Chapter 2: A Mathematical Toolkit

Chapter 2: A Mathematical ToolkitDr. Zalesinsky The Metric System

Length or distance is measured in metersMass is measured in grams Volume or capacity is measured in liters Time is measured in seconds Energy is measured in JoulesTemperature is measured in Kelvin (not degrees)Quantity is measured in moles

3The Liter (L)

4The Meter (m)

5Gram (g)

6Scientific NotationThe really small and really largeScientific Notation8Scientific Notation ExamplesChange to Scientific Notation:985,000,0000.0000674 9.85 x 1086.74 x 10-5Change to Standard Notation:8.27 x 1069.565x10-2 8,270,000.09565

9Using Scientific Notation with Calculator

10TI Graphing Calculator

ExamplesDo this calculation: (dont type in the x 10 partuse the EE or EXP button)Multiply:(8.76 x 10-10 )(7.9 x1011) = 692 or 6.92x102Divide: (9.43x1043)/(7.33x1023) =

(approximate) 1.3 x1020 be careful to turn your display into correct scientific notation 1.320 is not the same!

Significant FiguresUncertainty in Measurement English to Metric ComparisonsWhich is larger? Meter or yardMile or KilometerGallon or literPound or gramQuart or literCentimeter or inchGram or ounceWhat is the abbreviation for each unit? Meter = _____Gram = _____Liter = ______Second = ______Joule = _______Mole = _______

14Metric AbbreviationsThe BASE units for the metric system are gram, liter, meter, second, Kelvin, Joule and mole.

There are larger and smaller portions of each of these

Their abbreviations come in front of the units abbreviation (ex. centimeter = cm) 15Larger and Smaller PrefixesLarger1 billion = GIGA (G)1 million = MEGA (M)1,000 = kilo (k)100 = hecto (h)10 = deca (D, dk, or da)Smaller1trillion = pico (p)1 billion = nano (n)1 million = micro (m)1,000 = milli (m)100 = centi (c )10 = deci (d)

16Match the abbreviation with the nameCm = ________mg = ________ML = ________Gg = ________ms = ________km = _______mL = _______kJ = ________mm= _______Dg = _______CentimeterMilligramMegaliterGigagramMicrosecondKilometerMilliliterKilojouleMillimeterDecagram

17ConversionsKiloHectoDecaUNITDeciCentiMilli1.01003.09259473.600.0007650.76373063884300

18ConversionsGMkhDunitdcmmnp1.03.91x10-97x 1064037.6227848626

19Significant FiguresRead the correct number of significant figures

20Measure the following using significant figures

21Use Sig. Figs to find this measurement

22Use the correct number of sig. figs in this measurement

23What digit would be estimated in using Ruler A? OnesTenthsHundredthsThousandthsTens

24What decimal place is estimated when using Ruler B? OnesD. ThousandthsTenthsE. TensHundredths

25Measure the width of the rectangle using the correct number of sig figs. 3. 75 cmD. 3.60 cm3.6 cmE. 4.25 cm2. 6 cm

26Measure the length of the rectangle using the correct number of sig figs. 12.55 cmC. 12.0 cmE. 13.50 cm12. 5 cmD. 13. 5 cm

27How many sig figs should be in the correct measurement of the length of this rectangle? 2 sig figsC. 4 sig figsE. 1 sig fig3 sig figsD. 5 sig figs

28The width of this rectangle is 0.90 cm. How many significant figures are in this measurement? 3 sig figsD. infinite sig figs2 sig figsE. none of the above1 sig fig

29Data Table 1.1Dimension

WXYZLength (cm)Longer side

Width (cm)Shorter side

Data Table 1.2Rectangle

Measured Length# of sig figs in LengthMeasured WidthNumber of Sig Figs in Width

W

X

Y

Z

Data Table 1.5Dimension

WXYZLength (cm)Longer side

Width (cm)Shorter side

Data Table 1.6Rectangle

Measured Length# of sig figs in LengthMeasured WidthNumber of Sig Figs in Width

W

X

Y

Z

Calculations with Significant figuresCalculating with UncertaintyMultiplication and Division with Sig FigsThe least number of sig figs in the input is equal to the number of sig figs in the answer (output). Remember all conversion factors and counted numbers have INFINITE sig figs!Example: 8.03 g x 4.0 cm3/g = ? 35Addition and Subtraction with Sig FigsThe least number of decimal places in the input is the same number of decimal places in the output (answer). 12.573 m + 3847.9 m - 378 m = ?3482.473 (unrounded)3482 rounded to the correct number of decimal places

36Calculations with Sig FigsA rectangle has a width of 5.0 cm and a length of 8.40 cm. What is the area of this rectangle in cm2? ___________A rectangular prism has the following measurements: length 8.54 cm, width 7.80cm, and height 10.00 cm. What is the volume in cm3? ______________

37Data Table 1.2RectangleMeasured Length (cm)# of Sig Figs in LengthMeasured Width (cm)# of Sig Figs in WidthW12.2310.13X13.630.71Y3.322.42Z20.232.52Data Table 1.3RectangleJustified # of Sig Fig in AreaUnrounded Area (cm2)Rounded Area(cm2)Data Table 1.6RectangleMeasured Length (cm)# of Sig Figs in LengthMeasured Width (cm)# of Sig Figs in WidthW12.19410.094X13.514.612Y3.2732.493Z20.1942.383Data Table 1.7RectangleJustified # of Sig Fig in AreaUnrounded Area (cm2)Rounded Area(cm2)Visualizing Data2.3 Linear RelationshipsDependent (y) and independent (x) variables when graphed form a straight lineSlope is positive if they are DIRECTLY PROPORTIONALSlope is negative if they are INVERSELY PROPORTIONAL

Nonlinear RelationshipsQuadratic equations relate parabolic relationshipsSome inverse relationships are hyperbolic

Practice ProblemCreate a graph from the data chart givenDescribe the relationship (linear or non)If linear, find slope (in/direct) Volume of oil (cc)Concentration (ppm)00301.3401.5482.0493.05111.0