelings for what size of the number are involved in a situation where the precise count is not possible or essential.