Chapter 2 Sec 2.3 Scientific Measurement
14. accuracy 15. precision 16. percent error 17. significant figures 18. scientific notation 19. directly proportional 20. inversely proportional Vocabulary
Section3 Using Scientific Measurements Chapter 2 Objectives • Distinguish between accuracy and precision. • Determine the number of significant figures in measurements. • Perform mathematical operations involving significant figures. • Convert measurements into scientific notation. • Distinguish between inversely and directly proportional relationships.
2.3 Measurements and Their Uncertainty • A measurement is a quantity that has both a number and a unit • Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct. • International System of Measurement (SI) typically used in the sciences
Accuracy and Precision • Accuracy is the closeness of a measurement to thecorrect (accepted) value of quantity measured • Precision is a measure of how close a set of measurements are to one another • To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. • To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements
Accuracy and Precision Which target shows: 1. an accurate but imprecise set of measurements? 2. a set of measurements that is both precise and accurate? 3. a precise but inaccurate set of measurements? 4. a set of measurements that is neither precise nor accurate?
Where do these measurements come from? Recording Measurements
Section3 Using Scientific Measurements Chapter 2 Accuracy and Precision, continued Error in Measurement • Some error or uncertainty always exists in any measurement. • skill of the measurer • conditions of measurement • measuring instruments
F. Making Good Measurements • We can do 2 things: 1. Repeat measurement many times - reliable measurements get the same number over and over - this is PRECISION 2. Test our measurement against a “standard”, or accepted value - measurement close to accepted value is ACCURACY
Section3 Using Scientific Measurements Chapter 2 Accuracy and Precision, continued Percentage Error • Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.
G. Determining Error 1. Error = experimental value – accepted value *experiment value is measured in lab (what you got during experiment) * accepted value is correct value based on references (what you should have gotten) 2. Percent error = [Value experimental – Valueaccepted] x 100% Valueaccepted * Can put formula on notecard
Chapter 2 Section2 Units of Measurement 2.3 Practice Problems- Accuracy and Precision • (p.43) • 1. What is the percentage error for a mass measurement of 17.7 g, given that the correct value is 21.2 g?
Chapter 2 Section2 Units of Measurement 2.3 Practice Problems- Accuracy and Precision • (p.43) • 2. A volume is measured experimentally as 4.26 mL. What is the percentage error, given that the correct value is 4.15 mL?
Chapter 2 Section2 Units of Measurement 2.3 Practice Problems- Accuracy and Precision • (handout) • 3. Bruce’s three measurements are 19 cm, 20 cm, and 22 cm. Calculate the average value of his measurements and express the answer with the correct number of significant figures. • 4. Pete’s three measurements are 20.9 cm, 21.0 cm, and 21.0 cm. Calculate the average value of his measurements and express the answer with the correct number of significant figures. • Multiply the answer to problem #3 by the answer to problem #4. Express the answer in scientific notation with the correct number of significant figures. • Whose measurements are more precise? • The actual length of the object is 20 cm. Whose measurements are more accurate? • What is the error of Pete’s average measurement? • What is the percentage error of Pete’s average measurement? • Four boards each measuring 1.5 m are laid end to end. Multiply to determine the combined length of the boards, expressed with the correct number of significant figures.