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Accuracy and Error

Master accuracy and error with interactive lessons and practice problems! In this unit, you will learn how to deal with problems that require an exact answer versus those that require an approximate answer.

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Accuracy and Error

Study Guide

Key Definition

Accuracy refers to how close a measurement is to the true value. Error refers to the difference between the measured value and the true value.

Important Notes

Accuracy and error are important concepts in real-world problems.
Different problems require different levels of accuracy.
Some problems require exact answers, while others require approximations.

Mathematical Notation

$±$: indicates the uncertainty or tolerance in measurements.

$Δx = x_{measured} - x_{true}$: absolute error.

$\text{Relative error} = \frac{Δx}{|x_{true}|}$: relative error.

$\%\text{ error} = \left(\frac{Δx}{|x_{true}|}\right) \times 100\%$: percent error.

$x = \sqrt{a^2 + b^2}$: Pythagorean theorem.

Symbols are critical for understanding mathematical formulas and equations.

Why It Works

The concept of accuracy and error applies in real-world situations where measurements are taken. It helps us understand the precision of our measurements and calculations.

Remember

Always consider the level of accuracy required when solving a problem.

Quick Reference

Pythagorean Theorem:$x = \sqrt{a^2 + b^2}$

Understanding Accuracy and Error

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Accuracy refers to how close a measurement is to the true value. Error refers to the difference between the measured value and the true value.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the length of the hypotenuse in a right triangle with sides 3 and 7?

Real-World Problem

Question Exercise

Intermediate

Garden Fencing Scenario

Deanna is making a wire fence for her garden in the shape of a right triangle. The sides are 3 meters and 7 meters long. What is the length of the hypotenuse?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a measurement is reported as 5.67 with a precision of ±0.02, what is the range of possible actual values?

Challenge Quiz

Single Choice Quiz

Advanced

A measurement is reported as $\sqrt{50}$ with a precision of ±0.1. What is the range of possible actual values?

Recap

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Review key concepts and takeaways