Question

When $24.25\times {{10}^{3}}$ is rounded off to three significant figures, it becomes:
$\begin{align}
  & a)242 \\
 & b)243 \\
 & c)244\times {{10}^{2}} \\
 & d)24.2\times {{10}^{3}} \\
\end{align}$

Answer 1

Hint: All non zero digits are called as significant figures. In the above question it is given that the above number is rounded up to 3 significant figures. First we will discuss some of the rules for rounding off and then accordingly express the above value in terms of three significant figures.

Complete solution:
In the above question the number to be rounded off to three significant figures is $24.25\times {{10}^{3}}$. We now know that the non zero digits of a number are called significant figures. Hence we can conclude that the number of significant figures in the above number is 4 i.e. 2, 4, 2 and 5. Therefore we can conclude that in order to express the above number to three significant figures we have to round off 5. Now let us discuss some of the rules while rounding off 5.
If the digit to be dropped is 5, followed by a non zero digit then the preceding digit is increased by 1.
If the digit to be dropped is 5, then the preceding digit remains unchanged if it is even. Similarly, if the digit to be dropped is 5, then the preceding digit is increased by 1 if it is odd.
The preceding digit to five i.e. 2,is even. Therefore the digit remains unchanged when we drop 5.
Therefore, the above number in terms of three significant figures can be written as $24.2\times {{10}^{3}}$.

Hence the correct answer of the above question is option d.

Note:
It is to be noted that the power of a number cannot be rounded up. Hence we have made sure that when we round up 5, the power raised to the ten remains unchanged. It is also to be noted that if the above number corresponds to some measurement, then we would have to take into consideration the zeroes as well.