Question

a scale measures the weight of a light object to be 11.000 lbs ± 0.034 lbs. what is the uncertainty if this same scale is used to measure an object that weighs 78.000 lbs? assume that the percent uncertainty of the scale remains constant. (1 point) 0.034 lbs 0.044 lbs 0.240 lbs 0.310 lbs

Explanation:

Step1: Calculate the percent uncertainty of the first measurement

Percent uncertainty formula: $\text{Percent Uncertainty}=\frac{\text{Uncertainty}}{\text{Measurement}}\times100\%$.
For the first measurement: $\text{Measurement}=11.000$ lbs, $\text{Uncertainty}=0.034$ lbs.
Percent Uncertainty $=\frac{0.034}{11.000}\times 100\%$.

Step2: Use the same percent uncertainty for the second measurement

Let the uncertainty for the second measurement be $x$.
Second measurement: $\text{Measurement}=78.000$ lbs.
Since percent uncertainty remains the same, $\frac{x}{78.000}\times 100\%=\frac{0.034}{11.000}\times 100\%$.
Cross - multiply: $x=\frac{0.034\times78.000}{11.000}$.
Calculate $x=\frac{2.652}{11.000}=0.24109\approx0.240$ lbs.

Answer:

C. 0.240 lbs