Ch. 3 Notes---Scientific Measurement

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1 Ch. 3 Notes---Scientific Measurement Qualitative vs. Quantitative Qualitative measurements give results in a descriptive nonnumeric form. (The result of a measurement is an describing the object.) *Examples:,, long,... Quantitative measurements give results in numeric form. (The results of a measurement contain a.) *Examples: 4 6,, 22 meters,... Accuracy vs. Precision Accuracy is how close a measurement is to the of whatever is being measured. Precision is how close measurements are to. 1

2 Practice Problem: Describe the shots for the targets. Bad Accuracy & Bad Precision Good Accuracy & Bad Precision Bad Accuracy & Good Precision Good Accuracy & Good Precision 2

3 Significant Figures Significant figures are used to determine the of a measurement. (It is a way of indicating how a measurement is.) *Example: A scale may read a person s weight as 135 lbs. Another scale may read the person s weight as lbs. The scale is more precise. It also has significant figures in the measurement. Whenever you are measuring a value, (such as the length of an object with a ruler), it must be recorded with the correct number of sig. figs. Record the numbers of the measurement known for sure. Record one last digit for the measurement that is estimated. (This means that you will be of the device and what the next number is.) 3

4 Significant Figures Practice Problems: What is the length recorded to the correct number of significant figures? length = cm (cm) length = cm 4

5 Significant Figures Significant figures are all numbers known in a measurement with plus one Record the volume measurement shown in the ml 5

6 Rules for Counting Significant Figures in a Measurement When you are given a measurement, you will need to be aware of how many sig. figs. the value contains. (You ll see why later on in this chapter.) Here is how you count the number of sig. figs. in a given measurement: #1 (Non-Zero Rule): All digits 1-9 are significant. *Examples: 2.35 g = S.F g = S.F. #2 (Straddle Rule): Zeros between two sig. figs. are significant. *Examples: 205 m = S.F cm = S.F m = S.F. #3 (Righty-Righty Rule): Zeros to the right of a decimal point AND anywhere to the right of a sig. fig. are significant. *Examples: 2.30 sec. = S.F sec. = S.F km = S.F x m = S.F.

7 Rules for Counting Significant Figures in a Measurement #4 (Bar Rule): Any zeros that have a bar placed over them are sig. (This will only be used for zeros that are not already significant because of Rules 2 & 3.) *Examples: 3,000,000 m/s = S.F. 20 lbs = S.F. #5 (Counting Rule): Any time the measurement is determined by simply counting the number of objects, the value has an infinite number of sig. figs. (This also includes any conversion factor involving counting.) *Examples: 15 students = S.F. 29 Test Tubes = S.F. 7 days/week = S.F. 60 sec/min = S.F cm 3 / 1 dm 3 = S.F. 7

8 Significant Figures Significant figures are all numbers known in a measurement with plus one What digits are known with certainty? What digit is uncertain? Record the volume measurement shown in the ml 8

9 Scientific Notation Scientific notation is a way of representing really large or small numbers using powers of 10. *Examples: 5,203,000,000,000 miles = x miles mm = 4.2 x 10 8 mm Steps for Writing Numbers in Scientific Notation (1) Write down all the sig. figs. (2) Put the decimal point between the first and second digit. (3) Write x 10 (4) Count how many places the decimal point has moved from its original location. This will be the exponent...either + or. (5) If the original # was greater than 1, the exponent is ( ), and if the original # was less than 1, the exponent is ( )...(In other words, large numbers have ( ) exponents, and small numbers have (_) exponents. 9

10 Scientific Notation Practice Problems: Write the following measurements in scientific notation or back to their expanded form. 477,000,000 miles = miles m = m 6.30 x 10 9 miles = miles 3.88 x 10 6 kg = kg L = L 2.58 x 10 4 cm = cm 5200 g = g 10

11 Calculations Using Sig. Figs. When adding or subtracting measurements, all answers are to be rounded off to the least # of found in the original measurements. Example: + When multiplying or dividing measurements, all answers are to be rounded off to the least # of found in the original measurements. Practice Problems: 2.83 cm cm 2.1 cm = 36.4 m x 2.7 m = (only keep 2 decimal places) (only keep 2 sig. figs) (only keep 1 decimal place) g 35.2 ml = (only keep 3 sig. figs) 11

12 The SI System (The Metric System) 12

13 The SI System (The Metric System) The following are common approximations used to convert from our English system of units to the metric system: 1 m 1 kg 1 L 1.06 quarts km 454 grams 1 in 1 J 1 gallon 13

14 The SI System (The Metric System) Here is a list of common base units of measure used in science: Standard Metric Unit Quantity Measured kilogram, (gram) meter mole seconds Kelvin, ( Celsius) 14

15 Mass vs. Weight Mass depends on the amount of in the object. Weight depends on the force of acting on the object. may change as you move from one location to another; will not. You have the same on the moon as on the earth, but you less since there is less on the moon. Mass = 80 kg Weight = 176 lbs. Mass = kg Weight = 29 lbs.

16 Temperature Scales Liquid Nitrogen 16

17 Measuring Temperature Temperature is the or of an object. The Celsius temperature scale is based on the freezing point and boiling point of. F.P.= 0 C B.P.= 100 C The Kelvin temperature scale, sometimes called the absolute temp. scale, is based on the temperature possible, absolute zero. (All molecular motion would.) Absolute Zero = 0 Kelvin = 273 C To convert from one temp. scale to another: C = Kelvin 273 K= Celsius Practice Problems: Convert the following 25 C = K 473 K = C 17

18 Metric Conversions The metric system prefixes are based on factors of. Here is a list of the common prefixes used in chemistry: The box in the middle represents the standard unit of measure such as grams, liters, or meters. Moving from one prefix to another involves a factor of 10. *Example: 1 m = dm = cm = mm = µm = nm *Examples of measurements: 5 km 2 dl 27 µg 3 m 45 mm 18

19 The SI System (The Metric System) What is a derived unit? a unit that is a Quantity Derivation of the Quantity Area Length square m 2 Volume Length cube m 3 SI Unit Density Mass per unit volume kg m -3 Speed Acceleration Force Distance travelled per unit time Speed change per unit time Product of mass and acceleration m S -1 m s -2 kg m s -2 Symbol Newton (N) Pressure Force per unit area kg m -1 s -2 Pascal (Pa) Energy, work Product of force and distance kg m 2 s -2 Joule (J) Temperature How hot or cold K Celsius ( C) 19

20 Dimensional Analysis Problem Dimensional analysis uses conversion factors to convert from one unit to another. Ex From 1000m = 1km, we can write the following conversion factors: and A derived unit such as density can also be written as a conversion factor. Ex Show the conversion factor for a substance whose density is 3.5 g/ml and 20

21 Dimensional Analysis Problem Ex Write the conversion factor for a speed of 55 m/s and How do we use conversion factors?? Ex How many meters are in 73 km? = Ex How many nanometers are there in 2.67 meters? = 21

22 Dimensional Analysis Problem Ex Suppose you are hosting a party and need to decide how many drinks to have. You know that there will be 24 people attending and each person will consume 3 drinks. If the drinks are sold in packs of 12, how many will you need? SOLVE USING DIMENTIONAL ANALYSIS. 22

23 Dimensional Analysis Problem 1.A car is traveling 36 meters per sec, if the speed limit is 65 miles per hour is the car speeding? 23

24 Dimensional Analysis Problem 24

25 Metric Volume: Cubic Meter (m 3 ) 10 cm x 10 cm x 10 cm = Liter 25

26 Area and Volume Conversions Be careful making conversions when dealing with area and volume. Example Convert 380 km 2 to m km 2 X = Convert 4.61 mm 3 to cm mm 3 X = 26

27 Other Metric Equivalents For water only: 1 ml = 1 cm 3 1 L = 1 dm 3 1 L = 1 dm 3 = 1 kg of water or 1 ml = 1 cm 3 = 1 g of water Practice Problems: (1) How many liters of water are there in 300 cm 3? 300 cm 3 X X = (2) How many kg of water are there in 500 dl? 500 dl X X = 27

28 Density Density is a of an object s mass and its volume. Density does not depend on the of the sample you have. The density of an object will determine if it will float or sink in another phase. If an object floats, it is dense than the other substance. If it sinks, it is dense. The density of water is 1.0 g/ml, and air has a density of g/ml (or 1.29 g/l). Density = Mass/Volume 28

29 Practice Problems: Density (1) The density of gold is 19.3 g/cm 3. How much would the mass of a bar of gold be in pounds? Assume a bar of gold has the following dimensions: L= cm W= 9.02 cm H= 5.45 cm (1) What do we know? & (2) What do we need to know? Since we know the values for D and V we solve for by rearranging D=M/V into X = 29

30 Practice Problems: Density (2) Which picture shows the block s position when placed in salt water? (3) Will the following object float in water? Object s mass = 27 g Object s volume= 25 ml 30

31 Evaluating the Accuracy of a Measurement The Percent Error of a measurement is a way of representing the accuracy of the value. (Remember what accuracy tells us?) % Error = (Observed Value) (Accepted Value) x 100 (Accepted Value) Practice Problem: A student measures the density of a block of aluminum to be approximately 2.56 g/ml. The value found in our textbook tells us that the density was supposed to be 2.70 g/ml. What is the accuracy of the student s measurement? 31

32 Evaluating the Accuracy of a Measurement The Percent Deviation is very useful in determining how accurate the data collected by student teams is. In this case the data is usually compared either to a standard prepared by the instructor or by a quality control lab % Deviation= (Observed Value) (Mean) x 100 (Mean) Practice Problem: A student measures the density of a block of aluminum to be approximately 2.84 g/ml. The value found in our textbook tells us that the density was supposed to be 2.63 g/ml. What is the percent deviation of the student s measurement? 32

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