Errors and Significant Figures

By Angela Toh

Errors and Uncertainties

Multiple Choice

A measurement result is considered ________ if it is judged to be close to the true value.

• Precise

• Accurate

• An error

• Resolution

Multiple Choice

Which of the following are characteristics of random errors?

• Doing several trials and finding the average will minimize them

• The observed results will usually be consistently too high, or too low

• Proper design of the experiment can eliminate them

• There is no way to know what they are

Multiple Choice

Which of the following is a correct statement about systematic errors?

• They arise due to incorrect judgment of a measurement.

• Their magnitude depends on the experimenter’s skill.

• They are consistent in magnitude.

• They occur as a result of a person’s inability to perform the experiment correctly.

• All of the above

Multiple Choice

A student is measuring the length of a set of pipes. Unfortunately his ruler has been damaged and starts at 0.2cm, which he fails to notice. This damage causes:

• Random and systematic errors

• Random error

• Systematic error

• Neither random or systematic error

Multiple Choice

True or False?

Zero error are random errors.

• True

• False

Multiple Select

Which of the following errors as are Random errors?

• Student A uses same spatula for all chemicals and does not clean it

  between use.

• Student B takes only one titration reading.

• Student C only notices that the burette has an air bubble after the

  experiment.

• Student D notices that her thermometer is not properly calibrated.

• Student E measures the mass of sodium carbonate on the electronic

  balance while the fan is switched on.

Multiple Select

Which of the following errors as are Systematic errors?

• Student A uses same spatula for all chemicals and does not clean it

  between use.

• Student B takes only one titration reading.

• Student C only notices that the burette has an air bubble after the

  experiment.

• Student D notices that her thermometer is not properly calibrated.

• Student E measures the mass of sodium carbonate on the electronic

  balance while the fan is switched on.

Multiple Choice

True or False?

Repeating a reading never removes the systematic error.

• True

• False

Multiple Choice

What could reduce systematic errors?

• averaging a large number of measurements

• careful calibration of measuring instruments

• reducing the sample size

• repeating measurements

Multiple Choice

When a measurement is repeatable and consistent it is said to have...

• High precision
• Low precision
• High accuracy
• Low accuracy

Multiple Choice

A set of data are all close to each other, but they are not close to the actual value.  This set of data can be described as...

• accurate
• precise
• both precise and accurate

Multiple Choice

A set of data are not close to each other, but the average of the data is very close to the actual value.  This set of data can be described as...

• accurate
• precise
• both precise and accurate

Multiple Choice

It is a measure of how close measurements come to each other when they are made in the same way

• Accuracy
• Precision
• Error
• Extrapolation

Multiple Choice

?

• High Accuracy & High Precision
• High Accuracy & Low Precision
• Low Accuracy & High Precision
• Low Accuracy & Low Precision

Multiple Choice

Describe the accuracy and precision of the image

• Accurate and Precise
• Accurate and not precise
• Not Accurate and Precise
• not accurate and not precise

Multiple Choice

Which Student is the most Precise?

• Alex

• Shandra

• Luis

Multiple Choice

This image is an example of...

• precision ONLY
• accuracy ONLY
• BOTH precision and accuracy
• NEITHER precision and accuracy 

Multiple Choice

A set of data are all close to each other, but they are not close to the actual value.  This set of data can be described as...

• accurate
• precise
• both precise and accurate

Multiple Choice

This bullseye demonstrates...

• High Accuracy & High Precision
• High Accuracy & Low Precision
• Low Accuracy & High Precision
• Low Accuracy & Low Precision

Multiple Choice

This bullseye demonstrates...

• High Accuracy & High Precision
• High Accuracy & Low Precision
• Low Accuracy & High Precision
• Low Accuracy & Low Precision

Multiple Choice

?

• High Accuracy & High Precision
• High Accuracy & Low Precision
• Low Accuracy & High Precision
• Low Accuracy & Low Precision

Multiple Choice

Describe the accuracy and precision of the image

• Accurate and Precise
• Accurate and not precise
• Not Accurate and Precise
• not accurate and not precise

Multiple Choice

Describe the accuracy and precision of the image

• Accurate and Precise
• Accurate and not precise
• Not Accurate and Precise
• not accurate and not precise

Multiple Choice

This bullseye demonstrates...

• High Accuracy & High Precision

• High Accuracy & Low Precision

• Low Accuracy & High Precision

• Low Accuracy & Low Precision

Multiple Choice

Which is the more precise measurement?

• 4 mL

• 4.3 mL

• 4.30 mL

• 4.300 mL

Multiple Choice

A student's measured length during a science experiment was 12.00 cm. The actual size was 14.25 cm.

What was the percent error?

*Hint: You now know how to calculate error, and you should know how to calculate a percent, so put the two together to find this answer.

• 15.79%

• 18.75%

• 2.25%

Multiple Choice

Jessie estimates the weight of her cat to be 8 pounds. The actual weight of the cat was 10 pounds.

What was the percent error?

*Hint: You now know how to calculate error, and you should know how to calculate a percent, so put the two together to find this answer.

• 15%

• 20%

• 25%

• 30%

Multiple Choice

Measurements: 24.9, 25.2, 25.1, 24.8

True Value: 25.0

These measurements are…

• Accurate, but not precise

• Precise, but not accurate

• Both precise and accurate

• Neither precise nor accurate

Multiple Choice

Zed went to the store and bought a bag of chips.  He estimated there would be 350 chips in the package, but realized there were only 210 chips in that package.  What was his percent error?

• 35%
• 67%
• 85%
• 92%

Multiple Select

A student’s calculation was found to have a 35.5% error, and his experimental measurement was 15.6 cm. What are the possible values for the actual measurement?

• 5.538 cm

• 21.138 cm

• 10.062 cm

• 51.1 cm

Multiple Choice

What kind of error is Parallax error or the viewing consistently from the wrong angle for all readings?

• Systematic errors

• Random errors

• Both systematic and random errors

• Neither systematic nor random errors

Multiple Choice

What errors occur in time measurements by a clock that runs too fast or slow?

• Systematic errors

• Random errors

• Both systematic and random errors

• Neither systematic nor random errors

Multiple Choice

True or False?

Repeating a reading never removes the systematic error.

• True

• False

Multiple Choice

Repeated measurements of a quantity can reduce the effects of

• both random errors and systematic errors

• neither random errors nor random errors

• random errors

• systematic errors

Multiple Choice

Which student is the most ACCURATE?

• A

• B

• C

Multiple Choice

Systematic errors lead to a lack of:

• accuracy in the measurement.

• significant digits in the measurement.

• precision in the measurement.

• gradation of the measuring instrument

Multiple Choice

Random errors lead to a lack of:

• accuracy in the measurement.

• significant digits in the measurement.

• precision in the measurement.

• gradation of the measuring instrument

Multiple Choice

How many significant figures: 2016 m

• 1
• 2
• 3
• 4

Multiple Choice

How many significant figures: 153.0 mL

• 1
• 2
• 3
• 4

Multiple Choice

How many significant figures: 0.012 km

• 1
• 2
• 3
• 4

Multiple Choice

How many significant figures: 0.001 g

• 4
• 3
• 2
• 1

Multiple Choice

How many sig figs are there?
0.000008

• 1
• 2
• 6
• 7

Multiple Choice

How many sig figs are there?
100000000

• 1
• 9
• 10

Multiple Choice

What is the mass and uncertainty indicated by this electronic balance?

• 198.61 ± 0.01 g

• 198.61 ± 0.02 g

• 198.61 ± 0.05 g

• 198.61 ± 0.005 g

Multiple Choice

Based on the markings of this graduated cylinder, what is the estimated volume?

• 63.5 cm³

• 63 cm³

• 63.55 cm³

• 0.063 cm³

Multiple Choice

In this problem $$2\left(9.8\ cm\ +12.53\ cm\right)\ =$$ the answer should be.

• 44.0

• 44.7

• 44.6

• 44.66

• 45.00

Multiple Select

If the precision of your answer is specified, you should report your answer to that level of precision. However, if the required precision of the answer is not given (specified), what are the things to consider when deciding the number of digits to report (precision) when reporting a calculated value?

• Common sense

• The most precisely measured value used

• Accepted convention

• The targeted rule

• The least precisely measure value used

Multiple Choice

• Student A
• Student B
• Student C
• Cannot be determined

Multiple Choice

The correct result (indicating the proper number of significant figures) of the following addition is ________.

12 +     1.2 +    0.12 +  0.012

• 13

• 13.3

• 13.33

• 13.332