Mathematics
Grade 10
15 min
Precision
Precision
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1
Introduction & Learning Objectives
Learning Objectives
Define precision in the context of measurement.
Identify the unit of precision for any given measurement.
Calculate the greatest possible error (GPE) for a measurement.
Determine the interval of possible actual values for a measurement using its GPE.
Compare the precision of two or more different measurements.
Apply the concept of precision to find the range of possible values for calculations involving perimeter and area.
If two Olympic sprinters finish a race with times of 10.1s and 10.12s, who really won? ⏱️ The answer depends on the precision of the stopwatch!
This tutorial explores the mathematical concept of precision, which is the level of detail in a measurement. You will learn how to quantify precision, understand the inherent error in every mea...
2
Key Concepts & Vocabulary
TermDefinitionExample
MeasurementA numerical value assigned to a physical quantity, obtained using a measuring instrument. Every measurement has a degree of uncertainty.The length of a pencil is measured as 18 cm.
Unit of PrecisionThe smallest unit used to make a measurement. It is determined by the finest markings on the measuring instrument.If a ruler is marked in millimeters, the unit of precision is 1 mm. If a weight is given as 74.3 kg, the unit of precision is 0.1 kg.
PrecisionThe level of detail or exactness of a measurement. A smaller unit of precision indicates a more precise measurement.A measurement of 5.43 m is more precise than a measurement of 5.4 m because its unit of precision (0.01 m) is smaller than the unit of precision for 5.4 m (0.1 m).
Greatest Possible Error (GPE)Th...
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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 measurement. First, identify the smallest unit the measurement is recorded in (the unit of precision), then divide it by two.
Measurement Interval Formula
[\text{Measurement} - \text{GPE}, \text{Measurement} + \text{GPE}]
This formula defines the range that contains the true value of the measurement. The lower bound is the measurement minus the GPE, and the upper bound is the measurement plus the GPE.
Rule for Comparing Precision
Smaller Unit of Precision = More Precise Measurement
To compare the precision of two measurements, find the unit of precision for each. The measurement with the smaller unit of precision is co...
4 more steps in this tutorial
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Challenging
A rectangular plot of land is measured as 20 m long and 10 m wide, to the nearest meter. What is the range of possible values for its area?
A.[195 m², 205 m²)
B.[185.25 m², 215.25 m²)
C.[190 m², 210 m²)
D.[180 m², 220 m²)
Challenging
Two metal rods are measured as L1 = 30.4 cm and L2 = 12.7 cm. What is the maximum possible length if the rods are laid end-to-end?
A.43.1 cm
B.43.15 cm
C.43.2 cm
D.43.3 cm
Challenging
The radius of a circular pool is measured as 10 meters, to the nearest meter. Using π ≈ 3.14, what is the maximum possible area of the pool's surface?
A.346.185 m²
B.314 m²
C.298.465 m²
D.330.125 m²
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