Final answer:
The mass of the cart is 500 g with a standard deviation of 5 g after conversion from pounds to grams taking into account the error of propagation.
Step-by-step explanation:
The mass of the cart is given as (1.00 ± 0.01) lb, and given there are roughly 500 grams in a pound, the conversion to grams would be 1.00 lb x 500 g/lb = 500 g. The standard deviation must also be converted to grams, which involves multiplying the lb standard deviation by 500 g/lb. So the standard deviation for the mass of the cart in grams would be 0.01 lb x 500 g/lb = 5 g.
Therefore, the mass of the cart in grams is 500 ± 5 g. This uncertainty represents the error of propagation when converting units from pounds to grams. This standard deviation estimate ensures that measurements remain consistent across different unit systems.
To calculate the mass and standard deviation for the mass of the cart in grams, we need to convert the measurement from pounds to grams.
Given that there are roughly 500 grams per pound, we can multiply the measured mass (1.00 lb) by 500 to find the mass in grams:
Mass = (1.00 lb) * (500 g/lb) = 500 g
To calculate the standard deviation in grams, we can multiply the uncertainty (0.01 lb) by 500:
Standard Deviation = (0.01 lb) * (500 g/lb) = 5 g