Dimensional Analysis & Unit Conversions CHEMISTRY I Scientific Inquiry Measurement Dimensional Analysis & Unit Conversions Significant Digits

These Notes Cover: Scientific Inquiry Measurement Law vs. Theory Scientific Methods & Experimental Design Different Branches of Science Measurement Accuracy vs. Precision Units of Measure & Unit Conversions Estimated Digit & Significant Digits Scientific Notation

Scientific Inquiry – Law vs. Theory Scientific laws STATE what happens Repeatable Observable Generally Unchanging If there is an equation – it’s probably a law Scientific Theories EXPLAIN why or how a law works Based on many verified experiments Broad use of many hypotheses summarized into one theory Always TESTABLE, but never proven More likely to change than a law Changed to a “better” explanation Updated to include new test results Sometimes completely refuted and replaced with a new theory

Scientific Inquiry – Scientific Methods & Experimental Design Scientific Methods are systematic approaches to answering questions or solving problems Uses Observation and Guess and Check to rule out “wrong answers” and find “right answers” Generally, tests one variable at a time Draws conclusions based on observations (EVIDENCE BASED CONCLUSIONS) Science is done in Community Share results Share experimental procedures Debate different theories

Scientific Inquiry – Scientific Methods & Experimental Design Independent Variable The “tested” variable Manipulated by Experimenter Graphed on the Horizontal Axis Dependent Variable The responding variable Is OBSERVED by the Experimenter Graphed on the Vertical Axis

Scientific Inquiry – Scientific Methods & Experimental Design

Scientific Inquiry – Scientific Methods & Experimental Design Scientific Method & Experimental Design Constants Factors that are NOT changed during an experiment Keeping constants unchanging ensures that the I.V. is the only factor being tested Control (Group) An “untested” group used for comparison Minimize the “involvement” of the I.V. Hypothesis An educated guess about the outcome of an experiment TESTABLE Focuses on the question or problem If I.V. “changes,” then the D.V. “responds” Conclusion State if hypothesis was supported or not supported Discuss Sources of Error and “Confidence” in Results Suggest Other, Related Experiments, or Alternative Hypotheses

Scientific Inquiry – Fields of Science Types of Science Earth Science Geology Astronomy Life Science Biology Ecology Environmental Science Physical Science Chemistry Physics Technology vs. Science “Pure” Science Studies Natural Phenomena Develops Laws & Theories Generally Big Picture Often Slow Technology Application of Science Solve Problems Improves Processes Makes life easier

Scientific Inquiry - Measurement Measurement is making observations to collect quantitative data by comparing observed values with standard values All measures include: Numbers Units of measure Uncertainty When making scientific measurements the last digit in a measurement is the estimated digit The estimated digit is one place value smaller than smallest division of the measurement instrument All digits recorded are significant digits

Scientific Inquiry - Measurement Measurement – Accuracy vs. Precision Accuracy in measurement means measured values are close to the actual value - - Correctness in Measurement Precision in measurement means measured values are close to each other Repeatability in Measurement

Scientific Inquiry – Dimensional Analysis & Unit Conversions Units of Measure & Unit Conversion Units “describe” the property being measured Mass Mass is a measure of “how much matter is present” Measured in Grams (g) Pounds (lb) Volume Volume is a measure of “how much space is being taken up” Cubic Meters (m3) [ length x width x height ] Liters (L) Cubic feet (ft3) Gallons (gal)

Scientific Inquiry – Dimensional Analysis & Unit Conversions Units can be converted using “factors” that change the mathematical presentation, but not the actual value of the property Conversion factors are based on equalities between different units For example 1000 m = 1 km 1mL = 0.001 L 12 inches = 1 ft 2.54 cm = 1 inch Half of the units of the conversion factor “match” and will cancel with the units being converted Half of the units of the conversion factor are the “new” units

Scientific Inquiry - Measurement Unit Conversions Match the given units in the “reciprocal” position (on the diagnol) Put “wanted” units opposite “matched” unit Cancel matched unit Repeat 1 – 3 until “desired” unit is achieved Multiply or divide as necessary Re-write with new units and new mathematical value

Scientific Inquiry - Measurement Scientific Notation All ordinary notation numbers can be written as scientific notation numbers Coefficient x 10Exp Coefficient should be greater than or equal to 1 but less than ten. Small numbers (numbers less than 1) use negative exponents Large numbers (numbers greater than 10) use positive exponents

Scientific Inquiry – Measurement Significant Digits ‘Certain’ digits and one ‘estimated’ digit in a measure or calculated result A system of rounding that is used to maintain and present the precision of measure throughout calculations using measured values. Counting Significant Digits All non-zero digits in a measure are significant digits Entrained zeros (zeros between non-zero digits) are significant digits Leading zeros are NOT significant digits Trailing zeros in a value are significant IF there is a decimal point present in the value.

Scientific Inquiry – Measurement Adding and Subtracting with Significant Digits Calculate answer ‘normally’ Round answer to the smallest shared place-value of all inputs in the calculation Multiplying and Dividing with Significant Digits Round answer to the fewest number of sig digs present in all inputs in the calculation