DATA ANALYSIS Using the Metric System Scientific Notation Percent Error Using Significant Figures Accuracy and Precision Graphing Techniques

Using the Metric System A. Why do scientists use the metric system? The metric system was developed in France in 1795 - used in all scientific work because it has been recognized as the world wide system of measurement since 1960. SI system is from the French for Le Systeme International d’Unites. The metric system is used in all scientific work because it is easy to use. The metric system is based upon multiples of ten. Conversions are made by simply moving the decimal point.

Base Units (Fundamental Units) QUANTITY NAME SYMBOL _______________________________________________ Length meter m ----------------------------------------------------------------------------- Mass kilogram kg ------------------------------------------------------------------------------- Amount of Substance mole mol Time second s

Derived Units Base Units – independent of other units Derived Units – combination of base units Examples density  g/L (grams per liter) volume  m x m x m = meters cubed Velocity  m/s (meters per second

Metric Units Used In This Class QUANTITY NAME SYMBOL Length meter m centimeter cm millimeter mm kilometer km Mass gram g kilogram kg centigram cg milligram mg Volume liter (liquid) L (l) milliliter (liquid) mL (ml) cubic centimeter (solid) cm3

Metric Units Used In This Class Density grams/milliliter (liquid) g/mL grams/cubic centimeter (solid) g/cm3 grams/liter (gas) g/L Time second s minute min hour h volume measurement for a liquid and a solid ( 1 mL = 1 cm3) These are equivalents.

Equalities You Need To Know 1 km = 1000 m 1 m = 100 cm 1 m = 1000 mm 1L = 1000 mL 1kg = 1000g 1 g = 100cg 1 g = 1000 mg

Making Unit Conversions Make conversions by moving the decimal point to the left or the right using: “ king henry died unit drinking chocolate milk” Examples 10.0 cm = __________m 34.5 mL = __________L 28.7 mg = __________kg

SCIENTIFIC NOTATION Scientific Notation: Easy way to express very large or small numbers A.0 x 10x A – number with one non-zero digit before decimal x -exponent- whole number that expresses the number decimal places if x is (-) then it is a smaller if x is (+) than it is larger

PRACTICE Convert to Normal Convert to SN 2.3 x 1023 m 3,400,000, 3.4 x 10-5 cm .0000000456

Multiplying Calculating in Scientific notation Multiple the numbers Add the exponents (2.0 x 104) (4.0 x 103) = 8.0 x 107

Dividing 9.0 x 107 3.0 x 102 3.0 x 105 divide the numbers subtract the denominator exponent from the numerator exponent 9.0 x 107 3.0 x 102 3.0 x 105

Add Add or subtract get the exponents of all # to be the same calculate as stated make sure the final answer is in correct scientific notation form 7.0 x 10 4 + 3.0 x 10 3 = 7. 0 x 104 + .3 x 104 = 7.3 x 104 70,000 + 3,000 = 73000= 7.3 x104

subtract 7.0 x 10 4 - 3.0 x 10 3 = 7.0x 104 – .30 x 104 = 6.7 x 104 70,000 - 3 000 =67,000

PRACTICE Add: 2.3 x 103 cm + 3.4 x 105 cm Subtract: Multiply: : 2.3 x 103 cm X 3.4 x 105 cm   Divide: : 2.3 x 103 cm / 3.4 x 105 cm

Calculating Percent Error % Error =accepted value–experimental value X 100= % accepted or actual value Subtract -Divide then multiply by 100

Calculating Percent Error EXAMPLE – A student determines the density of a piece of wood to be .45g/cm. The actual value is .55g/cm. What is the student’s percent error? .55 - .45 X 100% = .10 = .18 x 100% = 18% .55 .55

The following lesson is one lecture in a series of Chemistry Programs developed by Professor Larry Byrd Department of Chemistry Western Kentucky University

Introduction If someone asks you how many inches there are in 3 feet, you would quickly tell them that there are 36 inches. Simple calculations, such as these, we are able to do with little effort. However, if we work with unfamiliar units, such as converting grams into pounds, we might multiply when we should have divided.

The fraction ( 4 x 5) / 5 can be simplified by dividing the numerator (top of fraction) and the denominator (bottom of fraction) by 5: = 4 Likewise, the units in (ft x lb) / ft reduces to pounds (lb) when the same units ( ft )are canceled: = lb

CONVERSION FACTOR A CONVERSION FACTOR is a given Ratio-Relationship between two values that can also be written as TWO DIFFERENT FRACTIONS. For example, 454 grams =1.00 pound, states that there are 454 grams in 1.00 pound or that 1.00 pound is equal to 454 grams.

Ratio-Relationship We can write this Ratio-Relationship as two different CONVERSION-FACTOR-FRACTIONS: These fractions may also be written in words as 454 grams per 1.00 pound or as 1.00 pound per 454 grams, respectively. The "per" means to divide by. or as

Example If we want to convert 2.00 pounds into grams, we would: first write down the given quantity (2.00 lbs) pick a CONVERSION-FACTOR-FRACTION that when the given quantities and fractions are multiplied, the units of pounds on each will cancel out and leave only the desired units, grams. We will write the final set-up for the problem as follows: = 908 grams

If we had used the other conversion-factor-fraction in the problem: We would know that the ABOVE problem was set-up incorrectly since WE COULD NOT CANCEL Out the units of pounds and the answer with pounds / grams makes no sense. =

Four-step approach When using the Factor-Label Method it is helpful to follow a four-step approach in solving problems: What is question – How many sec in 56 min What are the equalities- 1 min = 60 sec Set up problem (bridges) 56 min 60 sec 1 min Solve the math problem -multiple everything on top and bottom then divide 56 x 60 / 1

Using Significant Figures (Digits) value determined by the instrument of measurement plus one estimated digit reflects the precision of an instrument example – if an instrument gives a length value to the tenth place – you would estimate the value to the hundredths place

1. all non-zero # are Sig fig- 314g 3sf 12,452 ml 5sf 2. all # between non-zero # are sig fig 101m 3sf 6.01mol 3sf 36.000401s 8s 3. place holders are not sf 0.01kg 1sf

4. zeros to the right of a decimal are sig fig if 3.0000s 5sf Preceded by non-zero 0.002m 1sf 13.0400m 6sf 5. Zero to right of non-zero w/o decimal point 600m 1sf are not sig fig 600.m 3sf 600.0 m 4sf 600.00 m 5sf

RULES FOR USING SIGNIFICANT FIGURES use the arrow rule to determine the number of significant digits decimal present all numbers to right of the first non zero are significant (draw the arrow from left to right) ----------> 463 3 sig. digits ----------> 125.78 5 sig. digits ----------> .0000568 3 sig. digits ----------> 865 000 000. 9 sig. digits

RULES FOR USING SIGNIFICANT FIGURES use the arrow rule to determine the number of significant digits decimal not present < -------- all numbers to the left of the first non zero are significant (draw arrow from right to left) 246 000 <---------- 3 sig. digits 400 000 000 <---------- 1 sig. digit

Use appropriate rules for rounding If the last digit before rounding is less than 5 it does not change ex. 343.3 to 3 places  343 1.544 to 2 places  1.54 If the last digit before rounding is greater than 5 – round up one ex. 205.8 to 3 places  206 10.75 to 2 places  11

use fewest number of decimal places rule for addition and subtraction 1) 2) 3) 4) 24.05 5.6 237.52 88 123.770 28 - 21.4 - 4.76 0.46 8.75 10.2 7 _________ ______ _______ ______

Use least number of significant figures rule for multiplication and division 23.7 x 6.36 2) .00250 x 14 3) 750. / 25 4) 15.5 / .005

Reliability of Measurement ACCURACY – how close a measured value is to the accepted value PRECISION – how close measurements are to one another - if measurements are precise they show little variation * Precise measurements may not be accurate

Are his results precise? Precision- refers to how close a series of measurements are to one another; precise measurements show little variation over a series of trials but may not be accurate. LESS THAN .1 IS PRECISE Oscar performs an experiment to determine the density of an unknown sample of metal. He performs the experiment three times: 19.30g/ml 19.31g/ml Certainty is +/- .01 Are his results precise?

Are his results accurate? Need to calculate percent error. Accuracy – refers to how close a measured value is to an (theoretical) accepted value. The metal sample was gold( which has a density of 19.32g/ml) Certainty is +/- .01 Are his results accurate? Need to calculate percent error. 5% OR LESS IS ACCURATE Oscar finds the volume of a box 2.00cm3 (ml) It is really 3.00ml is it precise? Accurate? Percent error

Oscar finds the volume of a box 2.00cm3 (ml) It is really 3.00ml is it precise? To know if it is precise you need more trials Accurate? Percent error Actual - Experimental X 100% = Actual 3-2 3 X 100 = 33.3%

Activity: basket and paper clip 1. Throw 3 paper clips at basket 2. Measure the distance from the basket to determine accuracy and precision Cm3= ml and dm3= l Liter

Graphing graph – a visual representation of data that reveals a pattern Bar- comparison of different items that vary by one factor Circle – depicts parts of a whole Line graph- depicts the intersection of data for 2 variables Independent variable- factor you change Dependent variable – the factor that is changed when independent variable changes

Graphing Creating a graph- must have the following points Title graph Independent variable – on the X axis – horizontal- abscissa Dependent variable – on Y axis – vertical- ordinate Must label the axis and use units Plot points Scale – use the whole graph Draw a best fit line- do not necessarily connect the dots and it could be a curved line.

Interpreting a graph Run X2 –X1 Slope- rise Y2 –Y1 relationship direct – a positive slope inverse- a negative slope equation for a line – y = mx + b m-slope b – y intercept extrapolate-points outside the measured values- dotted line interpolate- points not plotted within the measured values-dotted line

WORK ON GRAPHING EXERCISES Graphical analysis – click and go

GRAPHING LAB Creating a graph- must have the following points 1.Title graph 2. Independent variable –on the X axis–horizontal- abscissa 3. Dependent variable – on Y axis – vertical- ordinate 4. Must label the axis and use units 5. Plot points 6. Scale – use the whole graph 7. Draw a best fit line- do not necessarily connect the dots and it could be a curved line.

GRAPHING Interpreting a graph Run X2 –X1 Slope= rise Y2 –Y1 relationship direct relationship– a positive slope Inverse relationship- a negative slope equation for a line – y = mx + b m-slope b – y intercept extrapolate-points outside the measured values- dotted line interpolate- points not plotted within the measured values-dotted line

Bulldozer Lab