Final answer:
To find the uncertainty in mass with a 3% uncertainty for a 65 kg measurement, multiply 65 kg by 3% expressed as a decimal (0.03), resulting in an uncertainty of 1.95 kg.
Step-by-step explanation:
If a bathroom scale reads a mass as 65 kg with a 3% uncertainty, the uncertainty in mass can be calculated by taking 3% of 65 kg. To do this, we multiply the mass by the uncertainty percentage expressed as a decimal.
The uncertainty in mass (in kilograms) = 65 kg × 0.03 = 1.95 kg.
The mass can therefore be reported to be 65 kg ± 1.95 kg, conveying that the actual mass could be as low as 63.05 kg or as high as 66.95 kg, based on the maximum uncertainty. When it comes to reporting the percent uncertainty in the sum of other such measurements, the relative uncertainties should be added together assuming they are independent, and the final percent uncertainty can be calculated similarly, by taking the percentage of the sum.