Question

The mass and volume of a body are $4.237g$ and $2.5c{m^3}$, respectively. What is the density of the material of the body in correct significant figures?
A. $1.6948gc{m^{ - 3}}$
B. $1.69gc{m^{ - 3}}$
C. $1.7gc{m^{ - 3}}$
D. $1.695gc{m^{ - 3}}$

Answer 1

Hint: Use the formula for density, $\rho = \dfrac{M}{V}$ and use the rule for significant figures of division to determine the density of the material of the body in correct significant figures.

Complete step by step answer:

First, compute the density. We will use the formula for density calculation,
$ \Rightarrow \rho = \dfrac{M}{V}$
We substitute the mass as 4.237g and volume as $2.5c{m^3}$ in the above equation,
$ \Rightarrow \rho = \dfrac{{4.237}}{{2.5}}g/c{m^3}$
Calculating the above we obtain,
$ \Rightarrow \rho = 1.6948g/c{m^3}$
Now, we know that mass, M = 4.237 g has 4 significant figures, and volume, $V = 2.5c{m^3}$ has 2 significant figures.
Since density involves division of the two, we use the rule for Multiplication and Division of significant figures that states – The least number of significant figures in any number of the problem determines the number of significant figures in the answer.
Therefore, our answer should have 2 significant figures. Hence, the density value would be written as:
$ \Rightarrow \rho = 1.7g/c{m^3}$

Note: Since all the options have the same value with the different number of significant figures; an alternative method can be to just solve the question by using only the rule for multiplication and division of significant figures. Hence, we can imply that the number of significant figures for density as 2 and the only option with 2 significant figures is option C which is obviously the correct answer.
Additional Information: For addition and subtraction we use the following rules:
 1. Count the number of significant figures in the decimal portion only of each number in the problem.
2. Add or subtract normally
3. Your final answer should not have more significant figures to the right of the decimal than the least number of significant figures in any number in the problem.