7 Percent Error Always some error in a measurement Instrument, limits of measurer, calibrations% error – calculated by the following formula…% error = Valueexp – Valueacc x 100Valueacc
8 Objective/Warm-Up SWBAT review dimensional analysis, density, and metric conversions.Record the measurement for each cylinder.
9 Significant FiguresSig figs – all the digits known with certainty plus one final digit, which is somewhat estimated or uncertainGraduated cylinder example42.5 mL - the 5 is the estimated number
10 Rules for Determining Sig. Figs. All non zero digits are significantZeros at the end only count if there is a decimal pointDecimal = go to 1st non zero and count everything to the rightExact numbers have infinite significant figures (1m = 1000mm)Calculators exaggerate precision
11 Sig. Fig Examples How many sig figs are in… 203000 1000.00 0.00052 79.810
13 Objective/Warm-Up How many significant figures in these numbers? SWBAT review conversions and SI units.What is the measurement shown in the graduated cylinder?How many significant figures in these numbers?5.00703.40003500
14 Objective/Warm-UpSWBAT accurately and precisely measure volume and calculate using scientific notation.How many sig figs are in…20300079.810
15 Significant FiguresMultiplication and division sig. figs = answer has no more figs. than the msmt. with the least # of sig. figs.#’sx #’s#’s = 14.24
16 Multiply/Divide with Sig Figs Your answer must have the same number of sig figs as the measurement with the fewest number of sig figs.Calculate the volume if L = 3.65 cm, W = 3.20 cm, and H = 2.05 cmV = cm3,after rounding to the correct number of sig figs, V=23.9 cm3
17 Significant FiguresAddition and subtraction = answer has no more numbers to the right of the decimal pt. than the number with the least numbers to the right of the decimal2.8 79= 220.4
18 Addition/Subtraction with Sig Figs Your answer must have the same number of decimal places as the value with the fewest decimal places=77.218Round so that the answer is 77.2
19 Check-Up How can we judge accuracy? How can we judge precision? How do accuracy and precision relate to measurement?
20 Objective/Warm-UpStudents will be able to use significant digits and scientific notation in calculations.Warm-Up: Section Review Worksheet
21 Scientific Notation 29640000000000000000000 copper atoms in 1 penny 2.964 x 1022 atoms2 Parts to scientific notation# between 1 and 10Power of 10
22 Scientific NotationWe use the idea of exponents to make it easier to work with large and small numbers.10,000 = 1 X 104250,000 = 2.5 X 105Count places to the left until there is one number to the left of the decimal point.230,000 = ?35,000 = ?
23 Scientific Notation Continued = 6 X 10-5= 4.5 X 10-4Count places to the right until there is one number to the left of the decimal point0.003 = ?= ?
24 Scientific Notation Examples Change from scientific notationthe distance from Pluto to the Sun is 5.9×10 12 metersthe Milky Way disk radius is 3.9×1020 meters.The speed of light is 3 x 10 8 meters/second.the sun is 1.5x 1011 meters from earthMass of proton : x kgMass of neutron: x kgMass of electron: × 10-31 kgChange into scientific notationkg is the mass of a dust particleA proton has a diameter of approximately mm