1. Accuracy and Precision
Chapter 1 Computing Tools
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2. Accuracy and Precision
Accuracy and precision are often used interchangeably, but have different definitions:
Accuracy is a measure of how close our answer is to the actual result. In the projectile example, the assumptions made in the mathematical model affect the accuracy of the results
Precision is a measure of the exactness of our calculations – important that we remember that our answer can be no more precise than our input values or of intermediate calculation results
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3. Significant Digits
In experimental work, where the precision of all of the input values is known, calculation rules involving the number of significant digits are followed
For quantities with decimal points, the number of significant digits is defined as the number of digits between the first non-zero digit and the last digit.
Examples:
significant digits
significant digits
significant digits
significant digits
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4. How Many Significant Digits? 8
-77.32 4 3
3.44 X 108
100
Can't tell
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5. Rules for Working with Significant Digits
Addition and Subtraction: the number of digits to the right of the decimal point in the answer must be equal to the least number of digits to the right of any of the inputs.
Examples: = = 10.3 (1 digit)
10.0 – = = 10.0 (1 digit)
Multiplication and Division: the number of significant digits in the answer must equal the least number of significant digits of the input values.
Examples: X 5.52 = = 41.7 (3 digits)
1.0 / = = 0.22 (2 digits)
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6. Engineering Calculations
In engineering problems, the precision (number of digits) may be expressed as:
35 degrees +/- 3 degrees
35 degrees +/- 5%
36.5 to 34.7 inclusive
If no range is given: report results to 3 significant digits (some texts recommend 4 significant digits if the first significant digit is a “1”)
Remember that for the final answer to be precise to this number of digits, intermediate calculations should be carried out to more digits
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7. FOUL! Excessive Use of digits
Reporting Answers
Never report your answer to a ridiculous number of digits! If would sound wrong is you said it verbally; it is equally wrong if you report it in writing
FOUL! Excessive Use of digits
The answer is
centimeters
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8. Reporting Answers
The computer performs calculations to a large number of digits, but that doesn't mean the answer is that precise
How many digits do Excel and MATLAB carry through in calculations? Approximately 15 for most operations
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