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Scientific Measurement and Significant Figures Part 1: Scientific Notation Objective-express large and small numbers in scientific notation define scientific notation- a method of representing very large or very small numbers using the format M x10n M= the number between 1 and 10 n= an integer Original Number Larger than 1 2 500 000 000 Original Number Smaller than 1 0.0000579 2.5x109 5.79x10-5 * negative exponents are numbers smaller than 1 but larger than 0 Scientific Notation Practice _______________________________________ A D B C E Place the letters on the number line A. 0 B. 2.38 x10-2 C. 8.75 D. 2.38 x10-4 E. 8.56 x105 Part 2: Significant Figures Objective-identify significant figures in measurements Measurement: All measurements have uncertainty because instruments can’t be read to an infinite number of decimal places. All measurements have the last digit as an estimated one. define significant figuresAny 0 (s) sandwiched between significant figures are significant 1.) 30.5 ml = 3 2.) 5005 m = 4 3.) 0.207 grams = 3 Trailing 0 (s) in measurements WITH a decimal point are significant figures 1.) 30.0 ml = 3 2.) 50 m = 1 3.) 0.9050 grams = 4 If you want these to be significant—you can either add a decimal point, or put a line over the 0 you want to be significant 1.) 300 m = 1 2.) 300. m =3 3.) 300 m = 2 How can I use measurement, the metric system, and scientific notation to explain if a 0 is significant? T. O’Toole Leading 0 (s) are NOT significant figures-if you change the unit you can eliminate the 0’s 1.) $.05 = 1 2.) .0052 g = 2 3.) .070 L = 2 To Summarize: Do you think the 20,000,000 tons of debris was measured with an instrument? No--hyperbole Is there a difference between .005 kg and 5x10-3 kg? No—use scientific notation to determine they are equivalent. Your Turn: Identify the number of significant figures in the following: 1.0070 m = 5 17.10 kg = 4 100,890 L = 5 3.29x103 g = 3 0.0054 cm = 2 3,200,000 ml = 2 How do I get from where I am to where I’m going? The 10 Minute Makeover Customize your learning by choosing from the following options each night Complete the appropriate sections on the Portfolio Page Review the PPT file on the website Read pages 51-58 in the book Answer question #5 on page 58. The answers are in Appendix C. Check out the tutorial resources in the LiveBinder including the video example Review the skills from today’s Train Your Brain How can I use measurement, the metric system, and scientific notation to explain if a 0 is significant? T. O’Toole Calculating with Significant Figures Part 3: Calculating with Significant Figures Objective-round answers to significant figures Calculated Answers: Multiply and Divide The number of significant figures in the result equals the number in the least precise measurement used in the calculation. Example: 6.38 x 2.0 = 13 6.38 has 3, 2.0 has 2 therefore the final answer has 2 Practice 3.24 m x 7.0 m = 23 m 2 710 m / 3.0 s = 240 m/s 100.0 g / 23.7 cm3 = 4.22 g/cm3 1818.2 lb x 3.23 ft = 5870 ftlb 0.02 cm x 2.371 cm = .05 cm2 1.030 g / 2.87 ml = .359 g/ml Calculated Answers: Add and Subtract The number of decimal places in the result equals the number of decimal places in the least precise measurement. Example: 6.8 + 11.934 = 18.7 6.8 has tenths, 11.934 has thousandths therefore the final answer has tenths Practice 3.24 m + 7.0 m = 10.2 m 713.1 L – 3.872 L = 709.2 L 100.0 g – 23.73 g = 76.3 g 1818.2 lb + 3.37 lb = 1821.6 lb 0.02 cm + 2.371 cm = 2.39 cm 2.030 ml – 1.870 ml = .160 ml How can I use measurement, the metric system, and scientific notation to explain if a 0 is significant? T. O’Toole How do I get from where I am to where I’m going? The 10 Minute Makeover Customize your learning by choosing from the following options each night Complete the appropriate sections on the Portfolio Page Review the PPT file on the website Read pages 58-62 in the book Answer questions #7, 9, and 11 in the reading assignment. The answers are in Appendix C. Check out the tutorial resources in the LiveBinder including the video examples Complete the SYS Assignment “Calculating with Significant Figures” Review the skills from today’s Train Your Brain How can I use measurement, the metric system, and scientific notation to explain if a 0 is significant? T. O’Toole