1. PACKET #1: MATH & LAB SKILLS Reference Table: C, D, S, & T www.regentsprep.org

2. METRIC SYSTEM & CONVERSIONS (TABLE C & D) SI Unit of Measurement: 1960 scientists use a standard set of units called Systeme Internationale d’Unites or SI. Based on 7 base units but for purposes of the curriculum we will focus on the first 5. SI Unit of Measurement: 1960 scientists use a standard set of units called Systeme Internationale d’Unites or SI. Based on 7 base units but for purposes of the curriculum we will focus on the first 5. Conversion Factor: Convert a measurement from one unit to another. Simple ratio that relates two units that express a measurement of the same quantity. Do example and remember to state that the one that you want to find must always be on top. Conversion Factor: Convert a measurement from one unit to another. Simple ratio that relates two units that express a measurement of the same quantity. Do example and remember to state that the one that you want to find must always be on top.

5. LET’S PRACTICE!! a. 0.765 g to kilograms b. 17.3m to centimeters c. 1.34 g to milligrams d. 2.56m to kilometers e. 34.2 mg to grams f. 567 dm to meters g. 23745 kg to milligrams h. 5.13 m to millimeters

6. TEMPERATURE Kinetic Energy determines temperature. Kinetic Energy determines temperature. SI unit for temperature is Kelvin (Table T) SI unit for temperature is Kelvin (Table T) 0 Kelvin is called Absolute Zero 0 Kelvin is called Absolute Zero At Absolute Zero, there is no movement of particles, and therefore no kinetic energy. At Absolute Zero, there is no movement of particles, and therefore no kinetic energy.

7. Temperature Conversions Conversion between Kelvin & Celsius K = °C + 273 (Table T) Conversion between Fahrenheit & Celsius T °F = 1.80(T °C ) + 32

9. SIGNIFICANT FIGURES Scientists always report values using significant figures. It consists of all the digits known with certainty as well as one estimated or uncertain digit. Significant does not mean certain. The last digit or significant figure reported is uncertain or estimated. If you say mass is 10 g, can be anywhere between 8 and 12 or between 9.999 and 10.001. But if you say 10.0 – more precise to the nearest.1, can only be from 9.95 and 10.05 g. Scientists always report values using significant figures. It consists of all the digits known with certainty as well as one estimated or uncertain digit. Significant does not mean certain. The last digit or significant figure reported is uncertain or estimated. If you say mass is 10 g, can be anywhere between 8 and 12 or between 9.999 and 10.001. But if you say 10.0 – more precise to the nearest.1, can only be from 9.95 and 10.05 g.

10. SIGNIFICANT FIGURES Scientists always report values using significant figures. It consists of all the digits known with certainty as well as one estimated or uncertain digit. Significant does not mean certain. The last digit or significant figure reported is uncertain or estimated.

11. Rules for Calculating Significant Figures 1. All non-zero digits are significant. 788 = ____ SF ; 5 = ____SF ; 89319 = _____SF 2. Zeros between nonzero digits in a number are significant 1005 = _____SF ; 1.03 = ____SF 3. Zeros at the end of a # are significant if the # contains a decimal 0.0200 = _____SF ; 3.0= _____SF ; 405000 = ____SF

12. Rules for Calculating Significant Figures 4. Zeros at the beginning of a # are never significant. They merely indicate decimal placement. 0.02 = ____ SF ; 0.0026 = _____ SF 5. Exact numbers do NOT play a role in determining the # of SF in a calculated result.

13. 1. Determine if a decimal point is PRESENT or ABSENT in the question. 1. Determine if a decimal point is PRESENT or ABSENT in the question. 2. The letters “A” and “P” correspond to the Atlantic and Pacific Oceans. 2. The letters “A” and “P” correspond to the Atlantic and Pacific Oceans. 3. Start drawing your imaginary arrow from the appropriate “coast”. 3. Start drawing your imaginary arrow from the appropriate “coast”. 4. Once the arrow hits a nonzero digit, it and all of the digits after it are significant! 4. Once the arrow hits a nonzero digit, it and all of the digits after it are significant! REMEMBER ATLANTIC PACIFIC TRICK FOR A HELPFUL & EASY WAY OF DETERMINING THE # OF SIG. FIGS REMEMBER ATLANTIC PACIFIC TRICK FOR A HELPFUL & EASY WAY OF DETERMINING THE # OF SIG. FIGS

14. Pacific Atlantic

15. Determine the number of Significant Figures of the following:  4.004cm = _______ SD  6.023 x 10 23 g = ______SD  5000 m= ______ SD  3.549 kg = _____ SD  2.3 x 10 4 dm = _____ SD  0.00134 m 3 = _____ SD

16. Significant Figures in Calculations Rule for Multiplication and Division  The result contains the same # of SF’s as the measurement with the fewest # of SF’s  When the result contains more than the correct # of SF’s, it must be rounded to the correct #. Ex: (6.221cm) (5.2cm) = _____________ Ex: (6.221cm) (5.2cm) = _____________ Ex: 56/7.00 = ____________ Ex: 56/7.00 = ____________

17. Significant Figures in Calculations Rule for Addition and Subtraction  The result has the same # of decimal places as the measurement with the fewest decimal places.  Ex: 20.42 1.322 1.322 + 83.1_____ + 83.1_____

18. SCIENTIFIC NOTATION  Scientists often find it necessary to work with very large and very small numbers.  To simplify the handling of these numbers, it is common to convert them into a simpler form called the exponential form.

19. Summary of Rules to Follow when Writing Numbers in the Exponential Form 1) The exponent represents the # of places the decimal has been moved. 2) If the #’s numeric value is greater than one – positive exponent 3) If the #’s numeric value is less than one — negative exponent 4) Always shift the decimal point in a manner that gives you one sig. fig. to the left of the decimal point. 5) Always show all sig. digits.

20. Scientific Notation - Practice Write the following in exponential form: 1) 0.000341 2) 240,000 3) 0.60 4) 4.0 5) 820,000,000,000 6) 0.0000582

21. Scientific Notation- Converting from Exponential Form to Decimal Form  To convert a # from the exponential form into the decimal form, reverse the process performed when writing the exponential #  That is, move the decimal right or left the # of places represented by the exponent  It may be necessary to add “zeros” until the proper # of places has been counted  If positive exponent =move decimal right  If negative exponent =move decimal left

22. Practice Examples  Ex 1) Write 3 x 10 4 in decimal form  Ex 2) Write 2.1 x 10 -3 in decimal form  Ex 3) Write 8.2 x 10 -5 in decimal form

23. Multiplying Exponents Multiply the # portion Multiply the # portion Add the exponents Add the exponents Shift the decimal/exponent accordingly (only if necessary) Shift the decimal/exponent accordingly (only if necessary) Ex 1) (6.0 x 10 4 ) (8 x 10 7 ) Ex 2) (2.4 x 10 -11 ) (3.00 x 10 22 )

24. Dividing Exponents 1. Divide # portions 2. Subtract exponents 3. Shift decimal/exponent accordingly Ex 1) 2.7 x 10 10 Ex 2) 3.6 x 10 5 3.0 x 10 4 1.2 x 10 -18 3.0 x 10 4 1.2 x 10 -18

25. Addition/Subtraction of Exponents 1. To add or subtract exponents without a calculator, you must be sure that the #’s have the same exponent. If they do, skip to step 3. If they don’t proceed to step 2. 2. When the #’s you are adding/subtracting do not have the same exponent, you must shift/change the decimal/exponent accordingly. 3. Add/subtract # portion. (Exponents remain the same.) Ex 1) (2.0 x10 3 ) + (3.0 x 10 2 ) Ex 2) (6.5 x 10 6 ) - (2.6 x 10 4 )

26. Density (Table T)  The amount of mass in a unit volume of a substance Formula  Units for Density: g/cm 3 (solids) g/mL (liquids) g/mL (liquids)  Since every substance has a unique density, density can be used as a way of identifying a particular substance  Ex: density of water: ______________

27. REMEMBER!!!  Units for Volume: l x w x h – cm 3  Know that: 1 cm 3 = 1mL

28. Calculating Density 1. Calculate the density of mercury if 1.00 x 10 2 g occupies a volume of 7.36 cm 3. 2. Calculate the volume of 65.0g of the liquid methanol if its density is 0.791 g/mL. 3. What is the mass in grams of a cube of gold (density = 19.32 g/cm 3) if the length of the cube is 2.00 cm? 4. A student needs 15.0g of ethanol for an experiment. If the density of ethanol is 0.789 g/mL, how many milliliters of ethanol are needed?

29. Percent Error (Table T) Percent error: Compares what a student or researcher calculated, found, or measured in the lab (called the measured value) with what the accepted value is—(i.e. in a perfect world with no flaws, the value that would be obtained). Formula Practice Problem: If you measure the mass of oxygen in a sample to be 25.0g and the theoretical value is 30.0g, what is your % error?

30. GRAPHING (any questions?) The Independent Variable is always plotted on the horizontal or x-axis The Independent Variable is always plotted on the horizontal or x-axis The Dependent Variable is always plotted on the vertical or y-axis The Dependent Variable is always plotted on the vertical or y-axis  Direct Relationship – Both variables either increase or both decrease. An example of this is Charles’ Law which states that as temperature increases volume increases  Inverse Relationship – One variable increases while the other variable decreases. An example of this is Boyle’s Law which states as pressure increases volume decreases

31. REGENT’S REVIEW QUESTIONS 1. What is the product of (2.324 cm x 1.11 cm) expressed to the correct number of significant figures? A) 2.5796 cm2 B) 2.57964 cm2 C) 2.58 cm2 D) 2.5780 cm2

32. 2) If the observed value for a measurement is 0.80g and the accepted value is 0.70g, what is the percent error? A)0.14% B) 0.17% C) 14% D) 17% 3) Which measurement contains a total of three significant figures? A) 0.01000 g B) 0.0100 g C) 0.010 g D) 0.01 g

33. 4) Which milligram quantity contains a total of four significant figures? A) 3,100 mg B) 30,001 mg C) 0.3010 mg D) 3,010 mg 5) What is the sum of 0.0421 g + 5.263 g + 2.13 g to the correct number of significant digits? A) 7.435 g B) 7 g C) 7.4 g D) 7.44 g

34. 6) What is the number 2.1 x 10 3 expressed in conventional form with the proper number of significant digits? A)2,100 B) 21,000 C) 0.0021 D) 2,100 7) What is the number 8.90 x 10 -4 expressed in conventional form with the correct number of significant digits? A)0.00089 B)B) 89,000 C)C) 0.000890 D)D) 89,000

35. 8) In the laboratory, a student determined the percent by mass of water in a hydrated salt to be 17.3 percent. What is the percent error if the accepted value is 14.8 percent? A) 2.50% B) 27.1% C) 16.9% D) 5.92%