Percent Error Quiz: Master Your Scientific Accuracy

1. Relative (fractional) uncertainty is absolute uncertainty divided by the measured value.

True

False

Relative uncertainty compares uncertainty size to the measurement size. This helps compare measurement quality across different scales.

Explanation

Relative uncertainty compares uncertainty size to the measurement size. This helps compare measurement quality across different scales.

2. Absolute uncertainty is usually reported in:

No units

The same units as the measurement

Only percent

Only seconds

Absolute uncertainty represents a range around the measured value. It uses the same unit so it can be added/subtracted directly.

Explanation

Absolute uncertainty represents a range around the measured value. It uses the same unit so it can be added/subtracted directly.

3. A length is (25.0 ± 0.2) cm. The percent uncertainty is closest to:

0.08%

0.8%

8%

80%

Relative uncertainty is (0.2/25.0 = 0.008). Multiply by 100 to get 0.8%.

Explanation

Relative uncertainty is (0.2/25.0 = 0.008). Multiply by 100 to get 0.8%.

4. Which statement is most accurate?

High precision guarantees high accuracy

Precision and accuracy are different; uncertainty describes precision, error describes accuracy

Uncertainty and error are identical

Random errors cause bias

Uncertainty is about spread and measurement limits. Error compares to an accepted value and is affected by systematic bias.

Explanation

Uncertainty is about spread and measurement limits. Error compares to an accepted value and is affected by systematic bias.

5. Percent error is usually calculated as:

({accepted}/{measured}) * 100%

(|measured – accepted|/accepted) * 100%)

({measured}/{accepted- measured}) * 100%)

({accepted-measured}/{measured}) * 100%)

Use the absolute difference divided by the accepted value. The absolute value avoids negative percent errors.

Explanation

Use the absolute difference divided by the accepted value. The absolute value avoids negative percent errors.

6. If a value is multiplied by 10, the absolute uncertainty is multiplied by 10, but the percent uncertainty stays the ______ (assuming the same relative uncertainty).

Multiplying both the value and its absolute uncertainty by 10 keeps their ratio unchanged. That keeps percent uncertainty constant.

Explanation

Multiplying both the value and its absolute uncertainty by 10 keeps their ratio unchanged. That keeps percent uncertainty constant.

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7. For the same example (50.0 g measured, 49.0 g accepted), percent error is closest to:

0.5%

1.0%

2.0%

5.0%

(|50.0-49.0|/49.0 ≈ 1/49 ≈ 0.0204). Multiply by 100 gives about 2.0%.

Explanation

(|50.0-49.0|/49.0 ≈ 1/49 ≈ 0.0204). Multiply by 100 gives about 2.0%.

8. A measurement can have low percent uncertainty but high percent error.

True

False

Low percent uncertainty means tight measurement spread or fine resolution. A systematic bias can still make the result far from the accepted value.

Explanation

Low percent uncertainty means tight measurement spread or fine resolution. A systematic bias can still make the result far from the accepted value.

9. Percent uncertainty of 2% means the uncertainty is about 2% of the measured value.

True

False

Percent uncertainty gives a scaled sense of reliability. It helps compare different measurements fairly.

Explanation

Percent uncertainty gives a scaled sense of reliability. It helps compare different measurements fairly.

10. Relative uncertainty is unitless.

True

False

Dividing uncertainty by the measurement cancels the unit. That makes relative uncertainty a pure number.

Explanation

Dividing uncertainty by the measurement cancels the unit. That makes relative uncertainty a pure number.

11. The best overall summary is:

Percent error and percent uncertainty are the same

Absolute uncertainty is in measurement units; percent uncertainty scales uncertainty; percent error compares to an accepted value

Uncertainty is always zero

Repeating removes systematic error

Uncertainty describes how reliable the measurement is, while error measures how close it is to the accepted value. Both are needed for good reporting.

Explanation

Uncertainty describes how reliable the measurement is, while error measures how close it is to the accepted value. Both are needed for good reporting.

12. If the uncertainty is ±0.5 s, reporting 12.36 s would usually be too precise.

True

False

±0.5 means the tenths place is the limit. Extra digits imply certainty you don’t have.

Explanation

±0.5 means the tenths place is the limit. Extra digits imply certainty you don’t have.

13. When reporting (12.4 ± 0.5) s, the value and uncertainty should match in ______ place.

The uncertainty sets the last meaningful place. The measured value should be rounded to that same place to avoid false precision.

Explanation

The uncertainty sets the last meaningful place. The measured value should be rounded to that same place to avoid false precision.

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14. A stopwatch with reaction time variability mainly introduces:

Systematic error only

Random uncertainty

No error

Units error

Reaction time varies each trial. That creates scatter that can be reduced by repeats and averaging.

Explanation

Reaction time varies each trial. That creates scatter that can be reduced by repeats and averaging.

15. A mass is measured as 50.0 g, accepted value is 49.0 g. The absolute error is ______ g.

Absolute error is the magnitude of the difference: (|50.0-49.0|=1.0) g. This measures how far off the measurement is.

Explanation

Absolute error is the magnitude of the difference: (|50.0-49.0|=1.0) g. This measures how far off the measurement is.

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16. Percent error compares a measured value to an accepted value.

True

False

Percent error shows how far you are from the accepted value in percent terms. It is about accuracy, not just spread.

Explanation

Percent error shows how far you are from the accepted value in percent terms. It is about accuracy, not just spread.

17. Which report is best?

(8.237 ± 0.2) m

(8.2 ± 0.2) m

(8 ± 0.2) m

(8.20 ± 0.2) m

±0.2 sets the tenths place. 8.2 matches that; 8.237 is too precise.

Explanation

±0.2 sets the tenths place. 8.2 matches that; 8.237 is too precise.

18. A measurement is (3.00 ± 0.06) v. Relative uncertainty is:

0.002

0.02

0.2

2

(0.06/3.00 = 0.02). This corresponds to 2% uncertainty.

Explanation

(0.06/3.00 = 0.02). This corresponds to 2% uncertainty.

19. Percent error is based on the accepted value in the denominator, not the measured value (standard convention).

True

False

Using the accepted value makes the comparison anchored to the reference. Some contexts vary, but this is the common school/science convention.

Explanation

Using the accepted value makes the comparison anchored to the reference. Some contexts vary, but this is the common school/science convention.

20. Percent uncertainty = (relative uncertainty) × ______%.

Multiplying by 100 expresses the fraction as a percentage. This is often easier to interpret.

Explanation

Multiplying by 100 expresses the fraction as a percentage. This is often easier to interpret.

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Percent Error Quiz: Test Your Accuracy in Scientific Calculations

1. Relative (fractional) uncertainty is absolute uncertainty divided by the measured value.

2.

What first name or nickname would you like us to use?

2. Absolute uncertainty is usually reported in:

3. A length is (25.0 ± 0.2) cm. The percent uncertainty is closest to:

4. Which statement is most accurate?

5. Percent error is usually calculated as:

6. If a value is multiplied by 10, the absolute uncertainty is multiplied by 10, but the percent uncertainty stays the ______ (assuming the same relative uncertainty).

7. For the same example (50.0 g measured, 49.0 g accepted), percent error is closest to:

8. A measurement can have low percent uncertainty but high percent error.

9. Percent uncertainty of 2% means the uncertainty is about 2% of the measured value.

10. Relative uncertainty is unitless.

11. The best overall summary is:

12. If the uncertainty is ±0.5 s, reporting 12.36 s would usually be too precise.

13. When reporting (12.4 ± 0.5) s, the value and uncertainty should match in ______ place.

14. A stopwatch with reaction time variability mainly introduces:

15. A mass is measured as 50.0 g, accepted value is 49.0 g. The absolute error is ______ g.

16. Percent error compares a measured value to an accepted value.

17. Which report is best?

18. A measurement is (3.00 ± 0.06) v. Relative uncertainty is:

19. Percent error is based on the accepted value in the denominator, not the measured value (standard convention).

20. Percent uncertainty = (relative uncertainty) × ______%.