10 Questions
Why is accuracy important in making measurements?
To save time and money by avoiding mistakes
What is the definition of accuracy?
How close a measurement is to the true or accepted value
What is the purpose of calculating percent error?
To know exactly how accurate your measurements are
What does the word 'error' mean in the context of measurements?
A mistake or deviation from what is expected
What is the formula for calculating percent error?
|(true value - measured value)| / true value
Why are the absolute value symbols used in the formula for calculating percent error?
To ensure that the result is always positive
What was the percent error in the measurement of the room's width?
20%
What was the actual width of the room?
7.5 ft
Why did the new rug not fit in the room?
The rug was too big
What is the importance of accuracy in fields like construction, science, and engineering?
It ensures that the final product is safe and functional
Study Notes
Importance of Accuracy
- Accuracy is crucial in various fields, including construction, science, and engineering, to avoid wasting time and resources.
- Inaccurate measurements can lead to undesirable outcomes, such as buying a rug that does not fit a room.
Definition of Accuracy
- Accuracy refers to how close a measurement is to the true or accepted value.
Calculating Percent Error
- Percent error is a ratio of the difference between the true value and the measured value, multiplied by 100.
- Formula: |(measured value - true value)| / true value × 100
- The numerator is enclosed by absolute value symbols to ensure a positive value.
Examples of Percent Error
- Example 1: Measuring a room's width (measured: 9 ft, true value: 7.5 ft) = 20% error
- Example 2: Measuring acceleration due to gravity (measured: 8.7 m/s², true value: 9.8 m/s²) = positive percent error (using absolute value)
Key Points
- Percent error is always positive, regardless of whether the measurement is larger or smaller than the true value.
- The absolute value symbol ensures a positive numerator in the percent error formula.
Learn why accuracy is crucial in measurement through a relatable anecdote about buying a new rug. See how inaccurate measurements can lead to unwanted consequences.
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