6Significant Figures:Digits in a measurement having values that are known with certainty plus one digit having a value that is estimated.
7Reading Volume: Significant Figures on an Instrument
8Measurements that contain a greater number of significant figures are more precise than measurements that contain fewer significant figures.Always select an instrument that gives you the most significant figures. Onlyreport as many sig figs as thatinstrument allows
10All numbers 1-9 are significant. Zeros are sometimes significant, here's how you can tell:If a decimal point is present, starts on the Pacific side, move across until you get to a 1-9 digit, and start counting to the endIf a decimal point is absent, start on the Atlantic side, move across until you get to a 1-9 digit, and start counting to the end1.100 has ? sig figs, has ?,40.01 has ?1005 contains ? sig. Figs., 23,000 has ?, 1,045,090 has ?
11When multiplying or dividing measurements: round the answer to the same number of digits as the measurement having the fewest number of significant figures.When adding or subtracting measurements: round the answer to the same number of decimal places as the measurement having the fewest number of decimal places.
12123456.7890 Identify the LEAST PRECISE measurement. Higher precisionLower precisionIdentify the LEAST PRECISE measurement.Identify the MOST PRECISE digit (place) within that measurement.Round the answer to this digit (place).
13Conversion Commonly Used Prefixes: kilo = 1000 of something ( 1km= 1000m, kg)deci =0.1 of something (10 dm = 1m)centi = 0.01 of something (100 cm = 1m)milli = of something (103 mm = 1m)micro = (106 µm = 1m)nano = (109 nm = 1m)pico = (1012 pm = 1m)Refer to Conversion Chart to additional prefixes
14Conversion = = 1 = = 1 = = 1 All conversion factors are fractions. 100 cm cm1 m cm== 11 km103 m103 m== 11m10-6 µm1m10-6 µm== 1
15The Nature of Units Units are multiplied and divided like numbers are. 10 meters2 meters= (the units cancel out)10 meters x 10 meters x 10 meters = 103 m3 (the units combine as exponents)50 miles10 gallons= 5 miles/gallon (the units combine as a fraction)Only IDENTICAL UNITS on 2 numbers can be added or subtracted.The answer always has the same units.100 kg – 25 kg = 75 kg100 kg – 25 m = Meaningless Dribble
16How many seconds are in 54 days? Write the measurement with its unit.If it isn’t already a fraction, write it over 1.Set up conversion factors thatCancel units you want to get rid ofReplace with units you are looking forHave values on the top and bottom that are equivalentMultiply numbers across the topMultiply numbers across the bottomDivide to get answer, check units
17Scientific NotationThere has to be a better way to write those numbersRules for scientific notation1) Always express the number starting with the one’s place followed by any decimal digits, times a power of 10.2)To express a large number, count the number of decimal places needed to move to the one’splace, and make that number the exponent of ten.3) To express a very small number, count the number of decimal places needed to move to the one’s place, and make that number the NEGATIVE exponent of ten.4) After re-expressing the number in scientific notation, check it by writing out the expanded ten, and multiply it by the measured number.
18Scientific Notation Examples: 0.000000000000000000000000000000001 = x 1035
20Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each otheraccurate&preciseprecisebutnot accuratenot accurate¬ precise
21Instruments are...Precise if they give many significant digitsAccurate if calibrated to a standard
22Observed – True X 100 True Percent Error To report the accuracy of your measurementsObserved – TrueTrueX 100
23To report the precision of your measurements Average DeviationTo report the precision of your measurements1Average your measurements2Find the absolute values of the differences between each measurement and the average3Average these differences