Question

For $18.72g$ of a substance ‘X’ occupies $1.81c{m^3}$ . What will be its density measured in correct significant figures?
A. $10.3g\,c{m^{ - 3}}$
B. $10.34g\,c{m^{ - 3}}$
C. $10.4g\,c{m^{ - 3}}$
D. $10.3425g\,c{m^{ - 3}}$

Answer 1

In order to answer the given question we will use the density formula and substitute the given values in place of mass and volume and get the final answer. And we will also get to know about the correct significant figures according to the rules of it.

Complete answer: The term "uncertainty" refers to the spectrum of potential values from which the true value of a measurement can be found. Some widely used terminology would be redefined as a result of this description. The word accuracy, for example, is often used to refer to the difference between a measured outcome and the real or true value. This measurement uncertainty is important to communicate because uncertainty accumulates when you perform calculations, and it's important to know how much uncertainty remains at the end.
Given,
Mass of the substance= $18.72g$
Volume of substance= $1.81c{m^3}$
Now, we know that density of a substance is given by;
$Density\left( \rho \right) = \dfrac{{Mass\left( m \right)}}{{Volume\left( v \right)}}$
$Density\left( \rho \right) = \dfrac{{18.72g}}{{1.81c{m^3}}} = 10.3g/c{m^3}$
The answer to a multiplication or division problem should be rounded to the same number of significant figures as the calculation's least precise expression. $1.81$ with three important figures is the least accurate. As a result, the response would have three important numbers, such $10.3g/c{m^3}$
So, the correct option is: (A) $10.3g\,c{m^{ - 3}}$.

Note:
Significant figures (also known as significant digits) are used in statistical and mathematical calculations to ensure that numbers are accurate and precise. It's crucial to predict the final result's uncertainty, and this is where significant figures come in useful.