Mathematics
Grade 9
15 min
Percent error
Percent error
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1
Introduction & Learning Objectives
Learning Objectives
Define measured value, actual value, absolute error, and percent error.
Calculate the absolute error between a measured value and an actual value.
Correctly apply the formula to calculate percent error.
Interpret the meaning of a calculated percent error in the context of a real-world problem.
By the end of this lesson, students will be to solve word problems involving percent error in various measurement scenarios.
Use percent error to compare the relative accuracy of two different measurements.
You're in science class and your experiment's result is slightly different from the textbook value. 🧪 Did you make a mistake, or is a small error acceptable? Let's find out!
This tutorial will teach you how to calculate percent error, a powerful...
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Key Concepts & Vocabulary
TermDefinitionExample
Measured Value (or Experimental Value)The value you obtain when you actually perform a measurement with a tool (like a ruler, scale, or thermometer).You use a ruler to measure a line and get 15.2 cm. The measured value is 15.2 cm.
Actual Value (or Accepted/True Value)The correct, universally accepted, or theoretical value of a quantity. This is often given in a problem.The problem states that the actual length of the line is 15.0 cm. The actual value is 15.0 cm.
ErrorThe difference between the measured value and the actual value. It can be positive or negative.If you measure 15.2 cm and the actual length is 15.0 cm, the error is 15.2 - 15.0 = 0.2 cm.
Absolute ErrorThe absolute difference between the measured value and the actual value. It is always a positive number,...
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Core Formulas
Absolute Error Formula
Absolute Error = |Measured Value - Actual Value|
Use this first to find the magnitude of the error. The vertical bars `| |` mean absolute value, so the result is always positive.
Percent Error Formula
Percent Error = ( |Measured Value - Actual Value| / |Actual Value| ) * 100%
This is the main formula. It calculates the error as a percentage of the actual value. Note that the denominator must be the actual (or true) value, not the measured one.
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Challenging
A student is asked to draw a square with side lengths of 10 cm. They accidentally draw a square with side lengths of 10.5 cm. What is the percent error in the AREA of the square they drew?
A.5.0%
B.21.0%
C.10.25%
D.10.0%
Challenging
Scientist A measures a 1 km distance with an absolute error of 1 meter. Scientist B measures a 10 cm object with an absolute error of 1 cm. Which statement accurately compares their results?
A.Scientist A is more accurate because their percent error is much smaller.
B.Scientist B is more accurate because their percent error is smaller.
C.Scientist A is more accurate because their absolute error is smaller.
D.Both scientists have the same accuracy.
Challenging
Two measurements are made. Measurement X has a measured value of 52 and a percent error of 4%. Measurement Y has a measured value of 88 and a percent error of 10%. Assuming both measured values are greater than their respective actual values, what is the sum of the actual values for X and Y?
A.135
B.140
C.130
D.128
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