Final answer:
To calculate the lower and upper bounds of density, you need to establish the bounds of mass and volume and then use the formula ρ = m/V. The calculated bounds are 7.961 g/cm³ for the lower bound and 7.986 g/cm³ for the upper bound.
Step-by-step explanation:
Calculating the Lower and Upper Bounds of Density
The formula for calculating density (ρ) is ρ = m/V, where m is mass and V is volume. In this case, the mass (m) is given as 30.14 g, truncated to two decimal places (d.p.), and the volume (V) is given as 3.78 cm³, also truncated to two decimal places. To find the lower and upper bounds of the density, we need to determine the bounds of the mass and volume.
Since the measurements have been truncated to two decimal places, the lower bound of the mass will be slightly less than 30.14 g, and the upper bound will be slightly more. Specifically, the lower bound will be 30.135 g, and the upper bound will be 30.145 g. Similarly, for the volume, the lower bound will be 3.775 cm³ and the upper bound will be 3.785 cm³.
To calculate the lower bound of density, use the upper bound of volume and the lower bound of mass. Conversely, to calculate the upper bound of density, use the lower bound of volume and the upper bound of mass.
The calculations are as follows:
- Lower Bound of Density: ρ = 30.135 g / 3.785 cm³ = 7.961 g/cm³
- Upper Bound of Density: ρ = 30.145 g / 3.775 cm³ = 7.986 g/cm³
Therefore, the density of the substance has a lower bound of 7.961 g/cm³ and an upper bound of 7.986 g/cm³.