2 Significant Figures At the conclusion of our time together, you should be able to: Explain what significant figures are in a measurementDetermine the number of significant figures in any measurement
3 Significant FiguresThe significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.The numbers reported in a measurement are limited by the measuring tool.
4 How many sig figs are there in a given measurement?
5 Measurement and Significant Figures Every experimental measurement has a degree of uncertainty.The volume, V, at right is certain in the 10’s place, 10mL<V<20mLThe 1’s digit is also certain, 17mL<V<18mLA best guess is needed for the tenths place.
6 To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually is considered uncertain by plus or minus 1.No further insignificant digits should be recorded.The total number of digits used to express such a measurement is called the number of significant figures.All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.
7 Below are two measurements of the mass of the same object Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.
8 Does 1 = 2??? assume a = b multiply by b ab = b2 subtract a2 ab – a2 = b2 – a2factor eacha(b – a) = (b + a)(b – a)divide by (b – a)a = 2adivide by atherefore: 1 = 2
10 Reading a Meterstick. l I I I I cmFirst digit (known) = ?? cmSecond digit (known) = ? cmThird digit (estimated) betweenLength reported = cmor cmor cm
11 Known + Estimated Digits In 2.74 cm…Known digits 2 and 7 are 100% certainThe third digit 4 is estimated (uncertain)In the reported length, all three digits (2.74 cm) are significant including the estimated one
12 . l8. . . . I . . . . I9. . . . I . . . . I10. . cm Learning Check What is the length of the line?1) cm2) cm3) cmHow does your answer compare with your neighbor’s answer? Why or why not?
13 Zero as a Measured Number . l I I I I cmWhat is the length of the line?First digit ?? cmSecond digit ? cmLast (estimated) digit is cm
14 Always estimate ONE place past the smallest mark! 11.5 mL
15 So how many sig figs are there in a given measurement? 52.8 mL
19 Rule #2 – Sandwiched 0’s Zeros between non-zeros are significant Examples:7003 = 4=3
20 Rule #3 – Leading 0’sZeros appearing in front of non-zero digits are not significantAct as placeholdersCan’t be dropped, show magnitudeExamples:= 2=3
21 Rule #4 – Trailing 0’s with DP Zeros at the end of a number and to the right of a decimal point are significant.Examples:= 4= 4=3
22 Rule #5 – Trailing 0’s without DP Zeros at the end of a number and to the left of a decimal point aren’t significantExamples:= 127,300 =3
23 Interesting Answers to Catholic Elementary School Bible Questions: Many religions teach that you are to have only one wifeThis is called Monotony.
24 Easier Way to do Sig Figs!! Pacific/AtlanticPAIf a decimal point is present, start on the Pacific (P) side and draw an arrow through the number until you hit a non-zero digit. Count all numbers without an arrow through them.If a decimal is absent, start on the Atlantic (A) side and draw an arrow through the number until you hit a non-zero digit.
25 Examples:gramsdecimal present, start on “P” side, draw arrow, count digits without an arrow through it.Answer = 610,100 centimetersDecimal absent, start on “A” side, draw an arrow, count digits without an arrow through it.Answer = 3
26 Learning Check A. Which answer(s) contain 3 significant figures? 1) ) ) 4760B. All the zeros are significant in1) ) ) x 103C. 534,675 rounded to 3 significant figures is1) ) 535, ) 5.35 x 105
27 Learning CheckIn which set(s) do both numbers contain the same number of significant figures?1) and 22.002) and 403) and 150,000
28 Significant Figures and Numbers Some numbers are exact: There are60 seconds in 1 minute25 cents in 1 quarter12 eggs in one dozenThere is no uncertainty in any of these numbers.In other words there areeggs in 1 dozen(add as many zeros as you like)
29 Counting Numbers Counting numbers have infinite sig figs. Ex: 3 apples
30 Significant Figures Lets’ see if you can: Explain what significant figures are in a measurementDetermine the number of significant figures in any measurement
31 Learning CheckState the number of significant figures in each of the following:A mB LC gD mE. 2,080,000 bees
32 And Mathematical Calculations Significant FiguresAnd Mathematical Calculations
34 Significant Figures At the conclusion of our time together, you should be able to: Determine the number of significant figures needed for an answer involving calculations.Round math problems properly
35 Rules for Rounding Off If the digit to be removed is less than 5, the preceding digit stays the sameis equal to or greater than 5, the preceding digit is increased by 1In a series of calculations, carry the extra digits to the final result and then round offDon’t forget to add place-holding zeros if necessary to keep value the same!!1313
36 Significant Figure Math Rules Addition / Subtraction Problem:Penny Example = m using meter stickm using rulerm using calipersm using micrometerTo find the total = mBut most of my measurements have fewer decimal places than my best tool!!!
37 Significant Figure Math Rules Addition / Subtraction:Answers can’t have more numbers to the right of the decimal point than the number in the problem with the least amount of numbers to the right of the decimal point.Example = m m mCalculator says: m (wrong)Answer: m
38 Another Example of Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places.25.2 m one decimal placem two decimal places26.54 manswer 26.5 m one decimal place
39 Significant Figure Math Rules Let’s Try a Multiplication / Division Problem: Find the volume?0.041m high0.091 m wide0.034 m deepm3What should my answer be??
40 Significant Figure Math Rules Multiplication / Division Problem:14.1 cm3.3 cm4.23 cm242.3 cm246.53 cm2What should my answer be??
41 Significant Figure Math Rules Multiplication / Division:Your answer can’t have more sig figs than the number in the problem with the least amount of sig figsExample = cm x cmCalculator says: cm2 (wrong)Answer: cm2
42 Chemical Compound Quiz Which is denser: ice or water?WaterWhy??Ice Expands 1/7th!!!
43 Significant Figures Lets’ see if you can: Determine the number of significant figures needed for an answer involving calculations.Round math problems properly
44 Significant Figure Math Rules Remember this Problem:Penny Example = m using meter stickm using rulerm using calipersm using micrometerTo find the total = m0.076 m
45 Significant Figure Math Rules Remember This One:14.1 cm3.3 cm4.23 cm242.3 cm246.53 cm2What should my answer be??47 cm2
46 Significant Figure Math Rules How About This One: Find the volume?0.041m high0.091 m wide0.034 m deepm3What should my answer be??m3
47 Learning Check 1. 2.19 m X 4.2 m = A) 9 m2 B) 9.2 m2 C) 9.198 m2 m ÷ m =A) B) C) 60m X m =m X mA) B) C) 10
48 Learning CheckIn each calculation, round the answer to the correct number of significant figures.m m m =A) m B) m C) 257 mm m =A) m B) m C) 40.7 m
49 Euphemisms in Science We all know that some politicians and government spokesmen use certain euphemistic phrases to give an aura of respectability to descriptions of events or actions which would be offensive when expressed in plain English. The following is a list of Euphemisms in Science and their translations into plain English.“Handled with extreme care during the experiments...”Not dropped on the floor!