Question

How do I calculate each of these?- Fractional uncertainty in mass of liquid sample - Fractional uncertainty in volume of liquid sample - Fractional uncertainty in density of liquid sample - Uncertainty in density of liquid sample

Answer 1

Calculate fractional uncertainty by dividing absolute uncertainty by measured value for mass or volume. Add fractional uncertainties for mass and volume to find fractional uncertainty in density. Uncertainty in density is this fractional value multiplied by the calculated density.

Step-by-step explanation:

To calculate the fractional uncertainty of a liquid sample's mass or volume, you divide the absolute uncertainty by the measured value. For example, if a liquid's mass is measured as 20g ± 0.5g, the fractional uncertainty is 0.5g/20g = 0.025 or 2.5%. Similarly, if the volume is 10mL ± 0.2mL, then the fractional uncertainty in volume is 0.2mL/10mL = 0.02 or 2%.

To calculate the fractional uncertainty in density, you add the fractional uncertainties of mass and volume. If the density ρ = mass/volume and their fractional uncertainties are u(m) and u(V) respectively, then the fractional uncertainty in density u(ρ) is u(m) + u(V). For our example values, u(ρ) would be 2.5% + 2% = 4.5%.

The uncertainty in density itself is found by multiplying the fractional uncertainty by the calculated density value. If the calculated density is 2 g/mL, then the uncertainty in density is 4.5% of 2 g/mL, which equals 0.09 g/mL.

Answer 2

Fractional uncertainty is found by dividing the absolute uncertainty by the quantity itself. It is always the same for every measure: mass, volume, density, etc.

For example, if we have this measure 7.5+-0.1kg. The fractional uncertainty is:

`(0.1)/(7.5)=0.013`