Chapter 2 Sec 2.3 Scientific Measurement

Vocabulary 14. accuracy 15. precision 16. percent error 17. significant figures 18. scientific notation 19. directly proportional 20. inversely proportional

2.3 Measurements and Their Uncertainty A measurement is a quantity that has both a number and a unit 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. 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 International System of Measurement (SI) typically used in the sciences

Accuracy is the closeness of a measurement to the correct value of quantity measured Accuracy is the closeness of a measurement to the correct value of quantity measured Precision is a measure of how close a set of measurements are to one another 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 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 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?

A. Determining Error 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 – Value accepted ] x 100% Value accepted Value accepted

What is the measured value? Significant Figures in Measurement all known digits + one estimated digit

2.3 Practice Problems – Accuracy and Precision

B. Rules of Significant Figures 1. Every nonzero digit (1-9). Ex: 831 g = 3 sig figs 1. Every nonzero digit in a measurement is significant (1-9). Ex: 831 g = 3 sig figs 2. Zeros in the middle Ex: 507 m = 3 sig figs 2. Zeros in the middle of a number are always significant. Ex: 507 m = 3 sig figs 3. Zeros at the beginning are NOT Ex: g = 2 sig figs 3. Zeros at the beginning of a number are NOT significant. Ex: g = 2 sig figs

B. Rules of Significant Figures 4. Zeros at the end if they follow a decimal point. 4. Zeros at the end of a number are only significant if they follow a decimal point. Ex: g = 4 sig figs 2400 g = 2 sig figs 2400 g = 2 sig figs

Sig Fig Practice #1 How many significant figures in the following? m  5 sig figs kg  4 sig figs 100,890 L  5 sig figs 3.29 x 10 3 s  3 sig figs cm  2 sig figs 3,200,000 mL  2 sig figs 5 dogs  unlimited These all come from some measurements This is a counted value

C. Significant Figures in Calculations 1. answeras precise as the least precisemeasurement 1. A calculated answer can only be as precise as the least precise measurement from which it was calculated 2. Exact numbers (unlimited sig figs) 2. Exact numbers never affect the number of significant figures in the results of calculations (unlimited sig figs) counted numbers a) counted numbers Ex: 17 beakers defined quantities b) exact defined quantities Ex: 60 sec = 1min Ex: avagadro’s number = 6.02 x 10 23

C. Significant Figures in Calculations 3. multiplication and division: least number of sig figs 3. multiplication and division: answer can have no more sig figs than least number of sig figs in the measurements used. 4. addition and subtraction: least number of decimal places 4. addition and subtraction: answer can have no more decimal places that the least number of decimal places in the measurements used. (not sig figs)

Rounding Sig Fig Practice # m x 7.0 m CalculationCalculator says:Answer m 2 23 m g ÷ 23.7 cm g/cm g/cm cm x cm cm cm m ÷ 3.0 s m/s240 m/s

Rounding Practice # m m CalculationCalculator says:Answer m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.40 cm 710 m -3.4 m m707 m

Sec 2.3 Practice Problems – Significant Figures R61 Appendix C (1-7)

Sec 2.3 Practice Problems – Significant Figures

Scientific Notation An expression of numbers in the form m x 10 n where m (coefficient) is equal to or greater than 1 and less than 10, and n is the power of 10 (exponent) An expression of numbers in the form m x 10 n where m (coefficient) is equal to or greater than 1 and less than 10, and n is the power of 10 (exponent)

D. Rules of Scientific Notation 1. Multiplication – multiply the coefficients and add the exponents Ex: (3x10 4 ) x (2x10 2 ) = (3x2) x = 6 x Division – divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator Ex: (3.0x10 5 )/(6.0x10 2 ) = (3.0/6.0) x = 0.5 x 10 3 = 5.0 x 10 2

D. Rules of Scientific Notation 3. Addition – exponents must be the same and then add the coefficients Ex: (5.4x10 3 ) + (8.0x10 2 ) (8.0x10 2 ) = (0.80x10 3 ) (8.0x10 2 ) = (0.80x10 3 ) (5.4x10 3 ) + (0.80x10 3 ) = ( ) x 10 3 = 6.2 x Subtraction – exponents must be the same and then subtract the coefficients

Sec 2.3 Practice Problems – Scientific Notation

Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value. read as “y is proportional to x.” Section 3 Using Scientific Measurements Chapter 2

Direct Proportion Section 3 Using Scientific Measurements Chapter 2

Inverse Proportions Two quantities are inversely proportional to each other if their product is constant. read as “y is proportional to 1 divided by x.” Section 3 Using Scientific Measurements Chapter 2

Inverse Proportion Section 3 Using Scientific Measurements Chapter 2

Vocabulary 14. accuracy 15. precision 16. percent error 17. significant figures 18. scientific notation 19. directly proportional 20. inversely proportional