Scientific Measurement 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

Chapter 2 Objectives Distinguish between accuracy and precision. Section 3 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 the correct (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

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

Accuracy and Precision, continued Section 3 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

F. Making Good Measurements 2. Test our measurement against a “standard”, or accepted value - measurement close to accepted value is ACCURACY

Accuracy and Precision, continued Section 3 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

2.3 Practice Problems- Accuracy and Precision Chapter 2 Section 2 Units of Measurement 2.3 Practice Problems- Accuracy and Precision Set C (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?

2.3 Practice Problems- Accuracy and Precision Chapter 2 Section 2 Units of Measurement 2.3 Practice Problems- Accuracy and Precision Set C (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?

2.3 Practice Problems- Accuracy and Precision Chapter 2 Section 2 Units of Measurement 2.3 Practice Problems- Accuracy and Precision Set C (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.

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

Estimating Measurements The hundredths place is somewhat uncertain. Leaving it our would be misleading. Must estimate.. 6.35cm or 6.36cm

Error Probably not EXACTLY 6.35 cm Within .01 cm of actual value. 6.35 cm ± .01 cm 6.34 cm to 6.36 cm Even though the measurement is always uncertain it is important that you are very careful making your measurements and keep care of you equipment.

Significant Figures, continued Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Determining the Number of Significant Figures

H. Rules of Significant Figures 1. Every nonzero digit in a measurement is significant (1-9). Ex: 831 g = 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 of a number are NOT significant. Ex: 0.0056 g = 2 sig figs

H. Rules of Significant Figures 4. Zeros at the end of a number are only significant if a decimal point is present. Ex: 35.00 g = 4 sig figs 240. = 3 sig figs 2400 g = 2 sig figs 00.0350g = 3 sig figs

Sig Fig Practice #1 How many significant figures in the following? 5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs These all come from some measurements 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000 mL  2 sig figs This is a counted value 5 dogs  unlimited

I. Significant Figures in Calculations 1. A calculated answer can only be as precise as the least precise measurement from which it was calculated 2. Exact numbers never affect the number of significant figures in the results of calculations (unlimited sig figs) a) counted numbers Ex: 17 beakers b) exact defined quantities Ex: 60 sec = 1min Ex: avagadro’s number = 6.02 x 1023

I. Significant Figures in Calculations 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: a) decimal - answer can have no more decimal places than the least number of decimal places in the measurements used. (not sig figs) b) whole number- answer rounded so final sig fig is in the same place as the leftmost uncertain digit. ex: 5400 + 365 = 5800

Sec 2.3 Significant Figures

Rounding Sig Fig Practice #1 Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 23 m2 100.0 g ÷ 23.7 cm3 4.219409283 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 0.05 cm2 710 m ÷ 3.0 s 236.6666667 240 m/s

Rounding Practice #2 Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 10.2 m 100.0 g - 23.74 g 76.26 76.3 g 0.02 cm +2.378 cm 2.398 2.40 cm 710 m -3.4 m 706.6 707 m

Sec 2.3 Practice Problems – Significant Figures

Sec 2.3 Practice Problems – Significant Figures

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

J. Rules of Scientific Notation 1. Multiplication – multiply the coefficients and add the exponents Ex: (3x104) x (2x102) = (3x2) x 104+2 = 6 x 106 2. Division – divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator Ex: (3.0x105)/(6.0x102) = (3.0/6.0) x 105-2 = 0.5 x 103 = 5.0 x 102

J. Rules of Scientific Notation 3. Addition – exponents must be the same and then add the coefficients Ex: (5.4x103) + (8.0x102) (8.0x102) = (0.80x103) (5.4x103) + (0.80x103) = (5.4 +0.80) x 103 = 6.2 x 103 4. Subtraction – exponents must be the same and then subtract the coefficients

Sec 2.3 Practice Problems – Scientific Notation

Chapter 2 Direct Proportions Section 3 Using Scientific Measurements Chapter 2 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

Chapter 2 Inverse Proportions 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

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