Question

The volume of a standard can of soda is advertised to be 355 milliliters.† Suppose a quality control inspector opens a can of soda, measures its contents, and finds it to be 359.7 milliliters. (a) Compute the absolute error. (Simplify your answer completely.) AE = Correct: Your answer is correct. Interpret the result. The advertised volume was this many milliliters off of the inspector's measurement. The advertised volume was off by this much relative to the inspector's measurement. This is the ratio of the inspector's measurement to the advertised volume. The advertised volume was reduced by this proportion. The advertised volume has this much percent error with the inspector's measurement. Correct: Your answer is correct. (b) Compute the relative error. Round to three decimal places. (Simplify your answer completely.) RE = Incorrect: Your answer is incorrect. Interpret the result. The advertised volume was this many milliliters off of the inspector's measurement. The advertised volume was off by this much relative to the inspector's measurement. This is the ratio of the inspector's measurement to the advertised volume. The advertised volume was reduced by this proportion. The advertised volume has this much percent error with the inspector's measureme

Answer 1

The absolute error between the advertised and measured soda volume is 4.7 mL, indicating the advertised volume was 4.7 milliliters less than what was measured. The relative error rounded to three decimal places is 1.324%, showing the percentage by which the advertised volume deviated from the measurement.

Step-by-step explanation:

The absolute error (AE) is the difference between the measured value and the true value. For the can of soda, the absolute error would be the measured volume minus the advertised volume, which is:

AE = 359.7 mL - 355 mL = 4.7 mL

This result means that the advertised volume was 4.7 milliliters off from the inspector's measurement. The advertised volume was off by 4.7 mL relative to the inspector's measurement.

To compute the relative error (RE), you divide the absolute error by the true value and then multiply by 100 to get the percentage. The relative error is calculated as follows:

RE = (Absolute Error / True Value) × 100 = (4.7 mL / 355 mL) × 100

RE = 1.3239%

Since we need to round to three decimal places, the relative error will be:

RE = 1.324%

This means that the advertised volume has a relative error of 1.324% with the inspector's measurement, indicating the proportion by which the advertised volume was off relative to the actual measurement.