Measurements and Calculations Chapter 2 Notes Measurements and Calculations

The Scientific Method The scientific method is a logical approach to solving problems by observing and collecting data, formulating and testing hypotheses, then developing theories that are supported by data. The scientific method is broken into five steps

Five Steps of Scientific Method Observing and collecting data Observing uses the senses to obtain information Qualitative observation: non-numerical information Quantitative observation: numerical information Formulating hypotheses Hypotheses are testable statements Usually in the form of If - Then statements

Testing hypotheses Theorizing Design and implement an experiment that will test the If – Then statement Theorizing Model: explanation of how phenomena occur and how data or events are related Theory: broad generalization that explains a body of facts

Publish results This is done so that others can duplicate experiment to verify the results

SI Units of Measurements Quantity: something that has magnitude, size, or amount Weight: measure of the gravitational pull on matter Kilogram (kg) Mole: measure of the amount of a substance Length: measure of distance Meter (m) Time: system for measuring intervals Seconds (s)

Derived SI Units Volume: amount of space occupied by an object. Length X Width X Height Cm3 or mL Density: mass per unit of volume Grams per cm3 or mL

Conversion Factors Conversion factors are a ratio derived from the equality between two different units that can be used to convert from one unit to the other

Deriving Conversion Factors Set up an equality Write two possible combinations Pick combination that has the unit needed on top and the unit to cancel on bottom

Using Scientific Measurement Accuracy: closeness of a measurement to the accepted value Precision: closeness of a set of measurements made in the same way Percent error = accepted value – experimental value X 100% accepted value

Significant Figures All known digits plus one estimated digit Atlantic / Pacific rule If a decimal is ABSENT, start counting from the ATLANTIC (right) side with the first non-zero number and count all digits to the left If a decimal is PRESENT, start counting from the PACIFIC (left) side with the first non-zero number and count all digits to the right

Scientific Notation In scientific notation, numbers are written in the form of M X 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number Big numbers have positive exponents Small numbers have negative exponents

Examples of Scientific Notation 65,000 km = 6.5 x 104 km 0.00012 mm = 1.2 x 10-4 mm 560,000 km = 5.6 x 105 km 33,400 kg = 3.34 x 104 kg 0.0004120 m = 4.120 x 10-4 m

Mathematical Operations with Significant Figures Addition and Subtraction The answer can have no more places past the decimal than the least of the terms being added or subtracted Multiplication and Division The answer can have no more significant figures than the least of the terms being multiplied or divided

Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value y / x = k k is a proportionality constant y = k x Graphing the data gives you a straight line

Inverse Proportions Two quantities are inversely proportional to each other if their product is constant xy = k Graphing the data produces a curve called a hyperbola