Chapter 2 Sec 2.3Chapter 2 Sec 2.3Scientific MeasurementScientific Measurement

VocabularyVocabulary14. accuracy14. accuracy15. precision15. precision16. percent error16. percent error17. significant figures17. significant figures

18. scientific notation18. scientific notation19. directly 19. directly

proportionalproportional20. inversely 20. inversely

proportionalproportional

2.3 Measurements and Their 2.3 Measurements and Their UncertaintyUncertainty

A A measurementmeasurement is a quantity that is a quantity that has both a number and a unithas both a number and a unit

Measurements are fundamental to Measurements are fundamental to the experimental sciences. For that the experimental sciences. For that reason, it is important to be able to reason, it is important to be able to make measurements and to decide make measurements and to decide whether a measurement is correct.whether a measurement is correct.

International System of Measurement International System of Measurement (SI) typically used in the sciences(SI) typically used in the sciences

AccuracyAccuracy is the is the closenesscloseness of a measurement of a measurement to theto the correct valuecorrect value of quantity measured of quantity measured

PrecisionPrecision is a measure of how is a measure of how closeclose a set of a set of measurements are measurements are to one anotherto one another

To evaluate the To evaluate the accuracyaccuracy of a measurement, of a measurement, the measured value must be the measured value must be compared to the compared to the correct value. correct value.

To evaluate the To evaluate the precision precision of a measurement, of a measurement, you must you must compare the values of two or morecompare the values of two or more repeated measurementsrepeated measurements

Accuracy and PrecisionAccuracy and Precision

Accuracy and PrecisionAccuracy and Precision

Accuracy and PrecisionAccuracy 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 ErrorA. Determining Error1. 1. Error = experimental value – accepted value

*experiment value is measured in lab (what you got during *experiment value is measured in lab (what you got during experiment)experiment)

* accepted value is correct value based on references (what * accepted value is correct value based on references (what you you should have gotten)should have gotten)

2. 2. Percent error = [Value Percent error = [Value experimental experimental – Value– Valueacceptedaccepted] x 100%] x 100% ValueValueaccepted accepted

What is the measured value?

What is the measured value?

What is the measured value?

Significant Figures in Measurementall known digits + one estimated digit

2.3 Practice Problems – Accuracy and Precision2.3 Practice Problems – Accuracy and Precision

B. Rules of Significant FiguresB. Rules of Significant Figures

1. Every nonzero digit 1. Every nonzero digit in a measurement is significant (1-9). (1-9). Ex: Ex: 831 g = 3 sig figs831 g = 3 sig figs

2. Zeros in the middle 2. Zeros in the middle of a number are always significant. Ex: 507 m = 3 sig Ex: 507 m = 3 sig figsfigs

3. Zeros at the beginning 3. Zeros at the beginning of a number are NOT are NOT significant. Ex: 0.0056 g = Ex: 0.0056 g = 2 sig figs2 sig figs

B. Rules of Significant FiguresB. Rules of Significant Figures

4. Zeros at the end 4. Zeros at the end of a number are only significant if they follow a if they follow a decimal point.decimal point.Ex:Ex: 35.00 g = 4 sig figs35.00 g = 4 sig figs

2400 g = 2 sig figs2400 g = 2 sig figs

Sig Fig Practice #1Sig Fig Practice #1How many significant figures in the following?

1.0070 m 5 sig figs17.10 kg 4 sig figs

100,890 L 5 sig figs3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs3,200,000 mL 2 sig figs

5 dogs unlimited

These all come from some measurements

This is a counted value

C. Significant Figures in CalculationsC. Significant Figures in Calculations

1. 1. A calculated answeranswer can only be as precise as as precise as the least precisethe least precise measurementmeasurement from which it was calculated

2. 2. Exact numbersExact numbers never affect the number of significant figures in the results of calculations (unlimited sig figs)(unlimited sig figs)a) counted numberscounted numbers Ex: 17 beakersb) exact defined quantitiesdefined quantities Ex: 60 sec = 1min Ex: avagadro’s number = 6.02 x 1023

C. Significant Figures in CalculationsC. Significant Figures in Calculations

3. 3. multiplication and divisionmultiplication and division: : answer can have no more sig figs than least least number of sig figsnumber of sig figs in the measurements used.

4. 4. addition and subtractionaddition and subtraction: : answer can have no more decimal places that the least number of decimal placesleast number of decimal places in the measurements used. (not sig figs)

Rounding Sig Fig Practice #1Rounding Sig Fig Practice #1

3.24 m x 7.0 mCalculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

Rounding Practice #2Rounding Practice #2

3.24 m + 7.0 mCalculation Calculator says: Answer

10.24 m 10.2 m100.0 g - 23.74 g 76.26 g 76.3 g0.02 cm +2.378 cm 2.398 cm 2.40 cm710 m -3.4 m 706.6 m 707 m

Sec 2.3 Practice ProblemsSec 2.3 Practice Problems – Significant – Significant FiguresFigures

R61 Appendix C (1-7)R61 Appendix C (1-7)

Sec 2.3 Practice Problems – Significant FiguresSec 2.3 Practice Problems – Significant Figures

Sec 2.3 Practice Problems – Significant FiguresSec 2.3 Practice Problems – Significant Figures

Scientific NotationScientific Notation An expression of numbers in the form An expression of numbers in the form m x m x

1010n n where where mm (coefficient) is equal to or (coefficient) is equal to or greater than 1 and less than 10, and greater than 1 and less than 10, and nn is the is the power of 10 (exponent)power of 10 (exponent)

D. Rules of Scientific NotationD. Rules of Scientific Notation

1. Multiplication1. Multiplication – multiply the – multiply the coefficients and add the exponentscoefficients and add the exponentsEx: (3x10Ex: (3x1044) x (2x10) x (2x1022) = (3x2) x 10) = (3x2) x 104+24+2 = 6 x 10 = 6 x 1066

2. Division2. Division – divide the coefficients and – divide the coefficients and subtract the exponent in the subtract the exponent in the denominator from the exponent in denominator from the exponent in the numeratorthe numeratorEx: (3.0x10Ex: (3.0x1055)/(6.0x10)/(6.0x1022) = (3.0/6.0) x 10) = (3.0/6.0) x 105-25-2 = 0.5 x = 0.5 x 101033 = 5.0 x 10 = 5.0 x 1022

D. Rules of Scientific NotationD. Rules of Scientific Notation

3. Addition3. Addition – exponents must be the – exponents must be the same and then add the coefficientssame and then add the coefficientsEx: (5.4x10Ex: (5.4x1033) + (8.0x10) + (8.0x1022) )

(8.0x10(8.0x1022) = (0.80x10) = (0.80x1033) ) (5.4x10(5.4x1033) + (0.80x10) + (0.80x1033) = (5.4 +0.80) x 10) = (5.4 +0.80) x 1033 = 6.2 = 6.2 x 10x 1033

4. Subtraction4. Subtraction – exponents must be the – exponents must be the same and then subtract the same and then subtract the coefficientscoefficients

Sec 2.3 Practice Problems – Scientific NotationSec 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 MeasurementsChapter 2

xy

Direct Proportion

Section 3 Using Scientific MeasurementsChapter 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.”

yx1

Section 3 Using Scientific MeasurementsChapter 2

Inverse Proportion

Section 3 Using Scientific MeasurementsChapter 2

VocabularyVocabulary14. accuracy14. accuracy15. precision15. precision16. percent error16. percent error17. significant figures17. significant figures

18. scientific notation18. scientific notation19. directly 19. directly

proportionalproportional20. inversely 20. inversely

proportionalproportional