Question

What is the order of magnitude of $260$?
$\left( A \right){10^3}$
$\left( B \right){10^4}$
$\left( C \right){10^2}$
$\left( D \right)10$

Answer 1

Hint: To solve this we First we will write how to calculate the order of magnitude of a given value then represent that value in its scientific notation, scientific notation is an important term in physics to represent a number to make the calculation easier. From that we can find the order as a power of $10$.

Complete step by step answer:
Order of magnitude is the quantity of power of $10$ and that quantity is in a number or the number of powers of $0.1$ in a negative number. Generally the order of magnitude is usually written as $10$ to its $nth$ power. Where n represents the order of magnitude of the given number in its scientific notation. If we raise a number by one order of its magnitude then we are basically multiplying that number by $10$ and if we are decreasing a number by one order of its magnitude then we are basically multiplying that number by $0.1$.
Now as per the problem we need to find the order of magnitude of $260$.
The scientific notation of the given number is $2.60 \times {10^2}$.
Hence the order of magnitude is ${10^2}$.
Therefore the correct option is (C).

Note: Remember that scientific notation is a very important term as it is very useful because it allows us to easily write and make calculations with extremely small as well as extremely large numbers. In physics accurately calculation and interaction between pure mathematics is very important hence scientific notation is used.