Consider the following measurement. $49,0 \overline { 0 } 0 \mathrm {~W}$ Find the precision, the greatest possible error, the relative error and the percent of error (to the nearest hundredth of a percent).
A) 5 W; 10 W; 0.000102; 0.02%
B) 20 W; 5 W; 0.002041; 0.01%
C) 5 W; 20 W; 0.00010; 0.04%
D) 10 W; 5 W; 0.000102; 0.01%
E) 10 W; 5 W; 0.000102; 0.1%

Question

Quizplus · Accepted Answer

- Precision: The measurement has three decimal places, so the precision is 0.001 W.
- Greatest possible error: The last digit is uncertain, so the greatest possible error is half of the precision, which is 0.0005 W. 
- Relative error: The relative error is the greatest possible error divided by the measured value, which is 0.0005/49.000 = 0.0000102. (Note that this is the same for all choices, so it does not help us distinguish between them.) 
- Percent of error: The percent of error is the relative error multiplied by 100%, which is 0.00102%. 
Now we can compare the choices to see which ones have a greatest possible error less than or equal to 5 W. Choices A, B, and E have a greatest possible error of 10 W or more, so they can be eliminated. Choice C has a greatest possible error of 20 W, so it can be eliminated. Therefore, the only choice that satisfies the condition is D, which has a greatest possible error of 5 W.

Consider the Following Measurement 49,00‾0 W49,0 \overline { 0 } 0 \mathrm {~W}49,000 W

Consider the Following Measurement $49,0 \overline { 0 } 0 \mathrm {~W}$