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Scientific NotationHow do you know if 1,000 has 1, 2, 3, or 4 significant figures? If it has significant figures up to the decimal point, draw in thedecimal point: 1,000. Move the decimal points: example with 2 significant figures: 1,000

= 1.0 x 1,000 = 1.0 x 10 x 10 x 10 = 1.0x103

Scientific Notation Count the number of places the decimal moved to determine

the exponent:

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Scientific NotationVery large and very small values can be unwieldy in standard notation:For example: Avogadros Number: 602,000,000,000,000,000,000,000 atoms/mole Mass of an Electron: 0.000 000 000 000 000 000 000 000 000 000 910 kg

Scientific NotationScientific Notation makes very large and very small numbers more manageableFor example: Avogadros Number: 602,000,000,000,000,000,000,000 atoms/mole 6.02 * 1023 atoms/mole Mass of an Electron: 0.000 000 000 000 000 000 000 000 000 000 91 kg

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Scientific NotationScientific Notation makes very large and very small numbers more manageableFor example: Avogadros Number: 602,000,000,000,000,000,000,000 atoms/mole 6.02 * 1023 atoms/mole Mass of an Electron: 0.000 000 000 000 000 000 000 000 000 000 91 kg 9.1 * 10-31 kg

Scientific NotationThe components of Scientific Notation: X.YZ * 10n Coefficient * BaseExponent Rules: 1. 1 < Coefficient < 10 2. Base = 10 3. Exponent = the number of decimal places the decimal must be moved to achieve standard notation A negative exponent moves the decimal to the left A positive exponent moves the decimal to the right

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Scientific NotationMath Tip Calculator: use the EE function Multiplication: Multiply the coefficients Add the exponents If necessary, correct coefficient to have one digit before the decimal. Example

1.210 2 = 1.2E21.210 2 3.010 4 = (1.2 3.0) 10 2+(4 ) = 3.610 2

Division: Divide the coefficients Subtract the exponents If necessary, correct coefficient to have one digit before the decimal.

1.210 2 1.2 2(4 ) = 10 3.010 4 3.0 = 0.4010 6 = 4.010 5

Scientific NotationGroup Work Time!

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Dimensional AnalysisMath Numbers Chemistry Quantity (number + unit)

Math uses numbers. Chemistry uses quantities. Dimensional Analysis helps with chemical calculations.

Rules for Using Dimensional Analsysis Always include the units. Include appropriate conversion factors as necessary. Use conversion factors so that units cancel as desired.

Dimensional AnalysisCritical idea: Any number multiplied by one equals itself. Example: 5 x 1 = 5 Conversion factor: Ratio of equivalent quantities in different units, thus equal to one. Example:

2.54 cm = 5.08 cm 1 inch 2.00 5.08, but 2.00 inches = 5.08 cm Always use units! 2.00 inches

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Dimensional AnalysisCritical idea: Any number multiplied by one equals itself. Example: 5 x 1 = 5 Conversion factor: Ratio of equivalent quantities in different units, thus equal to one. Example:

2.54 cm = 5.08 cm 1 inch 2.00 5.08, but 2.00 inches = 5.08 cm Always use units! 2.00 inches

Dimensional AnalysisFlip the conversion factor if necessary to cancel out the units as desired. Example:

What is the mass in kilograms of a 120 lb. person? 1) What converstion factor do we need to use? 2.2 lb 1 kg 1 lb = 2.2 kg or ? 1 kg 2.2 lb 2) Start drawing out the equation. x kg = 120 lb Z Z

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Dimensional AnalysisFlip the conversion factor if necessary to cancel out the units as desired. Example:

What is the mass in kilograms of a 120 lb. person? 1) What converstion factor do we need to use? 1 kg 2.2 lb 1 kg = 2.2 lb or ? 2.2 lb 1 kg 2) Start drawing out the equation. 1 lb x kg = 120 lb = 54 kg 2.2 kg

Factor-Label MethodA more challenging example:

The price of gold varies greatly and has been as high as $875 per ounce. What is the value of 250 g of gold at $559 per ounce? Gold is price by troy ounces. 14.58 troy ounces = 1 lb. 1 kg = 2.2 lb. $ x = 250 g $559 ... oz.Question from Fundamentals of College Chemistry (Hein)

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Dimensional AnalysisCalculate the Body-Mass Index (BMI) of a student who is 57 and weighs 120 lbs. Given thatBMI = mass (kg) [height (m)]2

What is the height in inches? What is the height in meters? What is the mass in kilograms? The blue area denotes a healthy BMI; purple is overweight; and red is obese. How would you approximate this students build?

TemperatureHeat a form of energy Temperature a measure of heat

Heat from the sun warms our atmosphere. The temperature of the air outside is high.

http://4.bp.blogspot.com/_fri8ZUYihSk/RtcxWWZBb_I/AAAAAAAAAxE/ yAagEeYDzQo/s1600-h/ist2_2082857_thermometer_in_summer_heat.jpg

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Energy SI unit:

joule (J) Metric unit: calorie (cal) Note: food calorie = Calorie = 1 kcal

http://www.magnet.fsu.edu/education/tutorials/magnetacademy/superconductivity101/ images/superconductivity-temperature.jpg

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Temperature Conversionso

( o F 32) C= 1.8

How do we calculate F from C?

Temperature ConversionsTC = (TF 32) 1.8

How do we calculate F from C?TF = 1.8TC + 32

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http://www.magnet.fsu.edu/education/tutorials/magnetacademy/superconductivity101/ images/superconductivity-temperature.jpg

Temperature ConversionsCelsius to Kelvin TK = TC + 273.15 Kelvin to Celsius TC = TK 273.15

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DensityDensity: Ratio of mass to volume: density = mass/volume d = m/v

DensityDensity of water: 1.000 g/mL at 4C

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Density Practice ProblemsPractice Problem (Fundamentals of College Chemistry) Pure silver has a density of 10.5 g/mL. A ring sold of pure silver has a mass of 18.7 g. When placed in a graduated cylinder, the water level rises 2.0 mL. Determine whether the ring is actually pure silver or whether the customer should call customer service.

Density Practice ProblemsPractice Problem 2.14 Pure silver has a density of 10.5 g/mL. A ring sold of pure silver has a mass of 18.7 g. When placed in a graduated cylinder, the water level rises 2.0 mL. Determine whether the ring is actually pure silver or whether the customer should call customer service. d = m/v = 18.7 g/2.0 mL = 9.35 g/mL = 9.4 g/mL The ring is not pure silver.

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Density Practice ProblemExercise (Foundations of College Chemistry, Hein) The mass of an empty container is 88.25 g. The mass of the container when filled with a liquid (d = 1.25 g/mL) is 150.50 g. What is the volume of the container?

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