Today Turn in graphing homework on my desk Turn in graphing homework on my desk Post Lab discussion (redo graph??) Post Lab discussion (redo graph??) Go over Math Quizzes Go over Math Quizzes Measuring in Science & Rearranging Equations Notes Measuring in Science & Rearranging Equations Notes HOMEWORK: Rearranging Equations wkst HOMEWORK: Rearranging Equations wkst

Measuring in Science Practicing Accurate Measurement

Measuring in Science Why is this important? Why is this important? Understanding how to record and work with measurements accurately is essential for success in all science-related fields Understanding how to record and work with measurements accurately is essential for success in all science-related fields SI Units (Systeme International) SI Units (Systeme International) world wide system to eliminate confusion world wide system to eliminate confusion the metric system and the SI system can be used almost interchangeably the metric system and the SI system can be used almost interchangeably based on decimals based on decimals

SI Base Units Length Length Def: the distance from one point to another Def: the distance from one point to another Units: Meter, m Units: Meter, m Different forms: cm, mm, etc Different forms: cm, mm, etc

SI Base Units Mass Mass Def: the measure of a quantity of matter Def: the measure of a quantity of matter Units: Kilograms, kg Units: Kilograms, kg Different forms: g, mg, etc Different forms: g, mg, etc

SI Unit Bases Volume Volume Def: Length x Width x Height Def: Length x Width x Height Units: Liters, L Units: Liters, L Different forms: ml Different forms: ml Different metric forms: m 3, cm 3, cc, etc. Different metric forms: m 3, cm 3, cc, etc.

SI Unit Bases Time Time Unit: seconds Unit: seconds Temperature Temperature Unit: Kelvin Unit: Kelvin Amount of substance Amount of substance Unit: mole Unit: mole

METRIC PREFIX AND EQUIVALENTS PrefixPhoneticSymbolDecimal EquivalentExponential Equival ent Tera-Ter-uhT1,000,000,000, Giga-Gig-uhG 1,000,000, Mega-Meg-uhM 1,000, Kilo-Kill-uhk 1, Hecto-Hek-tuhh Deca-Dec-uhda Deci-Des-uhd Centi-Sent-uhc Milli-Mill-uhm Micro-Mi-crowu Nano-Nan-uhn Pico-Pea-koP Femto-Fem-toef Atto-At-toea

Percent Error Def: A way to show how close your value is to the accepted value Def: A way to show how close your value is to the accepted value = |measured value – accepted value| x 100 Accepted value

Percent Error Example Example Measured – 76.5 kg Measured – 76.5 kg Accepted – 77.9 kg Accepted – 77.9 kg Find the percent error.

Percent Error = |76.5 kg – 77.9 kg| x kg = 1.80 %

Rearranging Equations In Chemistry we work with numbers and a lot of different equations. It is essential to master the skill of rearranging equations to solve for a variable. In Chemistry we work with numbers and a lot of different equations. It is essential to master the skill of rearranging equations to solve for a variable. Use the following steps when working with problems. Use the following steps when working with problems.

Rearranging Equations 1. Identify what is given to you. 2. Answer the question: For what are you solving? 3. Set up the known equation using variables. 4. Rearrange equation, following the order of operations, to solve for the chosen variable. 5. Plug in the proper values and units. Solve Let’s refresh our memory on the Order of Operations!

Rearranging Equations When you have more than one operation in a math problem, you must follow the correct order of operations. When you have more than one operation in a math problem, you must follow the correct order of operations. Just remember: Just remember: “Please Excuse My Dear Aunt Sally” “Please Excuse My Dear Aunt Sally”

Order of Operations “Please” - parentheses “Please” - parentheses “Excuse” - exponents “Excuse” - exponents “My” - multipy “My” - multipy “Dear” - divide “Dear” - divide “Aunt” - add “Aunt” - add “Sally” - subtract “Sally” - subtract

Order of Operations When solving problems: When solving problems: Make sure the problem is copied down correctly Make sure the problem is copied down correctly Follow the order of operations Follow the order of operations Do each operation within each level from left to right Do each operation within each level from left to right Be careful not to reuse any numbers Be careful not to reuse any numbers Continue until all operations are done Continue until all operations are done

Rearranging Equations Example: A car crosses a major intersection going miles/hour. If the next light is 1.23 miles away. How long does it take the car to reach it? 1. Identify what is given to you. Speed = mi/hr Distance = 1.23 miles

Rearranging Equations 2. Answer the question: For what are you solving? We are solving for time We are solving for time 3. Set up the known equation using variables. Speed = distance s = d Speed = distance s = d time t time t

Rearranging Equations 4. Rearrange the equation to solve for chosen variable. s = d (t)s = d(t) t s = d s = d (t)s = d(t) t s = d t t t t t s = d t = d t s = d t = d (s) (s) s (s) (s) s

Rearranging Equations 5. Plug in the proper values and units. Solve. t = d t = 1.23 miles t = d t = 1.23 miles s mi/hr s mi/hr t = hours t = hours

Rearranging Equations Example: A car is traveling at 5 mi/hr and speeds up to 65 mi/hr. How much time does it take if the car is acceleration at a rate of 6 mi/hr 2. Example: A car is traveling at 5 mi/hr and speeds up to 65 mi/hr. How much time does it take if the car is acceleration at a rate of 6 mi/hr 2. Acceleration = (final velocity - initial velocity) Acceleration = (final velocity - initial velocity) time time

Significant Figures What are they and why do we use them? What are they and why do we use them? The number of digits in a measurement that is certain, plus one additional rounded off number that is uncertain The number of digits in a measurement that is certain, plus one additional rounded off number that is uncertain Significant figures indicate the reliability of measured data Significant figures indicate the reliability of measured data

Significant Figures Zeros in Numbers Zeros in Numbers 1.All nonzero integers are significant 2.All zeros to the LEFT of the first nonzero digit are not significant ex: ex: sig figs, 3 leading zeros not sig figs

Significant Figures 3.All zeros between nonzero digits are significant. Ex: , 6 sig figs 4.All zeros at the end of a number that has a decimal point are significant. Ex: 100 has 1 sig fig, 2 zeros but NO decimal has 5 sig figs, 4 zeros WITH decimal has 5 sig figs, 4 zeros WITH decimal

Significant Figures Identify the number of significant figures in the following examples: Identify the number of significant figures in the following examples: g__________ g__________ g__________ g__________

Significant Figures **5.Zeros at the end of a whole number that has no decimal point cause confusion because they may-or may not-be significant. The best way to prevent this type of confusion is to write the number in scientific notation. write the number in scientific notation.

Scientific Notation Scientific notation is used to write numbers that are very large or very small in an easier way Scientific notation is used to write numbers that are very large or very small in an easier way Diameter of an atom: Diameter of an atom: m m Diameter of atomic nucleus: Diameter of atomic nucleus: m m Distance from the Earth to the Sun Distance from the Earth to the Sun 150,000,000 km 150,000,000 km

Scientific Notation Scientific notation expresses a number multiplied by a power of 10. Scientific notation expresses a number multiplied by a power of 10. n x 10 p n x 10 p n is a number between 1 and 10 n is a number between 1 and 10 p is a power of 10 p is a power of 10Example: 300 is written as 3 x 10 2

Scientific Notation HOW TO write numbers in scientific notation: HOW TO write numbers in scientific notation: Move the decimal point to the left or right so that only one nonzero digit is to the left of the decimal point. Move the decimal point to the left or right so that only one nonzero digit is to the left of the decimal point. Multiply that number by 10 raised to a power equal to the number of places the decimal place was moved Multiply that number by 10 raised to a power equal to the number of places the decimal place was moved If you move the decimal to the left, p is positive If you move the decimal to the left, p is positive If you move the decimal to the right, p is negative If you move the decimal to the right, p is negative x x x x 10 -3

Scientific Notation = = = = 3. 1,456,983= 3. 1,456,983=

Scientific Notation ,456, ,456,983 = x 10 2 = 4.56 x = x 10 6

Scientific Notation m= 1.0 x m= 1.0 x = = 3. 1,456,983= 3. 1,456,983=

Uncertainty in Measurement Precision vs. Accuracy Precision vs. Accuracy Precision: Precision: When several measurements are taken that have close agreement When several measurements are taken that have close agreement Accuracy: Accuracy: How closely the measurements agree with the true value How closely the measurements agree with the true value

Uncertainty in Measurement How do we measure to one place of uncertainty? How do we measure to one place of uncertainty? What is the measurements at each arrow? What is the measurements at each arrow?

Uncertainty in Measurement How do we measure to one place of uncertainty? How do we measure to one place of uncertainty? What is the measurements at What is the measurements at each arrow? each arrow?

Uncertainty in Measurement Exact Numbers Exact Numbers Have no uncertain digits since there is no approximation involved Have no uncertain digits since there is no approximation involved 1 m = 1000mm 1 m = 1000mm Counted items or simple fractions (2/3 or ¼) Counted items or simple fractions (2/3 or ¼)

Calculations in Significant Figures Rounding Off Rounding Off Round up if >5 Round up if >5 Addition or Subtraction Addition or Subtraction When measured quantities are either added or subtracted, the answer retains the same number of digits to the right of the decimal as were present in the least precise value (the number containing the fewest number of digits to the right of the decimal). When measured quantities are either added or subtracted, the answer retains the same number of digits to the right of the decimal as were present in the least precise value (the number containing the fewest number of digits to the right of the decimal).

Calculations of Significant Figures Multiplication and Division Multiplication and Division When measured quantities are either multiplied or divided, the answer must contain the same number of significant figures as were present in the measurement with the fewest number of significant figures. When measured quantities are either multiplied or divided, the answer must contain the same number of significant figures as were present in the measurement with the fewest number of significant figures.

Example Calculations Addition Addition 46.1 g g g g g g g Answer with significant figures: g

Example Addition/Subtraction =______________ =______________ – 6.0 – =______________

Example Calculations Multiplication Multiplication 80.2cm3 s.f. 80.2cm3 s.f cm4 s.f cm4 s.f. X cm2 s.f cm Answer with significant figures: 2.1cm 3

Examples of Mult/Div x 1.2=______________ x 1.1 x 3.125=______________ / =______________

Converting Units When converting units, follow the steps below: When converting units, follow the steps below: Identify the starting unit Identify the starting unit Identify the final unit Identify the final unit Identify the conversion factor (ask yourself “How much of the starting unit fit in the final unit?”) Identify the conversion factor (ask yourself “How much of the starting unit fit in the final unit?”) Multiply using properly labeled units Multiply using properly labeled units Cancel units Cancel units Move decimal right or left accordingly Move decimal right or left accordingly

Converting Units Example: Example: Convert 125 grams into kilograms Convert 125 grams into kilograms Start unit:grams Start unit:grams Final unit:kilograms Final unit:kilograms Conversion factor Conversion factor There are 1000 grams in 1 kg There are 1000 grams in 1 kg Conversion factor: final unit/start unit Conversion factor: final unit/start unit 1kg/1000g 1kg/1000g Multiply Multiply 125 g X (1kg/1000g) = g 125 g X (1kg/1000g) = g (cancel out units and move decimal point) (cancel out units and move decimal point)

Converting Units Practice Problems Practice Problems kg =_______________g kg =_______________g cm =_______________m cm =_______________m 1.6 MW =_______________W 1.6 MW =_______________W 3 X s=_______________s 3 X s=_______________s 10 X 10 3 m=_______________m 10 X 10 3 m=_______________m