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MEASUREMENTS AND CALCULATIONS Chapter 2. 2.1 Scientific Method  A scientific method is a way to logically approach a problem by making observations,

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Presentation on theme: "MEASUREMENTS AND CALCULATIONS Chapter 2. 2.1 Scientific Method  A scientific method is a way to logically approach a problem by making observations,"— Presentation transcript:

1 MEASUREMENTS AND CALCULATIONS Chapter 2

2 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

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

4 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

5 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

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

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

8 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

9 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

10 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

11 2.2 Units of Measurement  Scientific Notation: a method to make writing and handling very large or very small numbers easy  = 3.4 x 10 7  = 7.6 x 10 -7

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

13 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

14 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

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

16 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

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

18 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 g 1kg = 2.5 x x mg 1x10 3 g 1x1x1x x 10 2 kg = 2.5 x kg 1 x 10 3

19 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)

20 Accuracy vs Precision

21 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

22 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 = % 4.08

23 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 g/cm 3 = 1.88 %

24 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!

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

26 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

27 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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