Finding the Density of an Aluminium Block Uncertainty Included

Measurements Mass (g) ±0.01g Length (cm) ±0.01cm Width (cm) Breadth (cm) 1 543.02 8.03 5.01 5.00 2 8.02 5.03 3 8.04

Mean value and Uncertainty LENGTH Mean value = 8.03 + 8.02 + 8.04 = 8.03 cm 3 Uncertainty = 8.04 – 8.02 = ±0.01 cm 2 Percentage Uncertainty = 0.01 = 0.12% 8.03

Mean value and Uncertainty WIDTH Mean value = 5.01 + 5.03 + 5.03 = 5.02 cm 3 Uncertainty = 5.03 – 5.01 = ± 0.01 cm 2 Percentage Uncertainty = 0.01 = 0.199% = 0.2% 5.02

Mean value and Uncertainty BREADTH Mean value = 5.00 + 5.00 + 5.00 = 5.00 cm 3 Uncertainty = ± 0.01 cm Percentage Uncertainty = 0.01 = 0.20% 5.00

Mean value and Uncertainty MASS Value = 543.02g Uncertainty = ± 0.01g Percentage Uncertainty = 0.01 = 0.0018% = 0.00% 543.02

Results DENSITY ρ = m/V = 543.02 / (8.03 x 5.02 x 5.00) ρ = 2.694 gcm-3

Uncertainty TOTAL UNCERTAINTY UNCERTAINTY OF ANSWER Uncertainty = 0.52 x 2.694 = ± 0.01 gcm-3 100

Answer Density = 2.69 ± 0.01 gcm-3 True Density = 2.70 gcm-3