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Geometry

Learn about precision and accuracy in measurements, absolute error, significant digits, and relative error with practical examples. Understand the importance of precision and accuracy in measurements.

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Geometry

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  1. Geometry Lesson 1 – 2 Extended Precision and Accuracy Objective: Determine precision of measurements. Determine accuracy of measurements.

  2. Precision • Precision refers to the clustering of a group of measurements. • Depends on the smallest unit of measure.

  3. Absolute Error • Absolute error of a measurement is equal to one-half the smallest unit of measure. • The smaller the unit the more precise the measurement. Smallest unit – 1 cm Absolute error – 0.5 cm

  4. Example • Find the absolute error of each measurement. Explain its meaning. • 6.4 cm Smallest unit of measure is 0.1 cm or 1 mm Absolute error is 0.1/2 cm Absolute error is 0.05 cm Means that it can be between 6.35 and 6.45 cm 6.4 – 0.5 & 6.4 + 0.5

  5. Example Smallest unit of measure is ¼ inch. • 2 ¼ inches Absolute error is ¼ / 2 in Absolute error is 1/8 in Means it can be between

  6. Example • Find the absolute error and explain its meaning. • 1 ½ inches Absolute error: ¼ in

  7. Example • Find the absolute error and explain its meaning. • 4 centimeters Absolute error: 0.5 centimeters (use decimal for metric) 4 + 0.5 cm Between 3.5 & 4.5 cm

  8. Significant digits • Precision in a measurement is usually expressed by the number of significant digits reported.

  9. Significant digits • Nonzero digits are always significant • In whole numbers, zeros are significant if they fall between nonzero digits. • In decimal numbers greater than or equal to 1, every digit is significant. • In decimal numbers less than 1, the first nonzero digit and every digit to the right are significant.

  10. Determine the number of significant digits. 3 significant digits Look at rule for whole numbers. • 779,000 mi • 50,008 ft • 430.008 m • 0.00750 cm • 230.004500 5 significant digits Look at rule for whole numbers 6 significant digits Look at rule of decimals > 1 3 significant digits Look at rule of decimals < 1 9 significant digits Look at rule of decimals > 1

  11. Accuracy • Refers to how close a measured value comes to the actual or desired value.

  12. Accuracy vs. Precision Accurate, but not precise Precise, but not accurate Accurate & precise Not accurate & not precise

  13. Relative Error • Relative error is the ratio of the absolute error to the expected measure.

  14. Find Relative error • A manufacturer measures each part for a piece of equipment to be 23 cm in length. Find the relative error of this measurement.

  15. Find the relative error • 3.2 mi • 1 ft • 26 ft

  16. Homework • Pg. 24 1 – 23 all

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