PACKET #1: MATH & LAB SKILLS Reference Table: C, D, S, & T

METRIC SYSTEM & CONVERSIONS (TABLE C & D) SI Unit of Measurement: scientists use a standard set of units called SI units (International System). 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.

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

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

Temperature Conversions Conversion between Kelvin & Celsius (Table T) K = °C + 273

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.

Rules for Calculating Significant Figures 1. All non-zero digits are significant (23,456) 2. Zeros between nonzero digits in a number are significant (1001) 3. Zeros at the end of a # are significant if the # contains a decimal (1.2000) 4. Zeros at the beginning of a # are never significant. They merely indicate decimal placement (0.0031)

REMEMBER ATLANTIC PACIFIC TRICK FOR A HELPFUL & EASY WAY OF DETERMINING THE # OF SIG. FIGS  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. 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!

Pacific Atlantic

Pacific Atlantic

Pacific Atlantic

Pacific Atlantic

Pacific Atlantic

Pacific Atlantic

Determine the number of Significant Figures of the following: 4.004cm = _______ SD 6.023 g = ______SD 5000 m= ______ SD 3.549 kg = _____ SD 2.3 dm = _____ SD 0.00134 m3 = _____ SD

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: 56/7.00 = ____________

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 + 83.1_____

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.

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

Scientific Notation - Practice Write the following in exponential form: 0.000341 240,000 0.60 4.0 820,000,000,000 0.0000582

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

Practice Examples Ex 1) Write 3 x 104 in decimal form

Density (Table T) Units for Density: g/cm3 (solids) or g/mL (liquids) The amount of mass in a unit volume of a substance. Specidifc to a substance in a given phase of matter. Units for Density: g/cm3 (solids) or g/mL (liquids)

REMEMBER!!! The density of water (liquid) is approximately 1 g/ml. Anything with a greater density will sink, anything with a lighter density will float to the top. Volume Calculation: l x w x h = cm3 Know that: 1 cm3 = 1mL Table S in your Reference Table has accepted values of density for some given elements on the Periodic Table.

Calculating Density Calculate the density of mercury if 1.00 x 102 g occupies a volume of 7.36 cm3. Calculate the volume of 65.0g of the liquid methanol if its density is 0.791 g/mL. What is the mass in grams of a cube of gold if the length of the cube is 2.00 cm? 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?

Percent Error (Table T) Percent error: Compares what a student or researcher calculated, found, or measured in the lab with what the accepted value is (Table S = accepted values) Practice Problem: A student determines that the electronegativity of the element Fluorine is 3.6, what is the % error?

GRAPHING (any questions?) The Independent Variable is always plotted on the horizontal or x-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

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

2)If the observed value for a measurement is 0 2)If the observed value for a measurement is 0.80g and the accepted value is 0.70g, what is the percent error? 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

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

6) What is the number 2.1 x 103 expressed in conventional form with the proper number of significant digits? 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? 0.00089 89,000 C) 0.000890 D) 89,000.

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%