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MEASUREMENTS AND CALCULATIONS Chapter 2

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2.1 Scientific Method A scientific method is a way to logically approach a problem by making observations, testing a hypothesis, gathering and analyzing data, and forming conclusions. There are many scientific methods

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observations Using your senses to gather information Qualitative: descriptive Quantitative: numerical Most science experiments utilize quantitative observations

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hypothesis A hypothesis is a testable statement Often written as “if-then” statements (Ex: if marigold flowers are watered with miracle grow, then their plant growth will be enhanced) Tested through experiments to determine if accepted or rejected

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data analysis This crucial step is used to determine if the hypothesis is accepted or rejected through statistical analysis (t-test, ANOVA, Mann-Whitney, etc) Both outcomes can be an important contribution to science since they can be used as a stepping stone for future experiments Graphs and charts that depict the results are often incorporated into a lab report

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conclusions Based on the results of the experiment, conclusions can be made Results can then be published and shared with colleagues

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models A visual, verbal, conceptual, or mathematical explanation for something abstract or difficult to explain Ex: model of an atom

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theory DON’T USE THE WORD THEORY INCORRECTLY!!!! A theory is a broad generalization that explains a body of facts or phenomenon and is supported by experimental evidence Theories can change as new advancements in science take place Ex: the Big Bang Theory

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law A generalized rule that is used to explain a body of observations in the form of a verbal or mathematical statement. Imply a cause and effect between the observed elements and must always apply under the same conditions Ex: Law of Gravity

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Science is…… Testable- Predictions are tested through experiments and the results either support or do not support the hypothesis or theory. NOTHING IS PROVEN IN SCIENCE! Tentative- Science CHANGES! All scientific explanations are the best we can do now. Through investigation and technological advancements, we understand more all the time

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2.2 Units of Measurement Scientific Notation: a method to make writing and handling very large or very small numbers easy 34000000 = 3.4 x 10 7 .000000076 = 7.6 x 10 -7

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Operations with Scientific Notation Exponents must match with addition and subtraction Exponents are added for multiplication Exponents are subtracted for division

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measurements Chemistry is qualitative and quantitative Measurements are used to represents quantities A quantity has magnitude, size or amount Ex: a liter is a unit of measurement while volume is a quantity

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SI Measurements SI units are used in science (7 base units) Mass-kilogram (kg) Length- meter (m) Temperature-Kelvin (K) Amount of a substance- mole (mol) All SI units can be modified by using prefixes Ex: kilo = 1000 = 1 x 10 3 1 kilometer = 1000 meters = 1 x 10 3 meters

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SI Prefixes Mega M 10 6 Kilo K 10 3 Base units (m, L, g) Centi c 10 -2 Milli m 10 -3 Micro µ 10 -6 Nano n 10 -9 Pico p 10 -12

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Derived units Formed by combinations of SI units Ex: meters/second Density = mass/volume Density is important for identifying substances Given in kg/m 3 Density of water = 1 kg/m 3

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Conversions Conversion factors express an equality between two different units Quantity given x conversion factor = quantity sought Remember: X = 1 1

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Factor Label Method Based on the number of equalities and multiplication and division in series Ex: convert 250,000 mg to kg 2.5 x 10 5 mg 1 x 10 -3 g 1kg = 2.5 x 10 5-3 x 1 1 1 mg 1x10 3 g 1x1x1x10 3 2.5 x 10 2 kg = 2.5 x 10 -1 kg 1 x 10 3

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2.3 Using Scientific Measurements Accuracy vs Precision Accuracy is the closeness of measurements to the true value or correct answer Precision refers to the closeness of a set of measurements to one another. (precision is more related to the way in which the measurements are made)

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Accuracy vs Precision

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Calculating Percent Error Percent error = value accepted – value experimental X 100 value accepted percent error will have a positive value if the accepted value is greater than the experimental value Will be negative if the accepted value is less than the experimental value

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Example #1 What is the percent error if the length of a wire is 4.25 cm if the correct value should be 4.08 cm? % error = v a – v e X 100 v a % error = 4.08 – 4.25 X 100 = - 4.2 % 4.08

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Example #2 The actual density of a material is 7.44 g/cm 3. A student measures density to be 7.30 g/cm 3. What is the percent error? % error = 7.44 g/cm 3 – 7.30 g/cm 3 x 100 7.44 g/cm 3 = 1.88 %

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Significant Figures Sig figs consist of all the digits known with certainty plus one final digit which is somewhat uncertain or estimated If the number has no zeroes, all digits are significant Follow the rules in the table!

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Rules for Determining Sig Figs 1. Always count nonzero digits Example: 21 has two significant figures, while 8.926 has four 2. Never count leading zeros Example: 021 and 0.021 both have two significant figures 3. Always count zeros which fall somewhere between two nonzero digits Example: 20.8 has three significant figures, while 0.00104009 has six 4. Count trailing zeros if and only if the number contains a decimal point Example: 210 and 210000 both have two significant figures, while 210. has three and 210.00 has five 5. For numbers expressed in scientific notation, ignore the exponent and apply Rules 1-4 to the number Example: -4.2010 x 10 28 has five significant figures

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Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value Example: doubling the mass of a sample doubles the volume

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Inverse Proportions Two quantities are inversely proportional if their product is constant Example: doubling the speed cuts the required time in half

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