Data Analysis. Si units Metric System Review SI units Used in nearly every country in the world,...

Data AnalysisData Analysis

Si unitsSi units

Metric System ReviewMetric System Review

SI unitsSI units

Used in nearly every country in the world, Used in nearly every country in the world, the Metric System was devised by French the Metric System was devised by French scientists in the late 18scientists in the late 18thth century. The goal century. The goal of this effort was to produce a system that of this effort was to produce a system that used the decimal system rather than used the decimal system rather than fractions as well as a single unified system fractions as well as a single unified system that could be used throughout the entire that could be used throughout the entire world.world.

In 1960, an international committee of In 1960, an international committee of scientists revised the metric system and scientists revised the metric system and renamed it the Systeme International renamed it the Systeme International d”Unites, which is abbreviated SI.d”Unites, which is abbreviated SI.

There are seven base units in SI. A base There are seven base units in SI. A base unit is a defined unit in a system of unit is a defined unit in a system of measurement that is based on an object or measurement that is based on an object or event in the physical world. event in the physical world.

The REAL kilogram, The REAL kilogram, the the International International Prototype Kilogram Prototype Kilogram (IPK)(IPK) is kept in the is kept in the International Bureau International Bureau of Weights and of Weights and Measures near Measures near Paris. Several official Paris. Several official clones of this clones of this kilogram are kept in kilogram are kept in various locations various locations around the globe. around the globe.

A subset of the prefixes is A subset of the prefixes is TTera- (12), era- (12), GGiga- iga- (9), (9), MMega- (6), ega- (6), MMicro- (-6), icro- (-6), NNano- (-9), ano- (-9), PPico- ico- (-12), (-12), FFemto- (-15), emto- (-15), AAtto- (-18): tto- (-18):

TThe he GGooey ooey MMonster onster MMay ay NNot ot PPick ick FFive ive AApples. pples.

Converting With SI (metric)Converting With SI (metric)

When converting within the metric system it When converting within the metric system it is simply a measure of moving the decimal is simply a measure of moving the decimal in the appropriate direction.in the appropriate direction.

Converting With SI (metric)Converting With SI (metric)

KKangaroos angaroos HHop op DDown own MMountains ountains DDrinking rinking CChocolate hocolate MMilkilk

KKilo ilo HHecto ecto DDeca eca MMeter eter DDeci eci CCenti enti MMilliilli 1000 100 10 1 .1 .01 .0011000 100 10 1 .1 .01 .001

1000 m = ______ km1000 m = ______ km .001 hg = ______ dg.001 hg = ______ dg 42.7 L = _____ cL42.7 L = _____ cL

Things to rememberThings to remember

1.1. The short forms for metric units are called symbols, NOT The short forms for metric units are called symbols, NOT abbreviationsabbreviations

2.2. Metric symbols never end with a period unless they are Metric symbols never end with a period unless they are the last word in a sentence.the last word in a sentence.

• RIGHT:RIGHT: 20 mm, 10 kg 20 mm, 10 kg• WRONG:WRONG: 20 mm., 10 kg. 20 mm., 10 kg.

3.3. Metric symbols should be preceded by digits and a space Metric symbols should be preceded by digits and a space must separate the digits from the symbolsmust separate the digits from the symbols

• RIGHT:RIGHT: the box was 2 m wide the box was 2 m wide• WRONG:WRONG: the box was 2m wide the box was 2m wide


4.4. Symbols are always written in the singular formSymbols are always written in the singular form• RIGHT:RIGHT: 500 hL, 43 kg 500 hL, 43 kg• WRONG:WRONG: 500 hLs, 43 kgs 500 hLs, 43 kgs• BUT:BUT: It is correct to pluralize the written out metric It is correct to pluralize the written out metric

unit names: 500 hectoliters, 43 kilogramsunit names: 500 hectoliters, 43 kilograms

5.5. The compound symbols must be written out with The compound symbols must be written out with the appropriate mathematical sign includedthe appropriate mathematical sign included

• RIGHT:RIGHT: 30 km/h, 12 cm/s 30 km/h, 12 cm/s• WRONG:WRONG: 30 kmph, 30 kph (do NOT use a p to 30 kmph, 30 kph (do NOT use a p to

symbolize “per”)symbolize “per”)• BUT:BUT: It is ok to write out “kilometers per hour” It is ok to write out “kilometers per hour”


6.6. The meaning of a metric symbol is The meaning of a metric symbol is different depending on if it is lowercase or different depending on if it is lowercase or capitalizedcapitalized

• mm is millimeters (1/1000 meters)mm is millimeters (1/1000 meters)• Mm is Megameters (1 million meters)Mm is Megameters (1 million meters)

A unit that is defined by a combination of A unit that is defined by a combination of base units is called a derived unit. The base units is called a derived unit. The derived unit for volume is the cubic derived unit for volume is the cubic centimeter (cmcentimeter (cm33), which is used to ), which is used to measure volume of solids, one cmmeasure volume of solids, one cm33 is is equal to 1 ml. 1000 mL is equal to 1 Liter. equal to 1 ml. 1000 mL is equal to 1 Liter.

Quantity measuredQuantity measured UnitUnit SymbolSymbol RelationshipRelationship

Length, width,Length, width,distance, thickness,distance, thickness,girth, etc.girth, etc.

millimetermillimeter mmmm 10 mm10 mm == 1 cm1 cm

centimetercentimeter cmcm 100 cm100 cm == 1 m1 m

metermeter mm

kilometerkilometer kmkm 1 km1 km == 1000 m1000 m

MassMass(“weight”)*(“weight”)*

milligrammilligram mgmg 1000 mg1000 mg == 1 g1 g

gramgram gg

kilogramkilogram kgkg 1 kg1 kg == 1000 g1000 g

metric tonmetric ton tt 1 t1 t == 1000 kg1000 kg

TimeTime secondsecond ss

TemperatureTemperature degree Kelvindegree Kelvin KK

AreaArea

square metersquare meter m²m²

hectarehectare haha 1 ha1 ha == 10 000 m²10 000 m²

square kilometersquare kilometer km²km² 1 km²1 km² == 100 ha100 ha

VolumeVolume

millilitermilliliter mLmL 1000 mL1000 mL == 1 L1 L

cubic centimetercubic centimeter cm³cm³ 1 cm³1 cm³ == 1 mL1 mL

literliter LL 1000 L1000 L == 1 m³1 m³

cubic metercubic meter m³m³

Another derived unit is Density is a ratio that Another derived unit is Density is a ratio that compares the mass of a unit to its volume. compares the mass of a unit to its volume. The unit for density is g/ cmThe unit for density is g/ cm3 3 or kg/mor kg/m33. .

Density = mass ÷ volume Density = mass ÷ volume

or or DensityDensity = = MassMass

VolumeVolume

Temperature ConversionsTemperature Conversions Temperature Temperature is defined as the is defined as the average average

kinetic energy of the particles in a sample of kinetic energy of the particles in a sample of matter. The units for this are oC and Kelvin matter. The units for this are oC and Kelvin (K). Note that there is no degree symbol for (K). Note that there is no degree symbol for Kelvin.Kelvin.

HeatHeat is a measurement of the is a measurement of the totaltotal kinetic kinetic energy of the particles in a sample of matter. energy of the particles in a sample of matter. The units for this are the calorie (cal) and The units for this are the calorie (cal) and the Joule (J).the Joule (J).

bb The following equation can be used to convert The following equation can be used to convert

temperatures from Celsius (temperatures from Celsius (tt) to Kelvin () to Kelvin (TT) scales:) scales: TT(K) = (K) = tt(oC) + 273.15(oC) + 273.15 You are simply adding 273.15 to your Celsius You are simply adding 273.15 to your Celsius

temperature.temperature. Example: Convert 25.00 oC to the Kelvin scale.Example: Convert 25.00 oC to the Kelvin scale. TT(K) = 25.00 oC + 273.15(K) = 25.00 oC + 273.15 = 298.15= 298.15

Subtracting 273.15 allows Subtracting 273.15 allows conversion of a Kelvin conversion of a Kelvin temperature to a temperature to a temperature on the Celsius temperature on the Celsius scale. The equation is:scale. The equation is:

tt(oC) = (oC) = TT(K) - 273.15(K) - 273.15 You are simply subtracting You are simply subtracting

273.15 from your Kelvin 273.15 from your Kelvin temperature.temperature.

You are simply subtracting 273.15 from your You are simply subtracting 273.15 from your Kelvin temperature.Kelvin temperature.

Convert the following from the Celsius scale to the Convert the following from the Celsius scale to the Kelvin scale.Kelvin scale.

1. –200 1. –200 ooCC 2. –100 oC2. –100 oC 3. –50 oC3. –50 oC

4. 10 oC4. 10 oC 5. 50 oC5. 50 oC 6. 37 oC6. 37 oC

8. 100 oC8. 100 oC 9. –300 oC 9. –300 oC 10. 300 oC10. 300 oC

11. 273.15 oC11. 273.15 oC 12. -273.15 oC12. -273.15 oC

Convert the following form the Kelvin scale Convert the following form the Kelvin scale to the Celsius scale.to the Celsius scale.

1. 0 K1. 0 K 2. 100 K2. 100 K 3. 150 K3. 150 K

4. 200 K4. 200 K 5. 273.15 K5. 273.15 K

6. 300 K6. 300 K 7. 400 K7. 400 K 8. 37 K8. 37 K

9. 450 K9. 450 K 10. –273.15 K10. –273.15 K

Using your calculator to perform math operations with scientific notation

A calculator can make math operations with scientific notation much easier.

Using your calculator to perform math operations with

scientific notation A calculator can make math operations with

scientific notation much easier. To add 6.02 x 10-2 and 3.01 x 10-3, simply type the

following: 6.02 EXP +/- 2 + 3.01 EXP +/- 3 The calculator should read 6.321 –02. This

means 6.321 x 10-2.

Using your calculator to perform math operations with scientific notation

Calculators vary. Instead of EXP, some

have EE. Instead of +/-, some have (-). Only use the +/- or (-) if the exponent is negative.

It is also important to keep in mind that when the EXP button is hit, it is as though the button said “x 10 to the.” THERE IS NO NEED TO PRESS THE MULTIPLICATION BUTTON (unless the numbers in the problem are being multiplied together).

To multiply 6.02 x 10-2 and 3.01 x 10-3, simply type the following:

6.02 EXP +/- 2 x 3.01 EXP +/- 3 = The calculator should read 1.812 02 -04.

This means 1.812 02 x 10-4. If you are unsure, consult your teacher or the owner’s manual for the calculator.

Practice Section (3.37 x 104) + (2.29 x 105) (9.8 x 107) + (3.2 x 105) (8.6 x 104) – (7.6 x 103) (2.238 6 x 109) – (3.335 7 x 107) Multiplication and Division – Significant

digits should be used in your answers!!!!!!! (1.2 x 103) x (3.3 x 105) (7.73 x 102) x (3.4 x 10-3) (9.9 x 106) (3.3 x 103) 8. . (1.55 x 10-7) (5.0 x 10-4)

Dimensional Analysis

Dimensional analysis is the algebraic process of changing from one system of units to another. A fraction, called a conversion factor, is used. These fractions are obtained from an equivalence between two units.

http://www.youtube.com/watch?v=hQpQ0hxVNTg&list=PL8dPuuaLjXtPHzzYuWy6fYEaX9mQQ8oGr&index=2





For example, consider the equality 1 in. = 2.54 cm. This equality yields two conversion factors which both equal one:

cm 2.54

in 1


Note that the conversion factors above both equal one and that they are the inverse of one another. This enables you to convert between units in the equality. For example, to convert 5.08 cm to inches

5.08 cm x = 2.00 in

cm 2.54

in 1


For example, to convert 5.08 cm to inches5.08 cm x = 2.00 in

USING DIMENSIONAL ANALYSIS

You must develop the habit of including units with all measurements in calculations. Units are handled in calculations as any algebraic symbol:

Numbers added or subtracted must have the same units.

Representing DataRepresenting DataGraphingGraphing

Circle Graph (pie chart)Circle Graph (pie chart)

Useful for showing parts of a fixed whole.Useful for showing parts of a fixed whole.

Dimensional Analysis(Conversions)

Units are multiplied as algebraic symbols. For example: 10 cm x 10 cm = 10 cm2

Units are cancelled in division if they are identical.

For example, 27 g ÷ 2.7 g/cm3 = 10 cm3. Otherwise, they are left unchanged. For example, 27 g/10. cm3 = 2.7 g/cm3.


Now use dimensional analysis to solve the following English to metric measurement conversion problems:

(Use the equivalencies in the box on the previous page for your conversion factors).

Remember to use units so that you can cancel the ones you don’t want in your answer and keep the ones that you do!


1. Convert 5.00 lb to g(2270 g)

2. Convert 8.00 in. to m

( 0.203 m)


Try the rest of these on your own using dimensional analysis:

Convert 3.00 lb to g How many m are in 9.00 in?

Accuracy and Precision

Accuracy refers to how close a measured value is to the accepted value.

Precision refers to how close a series of measurements are to one another.

Accuracy and Precision

Percent Error

Ratio of an error to an accepted value

Percent Error is a way of expressing how far off an experimental measurement is from the accepted/true value. The formula for it is:

Percent Error is a way of expressing how far off an experimental measurement is from the accepted/true value. The formula for it is:

A 9th grade physical science student finds the density of a piece of aluminum to be 2.54 g/cm3. The accepted value is 2.7 g/cm3. What is the percent error? Show your work and make sure that you have the correct number of significant digits.

A student measures the length of a cube of metal to be 2.12 cm. The actual length is 2.21 cm. What is the percent error? Show your work and make sure that you have the correct number of significant digits.

A student performs an experiment and calculates the strength of an acid as 0.015 8 M. The actual strength is 0.016 5 M . What is the percent error? Show your work and make sure that you have the correct number of significant digits.


Bar GraphBar Graph Useful for understanding trends.Useful for understanding trends. Works well with data in catagories.Works well with data in catagories. Often used to show how quantities vary with Often used to show how quantities vary with

factors such as time, location, and factors such as time, location, and temperature. temperature.


Bar GraphBar Graph Independent variable plotted on the x-axisIndependent variable plotted on the x-axis Dependent variable plotted on the y- axisDependent variable plotted on the y- axis


Line Graphs (two coordinate graphs)Line Graphs (two coordinate graphs) Most of the graphs used in chemistryMost of the graphs used in chemistry Plot points have an x and y coordinatePlot points have an x and y coordinate Independent variable plotted on the x-axisIndependent variable plotted on the x-axis Dependent variable plotted on the y- axisDependent variable plotted on the y- axis

Line GraphsLine Graphs

Best fit line (trend line) Best fit line (trend line)

straight line drawn so as many points fall straight line drawn so as many points fall above the line as below the line.above the line as below the line.


Slope Slope Positive slope - Positive slope -

shows a direct shows a direct relationship relationship (e.g.as the IV (e.g.as the IV increases the DV increases the DV also increases)also increases)

Negative slope - Negative slope - shows a direct shows a direct relationship relationship (e.g.as the IV (e.g.as the IV increases the DV increases the DV also increases)also increases)

Line GraphsLine Graphs Slope Slope Positive slope - Positive slope -

shows a direct shows a direct relationship relationship (e.g.as the IV (e.g.as the IV increases the DV increases the DV also increases)also increases)

Negative slope - Negative slope - shows a direct shows a direct relationship relationship (e.g.as the IV (e.g.as the IV increases the DV increases the DV also increases)also increases)


Slope Slope Positive slope - shows a direct relationship Positive slope - shows a direct relationship

(e.g.as the IV increases the DV also (e.g.as the IV increases the DV also increases)increases)

Negative slope - shows a direct relationship Negative slope - shows a direct relationship (e.g.as the IV increases the DV also (e.g.as the IV increases the DV also increases)increases)

Significant FiguresSignificant Figures(Sig Figs)(Sig Figs)

Counting Significant DigitsCounting Significant Digits Quantities in chemistry are of two types:Quantities in chemistry are of two types: Exact numbersExact numbers – These result from counting – These result from counting

objects such as desks (there are 24 desks in this objects such as desks (there are 24 desks in this room), occur as defined values (there are 100 cm room), occur as defined values (there are 100 cm in 1 m), or as numbers in formulas (area of a right in 1 m), or as numbers in formulas (area of a right triangle = ½ B x H). They (24, 100, 1, and ½ for triangle = ½ B x H). They (24, 100, 1, and ½ for these examples) all have an infinite(∞) number of these examples) all have an infinite(∞) number of significant digits. B and H are measurements and significant digits. B and H are measurements and do notdo not have an infinite number of digits. have an infinite number of digits.

Inexact numbersInexact numbers – These are obtained – These are obtained from measurements and require judgment. from measurements and require judgment. Uncertainties exist in their values.Uncertainties exist in their values.

When making any measurement, always When making any measurement, always estimate one place past what is actually estimate one place past what is actually known. For example, if a meter stick has known. For example, if a meter stick has calibrationscalibrations to the 0.1 cm, the to the 0.1 cm, the measurement must be estimated to the 0.01 measurement must be estimated to the 0.01 cm. When making a measurement with a cm. When making a measurement with a digital readout, simply write down the digital readout, simply write down the measurement. The last digit is the measurement. The last digit is the estimated digit.estimated digit.

Significant digitsSignificant digits are all digits in a number are all digits in a number which are known with which are known with certaintycertainty plus one plus one uncertain digit. The following rules can be uncertain digit. The following rules can be used when determining the number of used when determining the number of significant digits in a number:significant digits in a number:

The following rules can be used when determining the number of The following rules can be used when determining the number of significant digits in a number:significant digits in a number:

RULERULE EXAMPLEEXAMPLE SIG SIG FIGSFIGS

1. All nonzero numbers are significant. 1. All nonzero numbers are significant. 132.54 g 132.54 g 55

2.2. All zeros between nonzero numbers All zeros between nonzero numbers

are significant. are significant. 130.0054 m 130.0054 m 77

3.3. Zeros to the right of a nonzero digit Zeros to the right of a nonzero digit but to the left of an understood but to the left of an understood decimal point are not significant decimal point are not significant

unless shown by placing a decimal unless shown by placing a decimal point at the end of the number. point at the end of the number.

190 000 mL190 000 mL

190 000. mL 190 000. mL

22

664.4. All zeros to the right of a decimal All zeros to the right of a decimal

point but to the left of a nonzero digit point but to the left of a nonzero digit are NOT significant. are NOT significant.

0.000 572 mg 0.000 572 mg 33

5.5. All zeros to the right of a decimal All zeros to the right of a decimal point and to the right of a nonzero point and to the right of a nonzero

digit are significant. digit are significant.

460.000 dm 460.000 dm 66

You can remember these rules or learn this You can remember these rules or learn this very easy shortcut.very easy shortcut.

If the number contains a decimal point, draw If the number contains a decimal point, draw an arrow starting at the an arrow starting at the leftleft through all zeros through all zeros and up to the 1st nonzero digit. The digits and up to the 1st nonzero digit. The digits remaining are significant.remaining are significant.

Try these:Try these: 0.002 50.002 5 1.002 51.002 5 0.002 500 00.002 500 0

14 100.014 100.0

If the quantity does not contain a decimal If the quantity does not contain a decimal point, draw an arrow starting at the point, draw an arrow starting at the rightright through all zeroes up to the 1st nonzero through all zeroes up to the 1st nonzero digit. The digits remaining are significant.digit. The digits remaining are significant.

Try these:Try these: 225225 10 00410 004 14 10014 100

103103

A good way to remember which side to start A good way to remember which side to start on is:on is:

decimal point decimal point ppresent, start at the resent, start at the PPacificacific decimal point decimal point aabsent, start at the bsent, start at the AAtlantictlantic

Practice Section - Practice Section - How many significant digits do How many significant digits do each of the following numbers have?each of the following numbers have?

Practice Section - How many significant digits do each of the following numbers have?

1. 1.050 _____ 6. 420 000 ______2. 20.06 _____ 7. 970 ______3. 13 _____ 8. 0.002 ______4. 0.303 0 ____ 9. 0.007 80 _____5. 373.109 ____10. 145.55 _____

Homework SectionHomework SectionHow many significant digits do the How many significant digits do the

following numbers possess?following numbers possess?1.1. 0.02 0.02 2.2. 0.0200.0203.3. 5015014.4. 501.0501.05.5. 5 0005 0006.6. 5 000.5 000.7.7. 6 051.006 051.008.8. 0.000 50.000 59.9. 0.102 00.102 010.10. 10 00110 001

11. 20.03 kg11. 20.03 kg12. The 60 in the equality 12. The 60 in the equality 60 s equals one min.60 s equals one min.13. The one in the above.13. The one in the above.14. 120 m14. 120 m15. 10 dollar bills15. 10 dollar bills16. 0.050 cL16. 0.050 cL17. The ½ in ½ mv217. The ½ in ½ mv218. 0.000 67 cm318. 0.000 67 cm3

Rounding RulesRounding Rules

Calculators often give answers with too Calculators often give answers with too many significant digits. It is often necessary many significant digits. It is often necessary to round off the answers to the correct to round off the answers to the correct number of significant digits. The last number of significant digits. The last significant digit that you want to retain significant digit that you want to retain should should be rounded up if the digit be rounded up if the digit immediately to the right of itimmediately to the right of it is is

(Each of the examples are being rounded to (Each of the examples are being rounded to four sig digs):four sig digs):


Rule Example 4 sig digs

….. greater than 5 532.79 532.8

….. 5, followed by a nonzero digit 17.255 1 17.26

….. 5, not followed by a nonzero, but has an odd digit directly in front of it.

3 213.5 3214

The last significant digit that you want The last significant digit that you want to retain should to retain should be rounded up if the be rounded up if the digit immediately to the right of itdigit immediately to the right of it is is

Rounding RulesRounding Rules The last significant digit that you want to retain The last significant digit that you want to retain

should stay the same if the digit immediately should stay the same if the digit immediately to the right of itto the right of it is: is:

Rule Example 4 sig digs

….. less than 5 5454.33 5454

….. 5, not followed by a nonzero, but has an even digit directly in front of it.

0.00785 0.0078


Practice Section - Practice Section - Round the following numbers to 3 sig digs.Round the following numbers to 3 sig digs. 1. 279.3 _________1. 279.3 _________ 4. 32.395 ________ 7. 18.294. 32.395 ________ 7. 18.29 ______________________

2. 42.353 ________2. 42.353 ________ 5. 32.25 ________ 8. 5 0015. 32.25 ________ 8. 5 001 ______________________

3. 18.77 _________3. 18.77 _________ 6. 7.535 _______ 9. 0.008 752 __________6. 7.535 _______ 9. 0.008 752 __________


Homework Section - Homework Section - Round the following numbers to 4 Round the following numbers to 4 significant digitssignificant digits

123 456123 456 0.093 4590.093 459 1.234 567 8901.234 567 890 222.251222.251 222.26222.26 222.24222.24 222.25222.25 222.35222.35 5 0005 000 19.99919.999


Slope Slope Use data points Use data points

to calculate the to calculate the slope of the slope of the line. line.

The slope is the The slope is the change in y change in y divided by the divided by the change in y.change in y.

Data Analysis. Si units Metric System Review SI units Used in nearly every country in the world,...

Documents

Transcript of Data Analysis. Si units Metric System Review SI units Used in nearly every country in the world,...