Chapter 1: MeasurementsCommon Metric UnitsCommon Metric UnitsCommon Metric UnitsScientific NotationScientific NotationScientific NotationMeasured & Exact NumbersMeasured & Exact NumbersMeasured & Exact NumbersMeasured & Exact NumbersMeasured & Exact NumbersMeasured & Exact NumbersLearning CheckSignificant FiguresSignificant FiguresLearning CheckSignificant Figures in CalculationsRounding NumbersLearning CheckMultiplication & DivisionAddition & SubtractionMixed CalculationsSI & Metric PrefixesSome equalitiesConversion FactorsUsing Conversion Factors / Dimensional AnalysisDimensional AnalysisDimensional AnalysisDimensional AnalysisDimensional AnalysisDimensional AnalysisDimensional AnalysisDimensional AnalysisDimensional AnalysisDensityDensity ProblemsDensity ProblemsChapter 1: MeasurementsThe metric systemBecoming more common in our country.The SI systemDeveloped in 1960, also called the international system of units.Set of seven standard quantities of which all others can be derived.Common Metric UnitsLengthMetric and SI unit is the Meter (m)1 m = 39.4 inches1 inch = 2.54 centimeters (cm)VolumeAmount of space occupied by a substanceMetric unit = Liter (L), SI unit = m31 L = 1.06 quarts946 milliliters = 1 quartCommon Metric UnitsMassMetric unit is the gram (g), SI unit is the kilogram (kg)1 kg = 2.2 pounds454 g = 1 poundTimeMetric and SI unit is the second (s)Common Metric UnitsTemperatureIndicates how hot or cold an object isMetric unit is Celsius (C) and SI unit is Kelvin (K)These will be discussed in more detail in Chapter 2.Scientific NotationUsed when numbers are really small or really large.General format:A x 10nA is a number between 1 and 10.n is the exponent on 10 (called the power) and is equal to the number of places that the decimal place is moved.Scientific NotationExamples0.000058 = 5.8 x 10-5•The decimal is moved five places to the right, hence the –5 power. Note that small numbers (0< x <1) will always have a negative exponent. 58,000 = 5.8 x 104•The decimal is moved four places to the left, hence the power of 4 is used. Note that large numbers (>1) will always have a positive exponent.Scientific NotationOn your calculator, use the EE or EXP key when entering these numbers.Example:(1.8 x 105) x (3.2 x 10-3) = 576 or 5.76 x 102Measured & Exact NumbersMeasured numbers are those which come from using any kind of a measuring device.Examples are: ruler, graduated cylinder, thermometer, scale, etc.Include both certain digits and one uncertain digit.Certain digits are digits that all would agree on.Uncertain digit is the last digit that requires YOU to make a “best guess.”Measured & Exact Numbers“Best Guess” depends on the smallest increments on the measuring device.A ruler may have markings for every 0.1cm. Your “best guess” might be to 0.05cm or even 0.02cm.Measured & Exact NumbersA graduated cylinder – depends on size.A 10-mL has markings every 0.2-mL.A 50-mL has markings every 1-mL.Measured & Exact NumbersA Thermometer has markings every degree.Measured & Exact NumbersIf a measurement results where it is exactly lined up with a mark, then a zero at the end may be needed.Not everyone will agree on the “best guess,” which means that all measured numbers have some uncertainty.Digital devices – the last digit in display is uncertain.Measured & Exact NumbersAn exact number is a either a counted number or an established relationship between two units.Examples are:12 computers in the room15 apples in the bag1 foot = 12 inches1 pound = 16 ouncesLearning CheckAre the following numbers exact or measured?There are 50 pages in a bookA coin weighs 2.87 grams There are 100 centimeters in one meterA graduated cylinder contains 40.0mL of waterSignificant FiguresGoal: Report answers from calculations by rounding the answer to the correct number of significant figures.Accuracy refers to measurement(s) that are close to the true (accepted) measurement.Precision refers to the agreement of values obtained while repeating the same measurement.In the lab, we desire both of these.Significant FiguresRules are:1. A number is significant if it is:a. A non-zero digitb. A zero between two non-zero digitsc. A zero at the end of a decimal numberd. Any digit in the coefficient of a number written in scientific notation2. A number is not significant if it is:a. A zero at the beginning of a decimal numberb. A zero used as the placeholder in a large number without a decimal point.Learning CheckHow many significant digits do each of the following measured numbers have?1.02 0.0045 91,0002.50 x 10-80.0150250.Significant Figures in Calculations A calculation (using measured numbers) is only as accurate as the number that had the least number of significance.Calculators almost NEVER provide answers with the proper significance.Thus, answers will need to be rounded (or possibly require additional zero’s).Rounding NumbersRules:1. If the first digit to be dropped is a 4 or less, it and all other following digits can be dropped.2. If the first digit to be dropped is a 5+, then the last retained digit is increased by one.3. If the digit to be dropped is exactly 5 (nothing after it), then round up if it makes the digit even or down if that makes the digit even.3.46, round to two s.f.’s.54.48, round to two s.f.’s.135.51, round to three s.f.’s.8.74528, round to three s.f.’s.Learning CheckMultiplication & DivisionThe final answer is rounded to have the same number of significant digits as the measurement with the fewest s.f.’s.Example: 24.65 x 0.67 = 16.5155 (calc.)Example: (2.85 x 67.4) / 4.39 = 43.756264 (calc.)Example: (8.00) / (0.250) = 32 (calc.)Addition & SubtractionThe final answer is rounded to have the same number of decimal places as the measured number with the fewest decimal places.Example: 2.045 + 34.1 = 36.145 (calc.)Example: 255 – 175.65 = 79.35 (calc.)Example: 89.15 – 82.95 = 6.2 (calc.)Mixed CalculationsApply the rules for each type of calculation.Don’t round intermediate answers – round only at the very end.Example: (23.8 + 4.25) / 67.85 = 0.413411938Example: (17.92 – 16.82) x 0.01957 = 0.021527SI & Metric Prefixes To increase or decrease metric units, prefixes are used as a multiplier.Prefixes that increase the size: G = giga, M = mega, 106 or 1,000,000k = kilo, 103 or 1,000Prefixes that decrease the size:d = deci, 10-1 or 0.1c = centi, 10-2 or 0.01m = milli, 10-3 or 0.001m = micro, 10-6 or 0.000001Some equalities1 m = 100 cm1 kg =