data analysis chapter 2. units of measurement is a measurement useful without a unit? is a...

Data AnalysisData Analysis

Chapter 2Chapter 2

Units of MeasurementUnits of Measurement

Is a measurement useful without a unit?Is a measurement useful without a unit?

SI UnitsSI Units

The metric system is used worldwide.The metric system is used worldwide.Long ago, inexact measurements were Long ago, inexact measurements were

used. For example:used. For example:Boundaries would’ve been marked off by walking & Boundaries would’ve been marked off by walking &

counting the number of steps.counting the number of steps.Time was measured with a sundial or an hourglass Time was measured with a sundial or an hourglass

filled with sand.filled with sand.

SI UnitsSI Units

The metric system was adopted in 1795 The metric system was adopted in 1795 by a group of French scientists.by a group of French scientists.

In 1960, an international committee of In 1960, an international committee of scientists met to update the metric system. scientists met to update the metric system. Called the SI system (Systeme Called the SI system (Systeme Internationale d’Unites)Internationale d’Unites)

Base UnitsBase Units

There are 7 base units in SI. A base unit is a There are 7 base units in SI. A base unit is a defined unit in a system of measurement that is defined unit in a system of measurement that is based on an object or event in the physical based on an object or event in the physical world.world.

The base unit for:The base unit for: Time is second… electrical current is…Time is second… electrical current is… Length is meter…Length is meter… amount of sub is… amount of sub is… Mass is kilogram…Mass is kilogram… luminosity is… luminosity is… Temp is…Temp is…

The prefixes used with SI units are The prefixes used with SI units are …(table 2-2)…(table 2-2)

Derived UnitsDerived Units

A derived unit is a unit that is defined by a A derived unit is a unit that is defined by a combination of base units. combination of base units.

Example: speed is meters/second (m/s)Example: speed is meters/second (m/s)

Get out your calculators!Get out your calculators!

VolumeVolume

Volume is the space occupied by an object.Volume is the space occupied by an object. 1 L= 1 dm1 L= 1 dm33 1 mL= 1 cm1 mL= 1 cm33

You would use a graduated cylinder to You would use a graduated cylinder to measure the volume of a liquid in the lab.measure the volume of a liquid in the lab.

You would measure length x width x height You would measure length x width x height to find the volume of a “regular” solid.to find the volume of a “regular” solid.

How would you find the volume of an How would you find the volume of an irregular solid?irregular solid?

DensityDensity

Density of a ratio that compares the Density of a ratio that compares the mass of an object to its volumemass of an object to its volume

D=m/vD=m/vEx 1 Calculate the density of a piece of Ex 1 Calculate the density of a piece of

aluminum that has the mass of 13.5g & aluminum that has the mass of 13.5g & a volume of 5.0cma volume of 5.0cm33. . What is this substance?What is this substance?

Ex 2 Suppose a sample of aluminum Ex 2 Suppose a sample of aluminum (Al) is placed in a graduated cylinder (Al) is placed in a graduated cylinder containing 10.5 mL of water & rises to containing 10.5 mL of water & rises to 13.5 mL. What is the mass of the 13.5 mL. What is the mass of the aluminum sample? aluminum sample? (Use the density from (Use the density from example 1)example 1)

DensityDensity

Density of a substance is a property Density of a substance is a property that doesn’t change, UNLESS altered that doesn’t change, UNLESS altered by an outside substance.by an outside substance.

DDwaterwater at STP is 0.998 g/cm at STP is 0.998 g/cm33

DDwaterwater at 4°C is 1.00 g/cm at 4°C is 1.00 g/cm33

** practice problems #1-3** practice problems #1-3

If we know the Density & dimensions of a If we know the Density & dimensions of a cube, can we determine the mass of the cube, can we determine the mass of the cube?cube?

If the DIf the Dairair= 0.00122 g/cm= 0.00122 g/cm33, then what is the , then what is the

mass of air in this room?mass of air in this room?

TemperatureTemperature

Temperature is the measure of how Temperature is the measure of how hot/cold an object is relative to other hot/cold an object is relative to other objects.objects.

Scales of temperature:Scales of temperature:Celsius- derived by Anders Celsius & used Celsius- derived by Anders Celsius & used

the point at which water freezes & boils to the point at which water freezes & boils to establish his scaleestablish his scaleFreezing point- 0Freezing point- 0° C° CBoiling point- 100° CBoiling point- 100° C

TemperatureTemperature

Kelvin (K)- derived by William Kelvin (K)- derived by William Thomson, known as Lord KelvinThomson, known as Lord KelvinKelvin is the SI base unit of temperatureKelvin is the SI base unit of temperatureConversion process of Celsius to KelvinConversion process of Celsius to Kelvin

Add 273Add 273

Conversion process of Kelvin to CelsiusConversion process of Kelvin to CelsiusSubtract 273Subtract 273

Ex. Ex.

**Practice problems 4-6**Practice problems 4-6

4. Convert 3574. Convert 357°C to Kelvin°C to Kelvin

5. Convert -39°C to Kelvin5. Convert -39°C to Kelvin

6. Convert 266 K to Celsius6. Convert 266 K to Celsius

Scientific NotationScientific Notation

Scientific notation- expresses a number Scientific notation- expresses a number as a number between 1 & 10 and then as a number between 1 & 10 and then raised to a power, or exponent.raised to a power, or exponent.

When a number is more than one, the When a number is more than one, the exponent is positive.exponent is positive.

If less than one, the exponent is If less than one, the exponent is negative.negative.


How do we convert data into Sci. Not. ?How do we convert data into Sci. Not. ? Move the decimal until you have a Move the decimal until you have a

number between 1 & 10.number between 1 & 10. The exponent in the number of times you The exponent in the number of times you

moved the decimal.moved the decimal. Put unit with answer.Put unit with answer.


** Practice problems 1-8** Practice problems 1-8

1.1. 700 m700 m

2.2. 38 000 m38 000 m

3.3. 4 500 000m4 500 000m

4.4. 685 000 000 000 m685 000 000 000 m

5. 0.0054 kg5. 0.0054 kg

6. 0.000 006 87 kg6. 0.000 006 87 kg

7. 0.000 000 076 kg7. 0.000 000 076 kg

8. 0.000 000 000 8 kg8. 0.000 000 000 8 kg

Calculations with Sci Not.Calculations with Sci Not.

How do we add/subtract using How do we add/subtract using Scientific Notation?Scientific Notation?Make sure exponents are the same.Make sure exponents are the same. If the exponent is too large, decrease it & If the exponent is too large, decrease it &

move the decimal that many times to the move the decimal that many times to the right.right.

If the exponent is too small, increase it & If the exponent is too small, increase it & move the decimal that many places to the move the decimal that many places to the left.left.


Ex. What is 2.70 x 10Ex. What is 2.70 x 1077 + 15.6 x 10 + 15.6 x 1066??

** practice problems 5-8** practice problems 5-8

5.5. 1.26x101.26x1044 kg + 2.5x10 kg + 2.5x1033 kg kg

6.6. 7.06x107.06x10-3-3 kg + 1.2x10 kg + 1.2x10-4-4 kg kg

7.7. 4.39x104.39x1055 kg – 2.8x10 kg – 2.8x1044 kg kg

8.8. 5.36x105.36x10-1-1 kg – 7.40x10 kg – 7.40x10-2-2 kg kg


How do we multiply/divide using sci. How do we multiply/divide using sci. not.?not.?Multiply/divide the factors(aka coefficients) Multiply/divide the factors(aka coefficients)

first.first.MultiplicationMultiplication

Add the exponents.Add the exponents.

DivisionDivisionSubtract the exponent of the denominator from Subtract the exponent of the denominator from

the exponent of the numerator.the exponent of the numerator.


Ex.1 What is (2 x 10Ex.1 What is (2 x 1033) x (3 x 10) x (3 x 1022))

Ex. 2 What is (9 x 10Ex. 2 What is (9 x 1088) / (3 x 10) / (3 x 10-4-4))

** practice problems 9-16.** practice problems 9-16.

9. (4x109. (4x1022 cm)x(1x10 cm)x(1x1088 cm) cm) 10. (2x1010. (2x10-4-4 cm)x(3x10 cm)x(3x1022 cm) cm) 11. (3x1011. (3x1011 cm)x(3x10 cm)x(3x10-2-2 cm) cm) 12. (1x1012. (1x1033 cm)x(5x10 cm)x(5x10-1-1 cm) cm) 13. (6x1013. (6x1022 g)/(2x10 g)/(2x1011 cm cm33)) 14. (8x1014. (8x1044 g)/( 4x10 g)/( 4x1011 cm cm33)) 15. (9x1015. (9x1055 g)/ (3x10 g)/ (3x10-1-1 cm cm33)) 16. (4x1016. (4x10-3-3 g)/(2x10 g)/(2x10-2-2 cm cm33))

Dimensional AnalysisDimensional Analysis

Dimensional analysis- method of problem-Dimensional analysis- method of problem-solving that focuses on the units used to solving that focuses on the units used to describe matter; often uses conversion describe matter; often uses conversion factors.factors.

Conversion factor- ratio of equivalent Conversion factor- ratio of equivalent values used to express the same quantity values used to express the same quantity in different units.in different units.

Ex 1 How many hours are in one year?Ex 1 How many hours are in one year?

Conversion FactorsConversion Factors GigaGiga MegaMega KiloKilo HectoHecto DecaDeca BASEBASE DeciDeci CentiCenti MilliMilli MicroMicro NanoNano (Angstro)(Angstro) PicoPico

Dimensional Analysis

• Ex. 1 How many meters are in 48 km?

Practice:

• What conversion factor should be used for the following conversion?

• A. 360 s ms

• B. 4800 g kg

• C. 6800 cm m

Practice using dimensional analysis1. 4.5 L = __________mL

2. 0.095mg = ____________cg

3. 9500 mm = ___________m

4. 0.575 km = ___________m

5. 100 cm = ___________mm

**Handout “Unit Conversion…”

ConversionConversion

Ex. 2 What is the speed of 550 meters Ex. 2 What is the speed of 550 meters per second in kilometers per minute?per second in kilometers per minute?

PracticePractice

6) How many seconds are there in 246) How many seconds are there in 24.0.0 hours? hours? 86,400 s86,400 s

7) the density of gold is 19.3 g/mL. What is gold’s 7) the density of gold is 19.3 g/mL. What is gold’s density in decigrams per liter?density in decigrams per liter?

193,000dg/L193,000dg/L

8) A car is travelling 908) A car is travelling 90.. kilometers per hour. What kilometers per hour. What is the speed in miles per minute? (1 km=0.62 mi)is the speed in miles per minute? (1 km=0.62 mi)

0.93 mi/min0.93 mi/min

ReliabilityReliability

How reliable are measurements?How reliable are measurements?Accuracy & Precision:Accuracy & Precision:Accuracy- refers to how close a Accuracy- refers to how close a

measured value is to an measured value is to an acceptedaccepted value.value.

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

Accuracy or precisionAccuracy or precision

Percent ErrorPercent Error

Percent error- ratio of an error to an Percent error- ratio of an error to an accepted value.accepted value.

% error= % error= accepted(book value) – exp (you)accepted(book value) – exp (you) x 100 x 100

accepted accepted% error= (error/accepted) x 100% error= (error/accepted) x 100 Ignore the negative sign, only the Ignore the negative sign, only the

amount of error matters.amount of error matters.

Percent ErrorPercent Error

Ex. You calculated the length of a steel Ex. You calculated the length of a steel pipe to be 5.2 m. The accepted length is pipe to be 5.2 m. The accepted length is 5.5 m. What is the percent error?5.5 m. What is the percent error?

Practice #1Practice #1The accepted density for Cu is 8.96 The accepted density for Cu is 8.96

g/mL. Calculate the percent error for g/mL. Calculate the percent error for the measurement 8.86 g/mL.the measurement 8.86 g/mL.

**Worksheet****Worksheet**

Significant FiguresSignificant Figures

Significant figures- include all known Significant figures- include all known digits plus one estimated digit.digits plus one estimated digit.

Rules:Rules:1.1. Non-zero numbers are always significantNon-zero numbers are always significant

Ex. 72.3 Ex. 72.3 Ex. 700Ex. 700

2.2. ““Sandwich zeros” are significant.Sandwich zeros” are significant. 60.560.5 809809 30.0730.07


3. Final zeros after the decimal are significant.3. Final zeros after the decimal are significant.a) 6.20a) 6.20b) 9.00b) 9.00c) 92.0c) 92.0d) 0.009200 d) 0.009200

4. “Place holding” zeros are not significant.4. “Place holding” zeros are not significant.e) 0.095e) 0.095f) 300f) 300g) 50g) 50h) 30,000h) 30,000


You can convert to scientific notation to You can convert to scientific notation to remove place holders.remove place holders. 30,000 = 3 x 1030,000 = 3 x 1044

Example: Determine the number of sig figs in Example: Determine the number of sig figs in the following masses. the following masses.

a) 0.000 402 30 ga) 0.000 402 30 g b) 405 000 kgb) 405 000 kg c) 8.20 x 10c) 8.20 x 1077

*** practice problems p39 # 31 & 32*** practice problems p39 # 31 & 32

Rounding Off NumbersRounding Off Numbers

Rounding to 3 sig figsRounding to 3 sig figs2.53202.5320 if the 4 if the 4thth sig fig is <5, do not change sig fig is <5, do not change

the 3the 3rdrd sig fig. sig fig.2.53602.5360 if the 4 if the 4thth sig fig is =>5, then round sig fig is =>5, then round

the 3the 3rdrd sig fig up. sig fig up.Examples:Examples:

55.845 55.845 (4 sf)(4 sf)32.065 32.065 (2 sf)(2 sf)87.62 87.62 (1 sf)(1 sf)36,549,555 36,549,555 (2 sf)(2 sf)

Addition/subtraction with sig figsAddition/subtraction with sig figs

Your answer must have the same number Your answer must have the same number of digits to the right of the decimal as the of digits to the right of the decimal as the measurement with the FEWEST digits to measurement with the FEWEST digits to the right of the decimal.the right of the decimal.

Ex. Add the following measurements: 28.0 Ex. Add the following measurements: 28.0 cm, 23.538 cm, 25.68 cm.cm, 23.538 cm, 25.68 cm.

** practice problems** practice problems

Multiplication/division w/ sig figsMultiplication/division w/ sig figs

Your answer must have the same number Your answer must have the same number of sig figs as the measurement with the of sig figs as the measurement with the fewest sig figs.fewest sig figs.

Ex. Calculate the volume of a rectangular Ex. Calculate the volume of a rectangular object w/ the following dimensions: object w/ the following dimensions: length= 3.65 cm, length= 3.65 cm,

width= 3.2cm, width= 3.2cm, height= 2.05 cm.height= 2.05 cm.

Multiplication/division w/ sig figsMultiplication/division w/ sig figs

**practice problems 7-14**practice problems 7-14Check old worksheetsCheck old worksheets **worksheet****worksheet**

Representing DataRepresenting Data

Graph- visual display of dataGraph- visual display of dataCircle graph- usually used to represent Circle graph- usually used to represent

percentages of something. percentages of something.


Bar graph- often used to show how a Bar graph- often used to show how a quantity varies with factors such as time, quantity varies with factors such as time, location, or temperature.location, or temperature. Independent variable- located on the x-axisIndependent variable- located on the x-axisDependent variable- located on the y-axisDependent variable- located on the y-axis

Bar GraphBar Graph

Progomphus Size vs. Time

0

0.5

1

1.5

2

2.5

3

3.5

Aug-08

Sep-08

Oct-08

Nov-08

Dec-08

Jan-09

Feb-09

Mar-09

Num

ber o

f Ind

ivid

uals

0.00

1.00

2.00

3.00

4.00

5.00

6.00

Hea

d ca

psul

e S

ize

(mm

)

#

high

low

mean


Line Graph- most often used in chemistryLine Graph- most often used in chemistryThe points on a line graph represent the The points on a line graph represent the

intersection of data for 2 variables.intersection of data for 2 variables. Independent variable- located on the x-axis.Independent variable- located on the x-axis.Dependent variable- located on the y-axisDependent variable- located on the y-axis

Best fit line- line drawn so that as many Best fit line- line drawn so that as many points fall above the line as fall below it. points fall above the line as fall below it. Straight best fit- there is a linear relationshipStraight best fit- there is a linear relationship

The variables are directly relatedThe variables are directly related

Curved best fit- there is a nonlinear Curved best fit- there is a nonlinear relationship.relationship.The variables are inversely relatedThe variables are inversely related

Interpreting DataInterpreting Data

First thing, ID the variables; independent & First thing, ID the variables; independent & dependentdependent

Notice what measurements were takenNotice what measurements were takenDecide if the relationship of the variables Decide if the relationship of the variables

is linear/nonlinear.is linear/nonlinear.

data analysis chapter 2. units of measurement is a measurement useful without a unit? is a...

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