1. Of what significance are... (drum roll please) A question that has plagued physics students for ages A mini-PowerPoint tutorial before the physics tutorial 1. Click the right arrow key to advance through the presentation. 2. Click the left arrow key to go back through the presentation.

2. So what exactly is a SIGNIFICANT FIGURE? A significant figure is defined as a reliably known digit used to locate a decimal point. Significant Figures, or sig figs for short, are number values that one knows through making measurements. Real measurements have a finite number of sig figs because their values can only be known within the limits of experimental uncertainty. That is, limitations in tool precision and the skill of the experimenter conspire to reduce the number of reliably known digits in every measurement.

3. The number of sig figs in a number value shows the precision (or detail) of a measurement. Having a number with lots of sig figs means that lots of digits are reliably known. … This also implies a greater degree of accuracy in measurement. The opposite is true for numbers containing few sig figs. Expressing a measurement, or calculation made based on two or more measurements, with the proper number of sig figs communicates a sophisticated level of understanding of the meaning behind the number value.

4. Rules of the Sig Fig game Part One: WHEN WHEN to concern yourself with Significant Figures 1. When writing measurements, or calculations based on measurements, in your LAB REPORTS. 2. When specifically asked to write your answer to a given question using the proper number of sig figs. That’s it! REALLY! Those are the only times. I should warn you, however, that your text has the annoying habit of presenting all of its answers rounded to the proper number of significant figures.

5. Rules of the Sig Fig game Part Two: HOW HOW to count Significant Figures 1. All non-zero digits are significant figures. 2. All zeroes between non-zero digits are also significant. 3. Use the Atlantic-Pacific rule to count significant zeroes. More on the Atlantic-Pacific rule in a minute. 4. If you are in doubt express your answer with 3 sig figs. Don’t just write what is on your calculator. On the AP Physics exam, they will give full credit for a correct answer if it has the right number of sig figs plus or minus one. Using three sig figs will almost always be satisfactory.

6. A P The A tlantic- P acific Rule for counting sig figs The “A” in Atlantic stands for decimal absent. If the decimal is absent, then start at the first non-zero digit and count all digits to the right of it (heading for the Atlantic Ocean on a map). Stop counting when you reach the last non-zero digit. The “P” in Pacific stands for decimal present. If the decimal is present, then start at the last digit and count all digits to the left of it (heading for the Pacific Ocean on a map). Stop counting when you reach the last non-zero digit.

7. A few simple applications of Atlantic-Pacific Rule Count the number of sig figs in each number value below. 1. All non-zero digits are significant figures. 2. All zeroes between non-zero digits are also significant. 3. Go back to the previous slide to review the Atlantic-Pacific rule as needed. Ex:809 Ex:0.0809 Ex:8090 Ex:8090. Ex:0.8090 Ex:809.000 Three. The zero is sandwiched between 8 and 9. Still Three. The zeroes to left of the 8 are not sig figs. Three. The zero after the 9 is not a sig fig. Four. The decimal makes the last zero a sig fig. Four again--for the same reason as in the last ex. Six. The decimal makes all of the zeroes sig figs. For more practice visit: after this tutorial.

8. GREAT!!! I know how to count sig figs, and I know when to count sig figs. But, WHY am I bothering to keep track of them Flommy-O?! It’s a fair, albeit a snotty, question to ask.

9. Fifty ways to … measure fifty. Okay, that was an exaggeration. How about three? Each value below is fifty, but contains a different number of significant figures and with a different meaning. 1.50 Only one sig fig, because there is no decimal present. 2.50. Two sig figs, because there is a decimal present. 3.50.0 Three sig figs, again because of the decimal present. The only digit that is reliable is the “5” and the measurement was rounded to the nearest ten. The actual value of the quantity is somewhere between 45 and 55 because there is no confidence in the ones digit. Both the “5”and the “0” are reliable. The measurement was rounded to the nearest whole. The actual value of the quantity is somewhere between 49.5 and 50.5. This much more precise than the previous measurement. The “5”and both “0’s” are reliable. The measurement was rounded to the nearest tenth. The actual value of the quantity is somewhere between 49.95 and 50.05. More sig. figs means more precision and implies more accuracy.

10. SCIENTIFIC NOTATION SCIENTIFIC NOTATION is a convenient way to write a value with the correct number of sig figs. General form of scientific notation:A x 10 B 1  A < 10B = integer The coefficient “A” has the same number of sig figs as the number when it is written in standard notation. Going back to the previous slide, here is how one would express fifty with one, two and three significant figures: 1.50 2.50. 3.50.0 One sig fig in 50 becomes 5 x 10 1 Two sig figs in 50. becomes5.0 x 10 1 Three sig figs in 50.0 becomes 5.00 x 10 1 For scientific notation practice visit:after the tutorial

11. With a modest amount of practice you will become a pro at counting sig figs in a measurement and then expressing the value in scientific notation. There’s only one hurdle remaining. NOOOOO!!! COMPUTING WITH SIG FIGS!

12. Rules for Computing with Proper Sig Figs: Remember that one is concerned only with sig figs in MEASURED quantities. Fundamental constants (like the speed of light or Planck’s constant) and counted numbers are assumed to have an infinite number of significant figures. The underlying rule is The underlying rule is … no computed valued based on measurements can have more sig figs than the least precise measurement in the calculation. 1. The addition (subtraction) rule. The number of decimal places in the answer should equal the smallest number of decimal places of any term in the sum. 2. The multiplication (division) rule. The number of sig figs in the answer should equal the smallest number of sig figs of any term in the product.

13. Examples involving the Addition Rule Perform the operations called for in each example. Feel free to use your calculator, but you will need to round your answer to the proper number of sig figs and express it in scientific notation. Ex:500.0 + 31.27 Ex:50.0 + 0.32 - 7 Answer: 531.3 = 5.313 x 10 2 The value on the calculator reads 531.27, but 500.0 is reliable to the tenths place only. The answer must be rounded to the nearest tenth---531.3. Answer: 43 = 4.3 x 10 1 The value on the calculator reads 42.68, but 7 is reliable to the nearest whole. The measurement seven has no places after the decimal. The answer must be rounded to the nearest whole---43.

14. Examples involving the Multiplication Rule Perform the operations called for in each example. Feel free to use your calculator, but you will need to round your answer to the proper number of sig figs and express it in scientific notation. Ex:500 * 4.2 Ex:500. * 4.2 Answer: 2000 = 2 x 10 3 The value on the calculator reads 2100, but 500 has only one sig fig. The answer must have only one sig fig. NOTE: The measurement 500 could have any value between 450 and 550. Answer: 2.1 x 10 3 The value on the calculator reads 2100 again. The number 500. has 3 sig figs this time, but 4.2 has only two sig figs. The answer must be rounded to two sig figs. There is no way to express the answer (2100) in standard notation.

15. Order! Order! Order in my court or I will hold you in contempt! Let’s see if you can put it all together before I rule that you have mastered the significance of sig figs.

16. Putting it all together in one example Suppose you run a 100. meter dash in a time of 15 seconds. What is your average speed during the dash expressed in with the proper number of significant figures and in scientific notation? Finding the average speed is not difficult. All one needs to do is divide the distance in meters by the time in seconds. Expressing your answer properly is the challenge. Distance = 100. metersthe zeros are sig figs. Time = 15 secondsno-brainer, 2 sig figs. Average Speed = ?Must have 2 sig figs.

17. Simply answering the question… Avg. Speed = 100. m / 15 s = 6.66666666 m/s Since 100. meters has 3 sig figs, and 15 seconds has only 2 sig figs, the answer must be rounded to 2 sig figs. ANSWER: 6.7 meters/second = 6.7 x 10 0 meters/second

18. First, let’s focus on the distance measurement: 100. meters The “1” and the two “0’s” are all reliable. This distance was measured with confidence to the nearest whole meter. The measurement indicates that the actual distance is at least 99.5 meters and at most 100.5 meters. Next, let’s focus on the time measurement: 15 seconds The “1” and the “5” are both reliable. This time was measured with confidence to the nearest whole second. The measurement indicates that the actual time it took you to run the distance was least 14.5 meters and at most 15.5 seconds. You should notice that there is some uncertainty in both the distance and time measures, so there must be uncertainty in the calculation of your average speed.

19. Putting it all together! The fastest possible speed you can have is when the distance is greatest and the time is least. Based on the uncertainty in the measurements, the distance you ran could have been as high as 100.5 m and the time as little as 14.5 seconds. The slowest possible speed you can have occurs when the distance is least and the time taken to run it is maximized. Again, based on the uncertainty in the measurements, the distance you ran could have been as low as 99.5 m and the time to run it as much as 15.5 seconds.

20. Continued... Based on the limited uncertainty in the distance and time measures your average speed must have been between 6.42 m/s and 6.93 m/s. The errors in measurements of distance and time were manipulated to amplify the separation between the fastest and slowest speeds. With a high degree of confidence you can claim an average speed of 6.7 m/s thanks to proper accounting of sig figs. You should notice that your best estimate of speed falls right in the middle of that range.

21. You’ve scaled Sig Fig Mountain and lived to tell about it. Are you ready to hike Factor Label Hill?