# Measurements and calculations

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Measurements and calculations
Chapter 2

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 = 3.4 x 107 = 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 Micro µ Nano n Pico p

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 105mg x 10-3 g 1kg = 2.5 x x 1 mg x103g 1x1x1x103 2.5 x 102 kg = 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 cm if the correct value should be 4.08 cm? % error = va – ve X 100 va % error = 4.08 – X 100 = % 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/cm3 x 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 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 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 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