Measurements and calculations

Measurements and calculations Chapter 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

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

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

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

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

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

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

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

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

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 107 • .000000076 = 7.6 x 10-7

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

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

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 103 • 1 kilometer = 1000 meters = 1 x 103 meters

SI Prefixes • Mega M 106 • Kilo K 103 • 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

Derived units • Formed by combinations of SI units • Ex: meters/second • Density = mass/volume • Density is important for identifying substances • Given in kg/m3 • Density of water = 1 kg/m3

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

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 105mg1 x 10-3 g1kg = 2.5 x 105-3 x 1 1 1 mg 1x103g 1x1x1x103 2.5 x 102 kg = 2.5 x 10-1kg 1 x 103

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)

Accuracy vs Precision

Calculating Percent Error • Percent error = valueaccepted – valueexperimental X 100 • valueaccepted • 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

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 = va – veX 100 va % error = 4.08 – 4.25 X 100 = - 4.2 % 4.08

Example #2 • The actual density of a material is 7.44 g/cm3. A student measures density to be 7.30 g/cm3. What is the percent error? • % error = 7.44 g/cm3 – 7.30 g/cm3x 100 7.44 g/cm3 = 1.88 %

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!

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 1028 has five significant figures

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

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

Measurements and calculations