Number vs. Quantity. Quantity - number + unit UNITS MATTER!! for a measurement to be useful, must include both a number and unit

Transcription

1 Measurement Data

2 UNITS MATTER!! Number vs. Quantity Quantity - number + unit for a measurement to be useful, must include both a number and unit

3 Measurements We make measurements every day: buying products, sports activities, and cooking Qualitative measurements are words, such as heavy or hot Quantitative measurements involve numbers (quantities), and depend on: reliability of the measuring instrument the care with which it is read Scientific Notation - Uses a number between 1& 9 with multiplied by 10 raised to a power (ex. 1.3 x 10 7 )

4 Accuracy, Precision, & Error It is necessary to make good, reliable measurements in the lab Accuracy how close a measurement is to the true value Precision how close the measurements are to each other (reproducibility)

5 Precision and Accuracy Neither accurate nor precise Precise, but not accurate Precise AND accurate

6 Accuracy, Precision, & Error Accepted value = the correct value based on reliable references Experimental value = the value measured in the lab

7 Accuracy, Precision,& Error Error = accepted value exp. value Can be positive or negative Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100% % error = error accepted value x 100%

8 Measurement Representation Graphing

9 Data Represented In Graphs Variables Is something that can change in a situation There are three types of variables: Independent Dependent Control

10 3 Kinds of Variables Independent Variable something that is changed by the scientist What is tested What is manipulated On x-axis of graphs

11 3 Kinds of Variables Dependent Variable something that might be affected by the change in the independent variable What is observed & measured Responds to independent variable The data collected during the investigation On y-axis of graphs

12 3 Kinds of Variables Controlled Variable a variable that is not changed Also called constants Allow for a fair test

13 DEPENDENT MANIPULATED RESPONDING INDEPENDENT AXIS AXIS

14 Dependent Variable Types of Graphs Line Graph shows the relationship between 2 variables Independent Variable

15 Types of Graphs Bar Graph shows information collected by counting

16 Types of Graphs Pie Graph shows distribution of parts within a whole quantity

17 Mass (g) Graphing & Density Δy M slope D Δx V Volume (cm 3 )

18 Measurement Units of Measurement

19 International System of Units Measurements depend upon units that serve as reference standards 1795, French adopted a system of standard units called the metric system 1960 an international committee of scientists met to update the system Syste`me Internationale d`unite`s, which is abbreviated SI

20 International System of Units It has simplicity, and is based on 10 or multiples of 10 7 base units Base Unit unit in a system of measurement that is based on an object or event in the physical world and independent of other units

21 SI Units Quantity Time Length Mass Temperature Amount of Substance Electric Current Luminous Intensity Unit Second (s) Meter (m) Kilogram (kg) Kelvin (K) Mole (mol) Ampere (A) Candela (cd)

22 Prefix Symbol Factor Sci. Not. Giga G 1,000,000, Mega M 1,000, Kilo k 1, Hecto h Deka da Unit Deci d Centi c Milli m Micro μ Nano n Pico p

23 Length In SI, the basic unit of length is the meter (m) meter is the distance that light travels through a vacuum in 1/299,792,458 of a second

24 Mass Mass is a measure of the quantity of matter present Weight is a force that measures the pull by gravityit changes with location (w= mg) Mass is constant, regardless of location

25 Mass The SI unit of mass is the kilogram (kg), even though a more convenient everyday unit is the gram 1kg is about 2.2 lbs kilogram is defined by the mass of a platinum-iridium metal cylinder kept in Sevres, France is the only base unit whose standard is a physical object

26 Time SI base unit for time is the second (s) second -frequency of microwave radiation given off by a cesium-133 atom is the

27 Volume The space occupied by any sample of matter. Calculated for a solid by multiplying the length x width x height; thus derived from units of length. SI unit = cubic meter (m 3 ) Everyday unit = Liter (L), which is non-si. (Note: 1mL = 1cm 3 )

28 Devices for Measuring Liquid Volume Graduated cylinders Pipets Burets Volumetric Flasks Syringes

29 The Volume Changes! Volumes of a solid, liquid, or gas will generally increase with temperature Much more prominent for GASES Therefore, measuring instruments are calibrated for a specific temperature, usually 20 o C, which is about room temperature

30 Derived Units Combination of base units. Volume = length length length 1 cm 3 = 1 ml 1 dm 3 = 1 L Density - mass per unit volume (g/cm 3 ) D = M V M D V

31 Density An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M =? M WORK: M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,220 g D V

32 Density 1) A liquid has a density of 0.87 g/ml. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/ml V =? M = 25 g M D V WORK: V = M D V = 25 g 0.87 g/ml V = 28.7 ml

33 Density 2) You have a sample with a mass of 620 g & a volume of 753 cm 3. Find density. GIVEN: M = 620 g V = 753 cm 3 D =? M D V WORK: D = M V D = 620 g 753 cm 3 D = 0.82 g/cm 3

34 Measurement Unit Conversions

35 Conversions in the Metric System 1. sometimes the base units are not handy to express a measurement ex. a meter would not be good to measure the width of a button, but you could use a millimeter 2. use a decimal multiplier to express very small or very large amounts (prefixes) 3. converting between units is done by moving the decimal point a number of spaces

36 4. convert to larger units by moving decimal to the left and convert to smaller units by moving the decimal to the right Giga Mega Kilo Hecto Deka u Deci Centi Milli Micro Nano example: 30 g to cg? = example: 500 ml to L? =

37 SI Prefix Conversions 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places. To the left or right?

38 SI Prefix Conversions 532 m = km NUMBER UNIT = NUMBER UNIT

39 move left move right SI Prefix Conversions Prefix Symbol Factor mega- M 10 6 kilo- k 10 3 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro nano- n 10-9 pico- p 10-12

40 KILO 1000 Units 1 2 HECTO 100 Units Ladder Method DEKA 10 Units 3 Meters Liters Grams DECI 0.1 Unit CENTI 0.01 Unit MILLI Unit How do you use the ladder method? 1 st Determine your starting point. 2 nd Count the jumps to your ending point. 4 km = m Starting Point Ending Point How many jumps does it take? 3 rd Move the decimal the same number of jumps in the same direction = 4000 m

41 SI Prefix Conversions 0.2 1) 20 cm = m 32 2) A = ma 45,000 3) 45 m = nm ) 805 dm = km

42 Dimensional Analysis The Factor-Label Method Units, or labels are canceled, or factored out cm 3 g 3 cm g

43 Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

44 Dimensional Analysis Lining up conversion factors: 1 in = 2.54 cm = cm 2.54 cm 1 in = 2.54 cm 1 = 1 in 1 in

45 Dimensional Analysis Your European hairdresser wants to cut your hair 8 cm shorter. How many inches will he be cutting off? cm 8 cm 1 in 2.54 cm = 3.15 in in

46 Dimensional Analysis How many milliliters are in 1 quart of milk? qt ml 1 qt 1 L qt 1000 ml 1 L = 946 ml

47 Dimensional Analysis 5) Assume your mass is 55 kg. How many pounds do you weigh? kg lb 55 kg 2.2 lb 1 kg = 121 lb

48 Dimensional Analysis 6) How many feet long is a 5K (5 km) race? km ft 5 km 1 mi km 5280 ft 1 mi = 16,408 ft

49 Dimensional Analysis 7) How many grams does a 10-lb. bag of potatoes weigh? lb g 10 lb 1 kg 2.2. lb 1000 g 1 kg = 4545 g

50 Dimensional Analysis 8) Taft football needs 550 cm for a 1st down. How many yards is this? cm yd 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 3 ft = 6.01 yd