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Learning Math Home
Session 2, Part C: Precision and Accuracy
 
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Session 2, Part C:
Precision and Accuracy (30 minutes)

In This Part: Measuring With Precision | Accuracy vs. Precision

We have learned that physical measurement involves error and that every physical measurement is an approximation. This leads us to a new question: How much error is involved in any given measurement? The terms precision and accuracy relate to how good an approximation is. For example, how precise were our measurements of the sides of the right triangles, and how accurate were our measurements of the distance from Mars to the Sun?

Since measurements are approximate, the most meaningful way of interpreting a measurement is as an interval with a lower bound and an upper bound. Imagine that we have measured a line segment, using a ruler divided into centimeters, and found the length to be 5 cm. To be more precise, we can state the measure as an interval -- either in words, 5 cm to the nearest 0.5 cm, or using notation, such as 5 cm 0.5 cm (read "5 cm plus or minus 0.5 cm"). Either presentation gives the center of the interval and the distance of the upper and lower bounds from this center (5 0.5 implies a lower bound of 4.5 and an upper bound of 5.5). We can also state that the maximum possible error for this measure is 0.5 cm (which is half the size of the measurement unit). Note 12

In summary, the precision of a measurement depends on the size of the smallest measuring unit -- whether the measurement is, for example, to the nearest 10 feet, to the nearest foot, or to the nearest tenth of a foot. The smaller the interval, the more we have "narrowed it down," and thus the more precise the measurement.



video thumbnail
 

Video Segment
Watch this video segment to see the participants discuss whether a measurement is an approximate or an exact value. They also discuss the role partitioning plays in answering this question.

Can you think of any other reasons that would support their conjecture?

If you are using a VCR, you can find this segment on the session video approximately 6 minutes and 4 seconds after the Annenberg Media logo.

 

 

Problem C1

Solution  

In Part A, we discussed how a unit can be partitioned into smaller subunits. How are partitioning and precision related?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think about what you would do to a measuring instrument if you wanted to measure something more precisely.   Close Tip

 

Problem C2

Solution  

When measuring length, the precision unit is determined by the smallest unit being repeated on the measuring tool (the smallest hash mark). Examine the rulers below (not drawn to scale), and identify the precision unit:


 

Problem C3

Solution  

The maximum possible error of a measurement is always half the size of the precision unit. For example, if the precision unit is 1 cm, the maximum possible error is 0.5 cm; if the precision unit is 4 cm, the maximum possible error is 2 cm, etc. What is the maximum possible error for each ruler above?


 

Problem C4

Solution  

In Problem B6, you measured isosceles right triangles and found that the hypotenuse of the triangle with legs of 3.0 cm was 4.2 cm. What is the precision unit? Give the interval that shows a more accurate measure of the hypotenuse.


Next > Part C (Continued): Accuracy vs. Precision

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