Mathematics
Grade 9
15 min
Greatest possible error
Greatest possible error
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1
Introduction & Learning Objectives
Learning Objectives
Define the concept of Greatest Possible Error (GPE) in the context of measurement.
Identify the smallest unit of measure (precision) for any given measurement.
Calculate the Greatest Possible Error for a given measurement.
Determine the range of possible actual values (lower and upper bounds) for a measurement.
Apply the concept of GPE to calculate the minimum and maximum possible perimeter and area of simple geometric shapes.
Solve real-world problems involving measurement uncertainty.
Ever measured a piece of wood for a project, cut it, and found it was just a tiny bit too short? 📏 Let's explore the hidden 'wiggle room' in every measurement!
This tutorial will introduce you to the concept of the Greatest Possible Error (GPE). You will l...
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Key Concepts & Vocabulary
TermDefinitionExample
MeasurementThe process of using a tool to assign a numerical value to a physical quantity, such as length, weight, or time.Using a ruler to find that a book is 23 cm long.
PrecisionThe level of detail in a measurement, indicated by the smallest unit of measure on the measuring tool.A measurement of 5.4 cm is more precise than a measurement of 5 cm because the smallest unit is 0.1 cm instead of 1 cm.
Greatest Possible Error (GPE)The maximum amount by which a measurement can be incorrect. It is always equal to half of the smallest unit of measure used.If a length is measured to the nearest centimeter (e.g., 10 cm), the smallest unit is 1 cm, so the GPE is 0.5 * 1 cm = 0.5 cm.
Measured ValueThe value that is read directly from the measuring instrument.If a digital scale...
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Core Formulas
Greatest Possible Error (GPE) Formula
GPE = 0.5 \times (\text{smallest unit of measure})
Use this formula to calculate the maximum potential error for any given measurement. First, identify the smallest unit the measurement is recorded in, then multiply it by 0.5.
Lower Bound Formula
\text{Lower Bound} = \text{Measured Value} - \text{GPE}
Use this formula to find the minimum possible actual value of the measurement.
Upper Bound Formula
\text{Upper Bound} = \text{Measured Value} + \text{GPE}
Use this formula to find the maximum possible actual value of the measurement.
Range of Possible Values Inequality
\text{Lower Bound} \le \text{Actual Value} < \text{Upper Bound}
This inequality expresses the complete range where the true value lies. Note the use of �...
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Challenging
The base and height of a right-angled triangle are measured as 10.4 cm and 7.6 cm, respectively. What is the maximum possible area of the triangle? (Area = 0.5 * base * height)
A.39.52 cm²
B.40.09875 cm²
C.38.94875 cm²
D.80.1975 cm²
Challenging
A rectangular box is measured to have dimensions 30 cm, 20 cm, and 10 cm. What is the minimum possible volume of the box?
A.6000 cm³
B.6315.375 cm³
C.5714.375 cm³
D.5850 cm³
Challenging
A piece of wire, W1, is measured to be 50 cm long. Another piece, W2, is measured to be 50.8 cm long. Is it possible for the two wires to have the same actual length?
A.Yes, because their possible ranges of length overlap.
B.No, because the measurements are different.
C.No, because the upper bound of W1 is less than the lower bound of W2.
D.Yes, but only if they are both exactly 50.5 cm long.
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