Anthony and Russel mass a rock to be 20.0g. They place the rock in a graduated cylinder with 25.0mL of water and note that the water level now reads 31.0mL. What is the density of the rock with the correct number of significant digits?
When a rock is placed in a cylinder, the volume of the water it misplaces will equal its own volume. So if the water level rose from 25.0 mL to 31.0 mL, the volume of the rock must be V = 31.0 - 25.0 = 6.0 mL = 6.0 cm^3. (When subtracting, the number of decimal places should remain the same.)
The density of the rock, `` ,can be calculated as the ratio of its mass m to its volume V. Since the mass of the rock in the air is known to be 20.0 g, rho = m/V = 20.0/6.0 = 3.33.... g/cm^3.
The number of significant digits should equal 2, the least number of the significant digits in the values of m and V. So, the density of the rock is
rho = 3.3 g/cm^3.