Scientific Notation •Large and small numbers can be difficult to use. For example: The mass of one iron atom is: 0.0000000000000000000000911 g The number of water molecules in one cup is: 7,910,000,000,000,000 000,000,000 molecules Scientific notation is a system in which an ordinary decimal number is expressed as a product of a number between 1 and 9 multiplied by 10 raised to a power.In scientific notation:Mass of an iron atom = 9.11 x 10-23gmolecules# of water molecules in one cup = 7.91x1024.Chapter 2: Measurement and Problem Solving Ch 2 Page 1Writing numbers in scientific notation Must be between 1 and 97070 = 7.07 x 1030.0004601 = 4.601 x 10-4 Express the following numbers in scientific notation:a) 16,020,000 mg b) 0.00001206 m c) 24 kmExpress the following numbers in decimal notation: a) 4.38x104 b) 8.770x10-15 c) 6.23x108Significant figures• A method for handling uncertainty in measurementScientific Notation Ch 2 Page 2•Two kinds of numbers are associated with physical quantities:and Exact numbersMeasured numbersExact numbers - we know the exact value - no approximation involved the exact valueMeasured numbers - we can never know Exact number examples:1 dozen eggs = 12 eggs exactlyA square has 4 sides (not 3.7 or 4.1)• All measured numbers carry with them a degree of uncertainty. The degree of uncertainty depends on the measuring device used.Exact and Measured Numbers Ch 2 Page 3Thermometer A marked off in 1 degree increments - can estimate temp as 29.2°C or 29.3°C Thermometer B divided into 0.1 degree increments - the temp can be estimated as 29.18°C or 29.19°C (Thermometer B is more precise)Significant Figures are the digits in any measurement that are known with certainty plus one digit that is uncertain. Precision Ch 2 Page 4Guidelines for Determining the Number of Significant Figures 45.1 49 1.2791. All nonzero digits are significant2. Confined zeros (or zeros between nonzero digits) ALWAYS count as significant 2.075 70.7 940005.008 62.00is a decimal point in the number 0.02000 78.000120003. Trailing zeros are significant if there4. Leading zeros (zeros to the left of the first nonzero number) are NOT significant. These 0.01450.000340.000002279 zeros merely "place" the decimal point.Significant Figures Ch 2 Page 55. In cases where there is no decimal point, assume trailing zeros are NOT significant. (These types of numbers should be 93,000,000 avoidedby using scientific notation).6040006310How many significant figures are in the following numbers?426406.004600515.020200200.00907,000,0006.022 x 10230.01260.01001.010010.010014.00840.008100.29000.00000030074.680 x 10-5Significant Figures Ch 2 Page 6Calculations with Significant Figures Rounding off is the process of deleting insignificant digits from a calculated number. If the digit to be dropped is less than 5, that digit and all digits that follow it are simply dropped 62.314 rounded to 3 sf becomes 62.3 9,017.000427 rounded to 8 sf = _________ 504.902 rounded to 4 sf becomes ______ If the digit to be dropped is 5 or greater, the last retained digit is increased by one 62.782 rounded to 2 sf becomes 63 726.679 rounded to 5 sf becomes ______4.056639 x 1017rounded to 4 sf = _________ Calculated quantities cannot be any more precise than the least precise piece of information that goes into the calculationsRounding Ch 2 Page 7Multiplying and Dividing: There can be no more total sig. figs. in the answer than there are in the quantity having the fewest sig. figs. • Adding and Subtracting: There can be no more decimal places in the answer than in the quantity with the least number of decimal places. 1270 cm365.6 x 0.0024 = 983.24 g = 46.014 g 27.8 g- 1.578 cm+ 1.4762 cm 1.52 cm(1.023 x 0.895)+ 0.16 = Calculations involving multiplication/division and addition/subtraction:(4.1792 - 4.024) x 57.884 =Calculations with Significant Figures Ch 2 Page 8Metric and SI Units• The metric system is much easier to use than English system. There are fewer units to learn and it is much easier to interconvert in the metric system• System used for scientific measurements (based on metric system) is called the SI System (System International). The SI System is used throughout the world.lMetric and SI Units Ch 2 Page 9Ex: kilo means a thousand so: 1 kilometer = 1000 meters 1 kilogram = 1000 grams 1 kiloliter = 1000 liters(5620000000 meters)5.62 Gm (gigameters) = 5.62 x 109meters (1.25 x 10-2liters in scientific notation)12.5 ml (milliliters) = 12.5 x 10-3liters 5 µs (microseconds) = 5 x 10-6seconds (0.000005 seconds)3.9 ng (nanograms) = ______________g Units of VolumeVolume is a measure of the amount of space occupied by on object. Volume is 3-dimensional so the units are ft3, cm3, in3... etc. Liter is also a volume unitMetric and SI Units Ch 2 Page 10A liter is the basic unit of measurement in themetric system. A liter is a volume equal to aperfect cube that is 10 cm on each side. (symbol for Liter is capital "L") = 1000 cm3 1 L = 10 cm x 10 cm x 10 cm10 cm10 cmConverting from One Unit to AnotherWe often need to convert from one unit to lbs kg miles km another: inches feetConversion factors are derived from equal quantities of two different units• To do this, use Conversion Factors!Ex. 1 foot = 12 inches conversion factors: 12 inches 1 foot 1 foot or 12 inches Unit Conversion Ch 2 Page 11How many inches are in 2.30 feet??? inches = 2.30 ft x 12 in (choose conversion cancellation of = 27.6 inches unwanted unit) 1 ft factor that allows Metric-to-Metric Conversion Factors You will need to know the metric conversions in Table 2.2 that are enclosed in the box.Ex. 0.01 meters = 1 cm or 100 cm = 1 meterConversion factors:0.01 m or 1 cm 100 cm