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# Accuracy, Precision, and Error in Measurements (15 Favorites)

LAB in Accuracy, Measurements, Significant Figures, Accuracy, Error Analysis, Error Analysis. Last updated April 3, 2020.

### Summary

In this lab, students make measurements of length and width using four measuring tools. They will measure the same object using measuring sticks of different precision. They will observe that the exactness of a measurement is limited by the precision of the measuring instrument.

Middle School, High School

### NGSS Alignment

This lab will help prepare your students to meet the following scientific and engineering practices:

• Scientific and Engineering Practices:
• Using Mathematics and Computational Thinking
• Analyzing and Interpreting Data

### Objectives

By the end of this lab, students should be able to:

• Distinguish between accuracy and precision.
• Apply the rules of significant figures to authentic measurements and calculations.
• Explain why all measurements have some degree of uncertainty that comes from a variety of sources.

### Chemistry Topics

This lab supports students’ understanding of:

• Accuracy
• Precision
• Significant figures and uncertainty

### Time

Teacher Preparation: 60 minutes (to prepare meter sticks, only the first time you do this lab)

Lesson: 30-40 minutes

### Materials

• A set of four measuring sticks for each group as identified in teacher notes, below
• A large object whose dimensions of length and width can be easily measured (see teacher notes for additional information).Examples include:
• Square or rectangular desktop
• Classroom door
• Blackboard/whiteboard
• Windows
• Large periodic table poster

### Safety

• No specific safety precautions need to be observed for this activity.

### Teacher Notes

• Prior to this activity, students should have been taught the concepts of significant figures, accuracy, precision, averages, and percent error.
• Other AACT resources that could help with these topics:
• Student groups should ideally have four members so each can make measurements with one measuring stick before switching until all members have used all measuring sticks.
• The object to be measured should be larger than the measuring sticks used in this activity so it forces the student with the least precise measuring stick to take a measurement that has at least one certain digit. Some examples include a square or rectangular desktop, the classroom door, blackboard/whiteboard, windows, or large periodic table poster. The object should be either a square or a rectangle to avoid confusion as to which side to measure.
• If you would rather measure smaller objects, such as a textbook, you could use a wooden 30.48cm (12 inch) ruler instead of a meter stick. It is much easier, and cheaper, to prepare these as opposed to a meter stick. If you do the lab in this manner, note that you won’t need the meter stick so students will only collect 3 data points (essentially just eliminating stick #4).
• Students will calculate area and report their measurements to the correct number of significant figures appropriate for the tool used to make the measurement.
• Students should use their average values as the accepted value when calculating percent error. Alternatively, you could supply the students with your own measurements for the accepted value of the object’s dimensions for use in determining the percent error.

Possible extensions:

• A more advanced application of the rules of significant figures while calculating values can be integrated into this activity by having students calculate area using measuring tools of two different precision values. For example, have students measure length with stick #2 and width with stick #3, then calculate area according to the rules for multiplying significant figures.
• Other possible extensions include having students calculate perimeters (using significant figures rules for addition) or volume for 3D objects (such as a teacher’s desk, a door, etc.)

Preparing measuring sticks:

• You can remove marks by sanding down the appropriate markings on wooden rulers or meter sticks (see pictures below) or covering them with tape.
• Stick #1: a standard wooden ruler or meter stick
• Stick #2: a standard wooden ruler or meter with the millimeter precision marks eliminated, leaving the 1 cm incremental marks
• Stick #3: a standard wooden ruler or meter stick with all precision marks eliminated with the exception of the 10 cm incremental marks
• Stick #4: a standard wooden ruler or meter stick with all precision marks eliminated ### Background

Measurements are an integral part of scientific research.Without the ability to make accurate and precise measurements, scientists would be unable to use their data to make reliable conclusions that could be reproduced by other scientists to verify their results.In this activity, you will examine how the quality of the tools a scientist uses affects the significant figures, and therefore the accuracy and precision, of their measurements and calculations.

### Prelab Questions

1. Using your class notes, textbook, or other reliable resource, define the following:
1. Accuracy:
2. Precision:
3. Significant Figures:
4. Percent Error:
2. Examine each of the four measuring sticks provided by your teacher. Indicate the precision of each in the table below:

 Stick # Precise to the nearest (m) 1 2 3 4

### Problem

How do the significant figures allowed by a measuring tool affect the precision, accuracy, and error of a measurement?

### Materials

• Set of prepared measuring sticks
• A large object whose dimensions of length and width can be easily measured, such as a rectangular or square desktop

### Procedure

1. Identify which group member is “Student A,” “Student B,” etc. and which measuring stick each student will use first.
2. Measure the length and width of the provided object with one of the provided measuring sticks, recording your data in the appropriate places in the table below.
3. For each measurement, circle the uncertain but significant digit (hint: last digit).
4. Independently of other group members, repeat steps 2-3 for each of the four measuring sticks. (Note: each group member should make their own measurements before sharing data.)
5. Calculate the area of the object as determined by the data obtained from each measuring stick. The calculated area must be reported to the correct number of significant figures appropriate for the measuring device used.
6. Once each group member has made their measurements with all four measuring sticks, complete the table with your group members’ data.
7. Each member of the group will calculate an average area measurement derived from the group’s collective data set. (You do not need to calculate average length or width measurements.)

### Results

 Student A Student B Student C Student D Average Stick #1 Length (m) X Width (m) X Area (m2) Stick #2 Length (m) X Width (m) X Area (m2) Stick #3 Length (m) X Width (m) X Area (m2) Stick #4 Length (m) X Width (m) X Area (m2)

### Calculations

Be sure to obey the rules of significant figures for all calculations.

1. Show a sample area calculation from the measurements of one of your measuring sticks.
2. Show a sample calculation for your average area from the area calculations of each group member from one of your measuring sticks.

### Analysis

Calculate the % error for your area calculation compared to the group’s average occurring from the use of each measuring stick.Show your work in the last column.

 Stick # Your Area Calculation Average Area Calculation 1 2 3 4
1. Explain how you applied the rules of significant figures in determining how many digits to record for the length and width measurements for each measuring stick.
2. Explain how you applied the rules of significant figures in determining how to round your area calculations for each measuring stick.
3. Explain which measuring stick provided the most precise and accurate measurements.
4. Is it possible to have a set of precise measurements that are not accurate? If so, provide an example of how this could happen.

### Conclusion

Explain how the different measuring tools affected the accuracy and precision of your measurements and the percent error of your area calculations. Cite specific data to support your explanation. Describe at least three potential sources of error.