In This Lesson: Measurement and Significant Figures (Lesson 3 of 6) Today is Thursday, February 8 th, 2018 Stuff You Need: Calculator Pre-Class: Get your calculators and get ready. Something else to do: What would it mean if I told you that when it comes to basketball, I m not very accurate but I am very precise? Last thing: Today (or maybe next class) I will teach you how 5 x 5 = 30.
Today s Agenda Measurement Significant Figures Where is this in my book? P. 62 and going for quite a few pages
By the end of this lesson You should be able to differentiate between accuracy and precision. You should be able to determine which digits of a number are significant.
Measurement Yes, in the world of chemistry, even a term such a measurement has a distinct definition. A measurement is a quantitative observation that consists of two parts: Number Scale (unit) If you leave out either one, I must deduct points. For example: 21 grams 6.63 x 10-34 Joule seconds
Uncertainty As it turns out, not every measurement is perfectly accurate. In any measurement there s a degree of uncertainty. For example, how many ml do you see here? 53 ml sounds good, but you can estimate one more digit. 52.9 ml? (In this class, you should estimate that extra digit) http://www.jce.divched.org/jcesoft/programs/cpl/sample/modules/gradcyl/pic/00322409.jpg
Accuracy versus Precision In addition to uncertainty, measurements also can be judged according to their accuracy or their precision. What s the difference? Accuracy is how close a measurement comes to reality. Precision is how repeatable a measurement is or the number of decimal places an instrument measures. 60% of the time, it works every time.
Accuracy versus Precision High Accuracy, High Precision 1. 2. High Accuracy, Low Precision Low Accuracy, High Precision Low Accuracy, Low Precision 3. 4. http://antoine.frostburg.edu/chem/senese/101/measurement/slides/img017.gif
Accuracy and Precision Suppose you have an electronic balance that provides measurements to two decimal places. It s certain to two. Other digits are uncertain. If the balance always gives you the same mass for the same object, it s precise. If it gives you the right mass, it s accurate. Are there ways in which it could be accurate but not precise? How about precise but not accurate? http://hxdzjs.net/uploadfile/20100601/20100601134741293.jpg
Pre-Class Part Deux Facebook was recently reported to have 1.6 billion users 1. Is it exactly 1,600,000,000? Could it possibly be 1,600,000,001? Why is it okay to just say 1.6 instead of all the zeroes? If you needed to calculate the circumference of a circle but you only knew the diameter was 8, what would you do? Most of us would multiply by pi (π). How much is pi, again? 1 Bloomberg Business Week March 24, 2016
Significant Figures Scientists need to be clear with one another about how many digits to which they are rounding. In other words, they need to be clear about the level of uncertainty they re willing to accept. One scientist may say pi is 3.141, another may say 3.141592654. To determine how many digits your answer should be, we use significant figures. Significant figures are the digits that count overall, they re used as a special form of rounding. Also known as Significant Digits, or Sig Figs, or Sig Digs.
4 Rules for Counting Sig Figs 1. If the number contains a decimal point, count from right to left until only zeros or no digits remain. Examples: 20.05 grams 4 sig figs 7.2000 meters 5 sig figs 0.0017 grams 2 sig figs
4 Rules for Counting Sig Figs 2. If the number does not contain a decimal point, count from left to right until only zeros or no digits remain. Examples: 255 meters 3 sig figs 1,000 kilograms 1 sig fig
Quick Interlude: Oceanic Sig Figs Here s a way to remember Rules 1 and 2, although it doesn t work in Hawaii: If there is a decimal point present, count in the direction of the Pacific (to the left). If the decimal point is absent, count in the direction of the Atlantic.
4 Rules for Counting Sig Figs 3. For numbers in scientific notation (M x 10 n ), count only the sig figs in the M number use rules 1 and 2 normally. Examples: 1.40 x 10-16 cm 3 sig figs 2 x 10 5 g 1 sig fig
4 Rules for Counting Sig Figs 4. Exact numbers and percentages have an infinite number of significant figures. Rare in this class (usually for unit conversions). 1 inch = 2.54 cm exactly 1 dozen = 12 eggs-actly
Counting Sig Figs How many significant figures in each of the following? 1.0070 m = 5 sig figs 17.10 kg = 4 sig figs 100,890 L = 5 sig figs 3.29 x 10 3 s = 3 sig figs 0.0054 cm = 2 sig figs 3,200,000. = 2 sig figs (the decimal point needs digits after it to count)
Now for some practice Significant Figures in Measurements and Calculations Part I choose 15. Difficult and/or Scientific Notation: 13, 14, 18-20 The competition will be afterward!
Now for a break Let s take a look at some pretty interesting uses of measurements (particularly in terms of accuracy). Parallel Parking video.
Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of digits after the decimal point in the result equals the number of digits after the decimal point in the least precise measurement. Round the end normally. 6.8 + 11.964 = 6.8 + 11.964 = 18.764 18.8
Adding and Subtracting Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 ml - 1.870 ml 0.16 ml 0.160 ml
Now for some practice Significant Figures in Measurements and Calculations Part II choose 5. Part III choose 3. Difficult and/or Scientific Notation: 28, 30 The competition will be afterward!
Rules for Significant Figures in Mathematical Operations Multiplication and Division: The number of significant figures in the result equals the number of significant figures in the least precise measurement used in the calculation. Round the end normally. 6.38 x 2.0 = 6.38 x 2.0 = 12.76 13 (2 sig figs)
Multiplying and Dividing Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 m 2 23 m 2 100.0 g 23.7 cm 3 4.219409283 g/cm 3 4.22 g/cm 3 0.02 cm x 2.371 cm 0.04742 cm 2 0.05 cm 2 710 m 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 5872.786 lb ft 5870 lb ft 1.030 g x 2.87 ml 2.9561 g ml 2.96 g ml
Now for some practice Significant Figures in Measurements and Calculations Part IV choose 5. Part V choose 3. Difficult and/or Scientific Notation (you must try one of these): 45, 46, 48, 50, 51, 55 The competition will be afterward!
Closure So, using sig fig rules, solve this problem: 5 x 5 =? 5 x 5 = 30 Now solve this one: 5.0 x 5.0 =? 5.0 x 5.0 = 25
Closure Part Deux Try this one: 15 g x 4.0 g =? 15 g x 4.0 g = 60 g but it needs to be 2 sig figs! 15 g x 4.0 g = 60.0 g is 3 sig figs! Write this down: When in doubt, make it scientific notation (we ll do this later). 6.0 x 10 1 g 2
Final FYI What about something like percent error? Percent Error ( Experiment al - Accepted Value Accepted Value ) 100 You re doing both subtraction and division, so which rule(s) apply? The answer is that multiplication/division trump addition subtraction. So use the least number of sig figs rule.
More sig fig practice: Do this: http://www.sciencegeek.net/chemistry/taters/unit0sigfigs.htm Then try 10: http://science.widener.edu/svb/tutorial/sigfigures.html
Transition CrashCourse Unit Conversion and Significant Figures