data analysis using the metric system scientific notation percent error using significant figures...

DATA ANALYSISUsing the Metric System

Scientific Notation

Percent Error

Using Significant Figures

Accuracy and Precision

Graphing Techniques

Using the Metric SystemA. 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 UnitsBase Units – independent of other unitsDerived Units – combination of base units

Examples density g/L (grams per liter) volume m x m x m = meters cubedVelocity m/s (meters per second

Metric Units Used In This ClassQUANTITY 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 hvolume measurement for a liquid and a solid ( 1 mL = 1 cm3) These are equivalents.

Equalities You Need To Know1 km = 1000 m1 m = 100 cm1 m = 1000 mm1L = 1000 mL1kg = 1000g1 g = 100cg1 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”

Examples1. 10.0 cm = __________m2. 34.5 mL = __________L3. 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

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

MultiplyingCalculating in Scientific notation

Multiplying- Multiple the numbers Add the exponents

(2.0 x 104) (4.0 x 103) = 8.0 x 107

Dividing divide the numbers subtract the denominator exponent from the

numerator exponent

9.0 x 107 3.0 x 102

3.0 x 105

AddAdd 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

PRACTICEAdd: 2.3 x 103 cm + 3.4 x 105 cmSubtract:  2.3 x 103 cm - 3.4 x 105 cmMultiply: : 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 ErrorEXAMPLE – 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 ByrdDepartment 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:

Likewise, the units in (ft x lb) / ft reduces to pounds (lb) when the same units ( ft )are canceled:

5

5 4

5

5 4 = 4

ft

lb ft

ft

lb ft = lb

CONVERSION FACTORA 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-RelationshipWe 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.

454 grams

1.00 pound

1.00 pound

454 gramsor as

ExampleIf 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:

pound 1.00

grams 454 pounds 2.00 = 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.

grams 454

pound 1.00 pounds 2.00

grams

2pounds 0044.0=

Four-step approachWhen using the Factor-Label Method

it is helpful to follow a four-step approach in solving problems:

1. What is question – How many sec in 56 min2. What are the equalities- 1 min = 60 sec3. Set up problem (bridges) 56 min 60 sec 4. 1 min5. Solve the math problem -multiple

everything on top6. 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. digits400 000 000 <---------- 1 sig. digit

Use appropriate rules for roundingIf 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 1.54If 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 figuresrule for multiplication and division

1) 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

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 19.30g/ml

Certainty is +/- .01 Are his results precise?

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

+/- .01Are his results accurate? Need to calculate

percent error. 5% OR LESS IS ACCURATEOscar 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 errorActual - Experimental X 100% = Actual 3-2 3 X 100 = 33.3%

Activity: basket and paper clip1. Throw 3 paper clips at basket2. Measure the distance from the basket to

determine accuracy and precisionCm3= 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

points1. Title graph2. Independent variable – on the X axis –

horizontal- abscissa3. Dependent variable – on Y axis – vertical-

ordinate4. Must label the axis and use units5. Plot points6. Scale – use the whole graph7. Draw a best fit line- do not necessarily connect

the dots and it could be a curved line.

Interpreting a graph Slope- rise Y2 –Y1

Run X2 –X1 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

points1.Title graph2. Independent variable –on the X axis–horizontal-

abscissa3. Dependent variable – on Y axis – vertical- ordinate4. Must label the axis and use units5. Plot points6. Scale – use the whole graph7. Draw a best fit line- do not necessarily connect the dots

and it could be a curved line.

GRAPHING Interpreting a graph

Slope= rise Y2 –Y1 Run X2 –X1

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