Mathematics
Grade 9
15 min
Precision
Precision
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1
Introduction & Learning Objectives
Learning Objectives
Define precision and distinguish it from accuracy.
Identify the unit of precision for a given measurement.
Calculate the Greatest Possible Error (GPE) of a measurement.
Determine the range of possible actual values for a measurement using the GPE.
Compare the precision of two or more measurements.
Apply the rules of precision when adding or subtracting measurements.
You measure a board to be 2.5 meters long, but is it *exactly* 2.50000... meters? 🤔 Let's explore the limits of our measurements!
This tutorial will introduce the concept of precision, which describes how detailed a measurement is. You will learn how to determine a measurement's precision, calculate its potential error, and correctly use precise measurements in calculations. Unders...
2
Key Concepts & Vocabulary
TermDefinitionExample
PrecisionThe level of detail or fineness of a measurement, indicated by the smallest unit on the measuring instrument. A more precise measurement has a smaller unit of measurement.A measurement of 5.25 cm is more precise than a measurement of 5.2 cm because the unit of precision is hundredths of a centimeter (0.01 cm) instead of tenths (0.1 cm).
AccuracyHow close a measured value is to the actual or true value. It is possible for a measurement to be precise but not accurate.If a scale is improperly calibrated and consistently reads 0.5 kg too high, a measurement of 10.53 kg is precise (to the nearest hundredth) but not accurate.
Unit of PrecisionThe smallest unit to which a measurement is made. It is determined by the place value of the last significant digit.For a m...
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Core Formulas
Greatest Possible Error (GPE) Formula
GPE = \frac{1}{2} \times (\text{Unit of Precision})
Use this formula to find the maximum potential error for any given measurement. First, identify the smallest unit of measurement (the unit of precision), then divide it by two.
Range of Measurement Formula
(\text{Measurement} - \text{GPE}) \le \text{Actual Value} < (\text{Measurement} + \text{GPE})
This inequality defines the lower and upper bounds for the true value of a measurement. The actual value can be equal to the lower bound but must be less than the upper bound.
Rule for Adding/Subtracting with Precision
Round the result to the same precision as the LEAST precise measurement.
When adding or subtracting measurements, the result cannot be more precise than the least pr...
4 more steps in this tutorial
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Challenging
A rectangular garden is 15.5 m long and 8 m wide. First, calculate its perimeter expressed to the correct level of precision. Then, determine the range of the actual perimeter.
A.Perimeter = 47 m; Range = 46.5 m to 47.5 m
B.Perimeter = 47.0 m; Range = 46.95 m to 47.05 m
C.Perimeter = 47 m; Range = 46 m to 48 m
D.Perimeter = 47 m; Range = 42 m to 52 m
Challenging
The Greatest Possible Error (GPE) of a length measurement is 0.05 m. Which of the following could have been the recorded measurement?
A.12.55 m
B.12.5 m
C.12 m
D.13.00 m
Challenging
A student measures the volume of a liquid as 52 mL using a beaker with markings every 1 mL. If they switch to a graduated cylinder with markings every 0.1 mL, what is the most likely effect on their next measurement and its GPE?
A.The measurement will be more precise, and the GPE will increase.
B.The measurement will be less precise, and the GPE will decrease.
C.The measurement will be more precise, and the GPE will decrease.
D.The measurement's precision and GPE will remain the same, but accuracy will improve.
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