Greatest possible error

Learning Objectives Define Greatest Possible Error (GPE) and its relationship to the precision of a measurement. Identify the smallest unit of measurement for any given value. 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 area of a rectangle. Apply the concept of GPE to calculate the minimum and maximum possible volume of a rectangular prism. If a blueprint says a beam must be 4.5 meters long, how much 'wiggle room' do the builders actually have? 🤔 Let's find out! Every measurement we take, no matter how careful we are, is an approximation. In this lesson, you'll learn how to qu...

TermDefinitionExample PrecisionThe level of detail of a measurement, determined by the smallest unit on the measuring instrument. A measurement to the nearest millimeter is more precise than one to the nearest centimeter.A measurement of 5.2 cm is more precise than a measurement of 5 cm. Unit of Measurement (Unit of Precision)The smallest increment used to make a measurement. This is the place value of the last significant digit.If a length is measured as 14.3 cm, the unit of measurement is 0.1 cm. If it's measured as 14 cm, the unit is 1 cm. Greatest Possible Error (GPE)The maximum amount a measurement can be off from its true value. It is always half of the unit of measurement.For a measurement of 14.3 cm, the unit is 0.1 cm. The GPE is 0.1 / 2 = 0.05 cm. Lower BoundThe smallest po...

Greatest Possible Error Formula GPE = \frac{1}{2} \times (\text{Unit of Measurement}) Use this formula to find the maximum potential error for any given measurement. First, identify the smallest unit of measurement, then divide it by two. Lower and Upper Bound Formulas Lower Bound = Measurement - GPE \\ Upper Bound = Measurement + GPE Use these formulas to calculate the minimum and maximum possible true values of a measurement once you have found the GPE. Range of Possible Values Inequality Lower Bound \le \text{Actual Value} < Upper Bound This inequality represents the complete range of possible true values. Note the use of 'less than or equal to' for the lower bound and 'less than' for the upper bound, as a value equal to the upper bound woul...