Question

In a research laboratory, a scientist measures the mass of a 1-carat diamond and finds it to be 200 milligrams, measured to the nearest hundred milligrams. The volume of the diamond is approximately 0.057 cubic centimeters. Find the density of the diamond in grams per cubic centimeter, expressing your answer to the appropriate level of accuracy. Use complete sentences to explain your reasoning.

Answer 1

Answer:

$D=3.5\ gr/cm^3$

Step-by-step explanation:

Density

The density of an object of mass m and volume V is given by

$\displaystyle D=\frac{m}{V}$

It can be expressed in common units like $gr/lt, Kg/m^3, gr/cm^3$ or any other combination of proper mass [M] by volume [V] units.

The data provided in the question is

$m=200\ mg = 0.2\ gr$

$V=0.057\ cm^3$

Thus, the measured density is

$\displaystyle D=\frac{0.2\ gr}{0.057 \ cm^3}$

$\boxed{D=3.5\ gr/cm^3}$

We have expressed the result with 1 decimal place because the mass was measured to the nearest hundred milligrams (or one-tenth grams). Any further decimal is senseless because that precision comes from calculations, not from measurements.