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Geometry Lesson 1 – 2 Extended Precision and Accuracy Objective: Determine precision of measurements. Determine accuracy of measurements. Precision Precision refers to the clustering of a group of measurements. Depends on the smallest unit of measure. 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 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 Example 2 ¼ inches Smallest unit of measure is ¼ inch. Absolute error is ¼ / 2 in 1 4 1 1 1 1 2 * 2 4 4 2 8 Absolute error is 1/8 in 1 1 2 in 4 8 Means it can be between 1 1 2 4 8 1 3 2 & 2 in 8 8 1 1 &2 4 8 Example Find the absolute error and explain its meaning. 1 ½ inches Absolute error: ¼ in 1 1 1 2 4 1 3 between 1 & 1 4 4 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 Significant digits Precision in a measurement is usually expressed by the number of significant digits reported. 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. Determine the number of significant digits. 779,000 mi 3 significant digits Look at rule for whole numbers. 50,008 ft 5 significant digits Look at rule for whole numbers 430.008 m 6 significant digits Look at rule of decimals > 1 0.00750 cm 3 significant digits Look at rule of decimals < 1 230.004500 9 significant digits Look at rule of decimals > 1 Accuracy Refers to how close a measured value comes to the actual or desired value. Accuracy vs. Precision Accurate, but not precise Not accurate & not precise Precise, but not accurate Accurate & precise Relative Error Relative error is the ratio of the absolute error to the expected measure. absolute error exp ected measure 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. 0.5 cm 0.022 or 2.2% 23 cm Find the relative error 3.2 mi 0.05 mi 0.0156 1.6% 3.2 mi 1 ft 0.5 ft 0.5 50% 1 ft 26 ft 0.5 ft 0.01923 1.9% 26 ft Homework Pg. 24 1 – 23 all