Law vs. Theory, Scientific Notation, Significant Digits - Recognition and Operation rules Metric System Introduction Dimensional Analysis Cartoon courtesy of NearingZero.net Observations Quantitative Data ex: 3.0 mL 4.2 inches Qualitative Data ex: blue water smooth zinc What is the difference? Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Precision has another meaning also. Neither Precise but not Precise AND accurate nor accurate accurate precise Reading the Thermometer in Terms of Precision and Accuracy Determine the readings as shown below on Celsius thermometers: Student A 44.0 oC Not Accurate, Precise Student B 35 oC Not Precise , Accurate Student C 54 oC Not Accurate Not Precise The zero shows uncertainty in the measurement. 3 5 . _ C _ _ 0 Reading the Thermometer Determine the readings as shown below on Celsius thermometers: 8 7 4 _ _ . _ C _ _ 0 3 5 . _ C Why Is there Uncertainty in Measurements? Measurements are performed with instruments No instrument can read to an infinite number of decimal places A measurement always has some degree of uncertainty. Which of these balances has the greatest uncertainty in measurement? The least uncertainty? Certain and Uncertain Digits are referred to as Significant Digits! What are significant digits? All known digits (certain) and one estimated digit (uncertain)or (uncertain) place value. For electronic devices – record all digits. The estimation is already present. For non-electronic devices, an estimated place value must be obtained from reading the instrument. The Thermometer and Significant Digits. o Determine the temperature by reading the scale on the thermometer at eye level. o Read the temperature by using all certain digits and one uncertain digit. o Certain digits are determined from the calibration marks on the thermometer. o The uncertain digit (the last digit of the reading) is estimated. o On most thermometers encountered in a general chemistry lab, the tenths place is the uncertain digit. Measuring Volume and Significant Digits Determine the volume contained in a graduated cylinder by reading the bottom of the meniscus at eye level. Read the volume using all certain digits and one uncertain digit. Together these are called significant digits. Certain digits are determined from the calibration marks on the cylinder. The uncertain digit (the last digit of the reading) is estimated. Use the graduations to find all certain digits There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are… 52 mL. Estimate the uncertain digit and take a reading The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is 0.8 mL . The volume in the graduated cylinder is 52.8 mL. 10 mL Graduate What is the volume of liquid in the graduate? 6 6 2 _ . _ _ mL 100mL graduated cylinder What is the volume of liquid in the graduated cylinder? _ _ 7 5 2 . _ mL Self Test Examine the meniscus below and determine the volume of liquid contained in the graduated cylinder. The cylinder contains: 7 6 . 0 mL _ _ _ 25mL graduated cylinder What is the volume of liquid in the graduate? 11 .5 0 _ _ _ mL Why are significant digits needed? 2nd meaning of precision. Significant digits express the sensitivity (divisions or calibration) of the measuring device. Balance Rules In order to protect the balances and ensure accurate results, a number of rules should be followed: Always check that the balance is level and zeroed (tared) before using it. Never weigh directly on the balance pan. Always use a piece of weighing paper or a weigh boat to protect it. Do not weigh hot or cold objects. Clean up any spills around the balance immediately. Remember, record all digits for electronic balances. Scientific Notation In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg Scientific Notation: A method of representing very large or very small numbers in the form: M x 10n M is a number between 1 and 9 1 M 10 n is an integer 2 500 000 000 . 9 8 7 6 5 4 3 2 1 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n 2.5 x 10 9 The exponent is the number of places we moved the decimal. 0.0000579 1 2 3 4 5 Step #1: Locate the decimal point. Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point 5.79 x 10 -5 The exponent is negative because the number we started with was less than 1. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION Learn to use your calculator! Remember: NO Locate the GRAPHING CALCULATORS!!!! correct function Practice: ADD problems 4 x 10 6 + 3 x 10 6 Use your calculator for practice. 7 x 106 4 x 106 - 3 x 10 6 1 x 106 A Problem for you… 2.37 x 10 -4 x 3.48 x 10-4 8.30676 x 10-8 Rounding Rule. 5 or greater, round up Less than 5, round down Rules for Counting (Recognizing) Significant Digits for measurements Use Pacific/Atlantic Rules Pacific = Decimal Present Atlantic = Decimal Absent RULE: Find the first nonzero number to the right or left of the arrow and every digit thereafter is significant. 3456 has 4 sig digs. .0486 has 3 “ “ 9.000 has 4 sig dig. Underline the estimated digit. Rules for Significant Digits in Mathematical Operations Multiplication and Division: # sig digs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76 13 (2 sig figs) Sig Dig Practice Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 m2 23 m2 100.0 g 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft 1.030 g 2.87 mL .358885 g/mL .359 g/mL Rules for Significant Digits in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. Least places to the right of the decimal. 6.8 + 11.934 = 18.734 18.7 (3 sig figs) Rules for Significant Digits in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. 6.8 + 11.934 = 18.734 18.7 (3 sig figs) Sig Dig Practice Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL Nature of a Measurement Measurement – quantitative (quantity) observation consisting of 2 parts Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63 x 10-34 Joule x seconds The Fundamental SI Units (le Système International, SI) Pg 34 Text Physical Quantity Name Abbreviation Mass kilogram kg Length meter m Time second s Temperature Kelvin K Electric Current Ampere A Amount of Substance mole mol Luminous Intensity candela cd SI Units Derived Quantity-Unit Pg 36 A combination of Quantities and SI base units Example: Density = m/v Area = L x W units 2 (squared) Volume – L x W x H units 3 (cubed) Volumetric Cube 1 ml = 1 cc = 1cm3 10 cm x 10cm x 10cm 1000cm3 = 1L Density = mass /volume What type of proportion is density? Example Calculations Page 40: Direct Proportion Direct Proportion Graph K (constant) = B / A Inverse Proportion Inverse (Indirect) Proportion Graph K (constant) = x y SI Prefixes common to Chemistry Pg 35 Prefix Unit Abbr. Exponent What does it mean? Mega M 10 6 One million times greater Kilo k 103 One thousand times greater Hecto h 10 2 One hundred times greater Deka da 10-1 Ten times smaller Centi c 10-2 One Hundred times smaller Milli m 10-3 One thousand times smaller Micro 10-6 One million times smaller Dimensional Analysis Dim. Analysis is a skill used to convert units. Dim. Analysis will use conversion factors = fractions equal to 1 of the same. Example of conversion factors 12 eggs or 1dozen 1 dozen 12 eggs Conversion question: How many eggs are in 12.5 dozen? Solution: ? = given ? eggs = 12.5 dozen x 12 eggs 1 dozen Dimensional analysis with metric Practice writing conversion factors. Write two conversion factors for each of the following: m and cm m and km m and mm Answers m and cm m and km m and mm 1m 1 km 1 m___ 100 cm 1000 m 1000 mm or or or 100 cm 1000 m 1000 mm 1m 1 km 1m Practice How many kg are in 10.5 g? Solution ? kg = 10.5 g x 1 kg__ = .0105 kg 1000 g Percent Error Percent Error = Actual – Theoretical x 100 Theoretical OR = Experimental – Accepted x 100 Accepted Types of Error Random Error (Indeterminate Error) - measurement has an equal probability of being high or low. Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration. Steps in the Scientific Method 1. Observations - quantitative - qualitative - what is the difference? 2. Formulating hypotheses - possible explanation for the observation 3. Performing experiments - gathering new information to decide whether the hypothesis is valid Outcomes Over the Long-Term Theory (Model) - A set of tested hypotheses that give an overall explanation of some natural phenomenon. Natural Law - The same observation applies to many different systems - Example - Law of Conservation of Mass Law vs. Theory A law summarizes what happens A theory (model) is an attempt to explain why it happens.
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