Question

Each side of a cube is measured to be $7.203m$. The volume of the cube to appropriate significant figure is:
(A) $31.3{m^3}$
(B) $313{m^3}$
(C) $373.7{m^3}$
(D) $37.3{m^3}$

Answer 1

Hint The volume of a cube is given by ${\left( {side} \right)^3}$. The number of significant digits of the product of two or more numbers, is equal to the number of significant digits of a multiplied number, with minimum significant digits.

Complete step by step answer
We know that the volume of a cube is given by ${\left( {side} \right)^3}$.
In this problem, it is given that side of the cube is $7.203m$.
So, we can calculate the volume of the given cube as
$V = {\left( {7.203} \right)^3}$
$ \Rightarrow V = 373.7147544{m^3}$
Looking at this volume, you may get an idea of why significant numbers are important. It is meaningless to have so many numbers after the decimal. For practical use, it is always preferable to consider up to $2nd$ or $3rd$ decimal.
Now, we look into the number we first multiplied, i.e. $7.203$.
This number has $4$ significant numbers.
So, according to the rules of significant digits, the product of two or more numbers should have as many significant digits as the number with a minimum of significant digits.
In this problem, we are multiplying the same number i.e. $7.203$. This number has $4$significant digits.
So we need the product with $4$significant digits.
So, rounding off the calculated volume up to $4$ significant digits, we get
$V = 373.7{m^3}$

Thus, Option (C) is correct.

Additional Information If we have two numbers, $5.601$ and$2.34$. The product of these two numbers will have $2$ significant digits. However, for addition or subtraction, we consider the number with the highest number of significant digits. So the result of the addition of these two numbers will have $3$significant digits.

Note: Don’t round off the number before multiplication, addition, or any arithmetic operation. It will give you the wrong answer. While rounding off the answer, be sure to follow the rules of rounding off a number to get a correct answer.