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Objectives

8.5 Scientific Notation. Objectives. NCSCOS. Recognize the need for special notation in scientific calculations. Perform computations involving scientific notation. 4.04. Proper names for very small and very large numbers. Time Conversion: 1 picosecond (ps) - 1 terasecond (Ts).

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Objectives

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  1. 8.5 Scientific Notation Objectives NCSCOS • Recognize the need for special notation in scientific calculations. • Perform computations involving scientific notation. 4.04

  2. Proper names for very small and very large numbers.

  3. Time Conversion: 1 picosecond (ps) - 1 terasecond (Ts)

  4. What is the actual distance of the Earth from the sun? about 149,600,000 km Planetary Data Modern Earth Science (1998), Table 29-1, pg 600, Holt, Rinehart, and Winston

  5. What is the actual wavelengths of yellow light? .000000565 to .000000590 m Visible Light Spectrum (nanometer) = 1 x 10-9 About.com: Physics by Andrew Zimmerman Jones, Visible Light Spectrum (http://physics.about.com)

  6. The structure of an atom can be described in terms of protons, neutrons, and electrons. Proton and neutrons make up the core of the atom, called the nucleus. Both the mass of a proton and neutron are about 1.7 x 10-27 kilograms each. Surrounding the nucleus are the electrons, having a mass of 9.1 x 10-31 kilograms. Write the mass of an electron in decimal form .00000000000000000000000000000091 kg (decimal point, followed by 30 zeros & 91) A typical X ray has a wavelength of about 0.000000000125 meter (decimal point and 9-zeros & 125). Write this number in scientific notation. = 1.25  10-10

  7. Text Book Example #1 The distance between Earth and Proxima Centauri, the nearest star, other than the sun, is about 24,000,000,000,000 (24 trillion) miles. Write this number in scientific notation. = 2.4  1013 24,000,000,000,000 One of the stars in the constellation Orion is named Betelgeuse, and is approximately 6 quadrillion (6,000,000,000,000,000) miles from Earth. Write the number in scientific notation. = 6  1015 6,000,000,000,000,000

  8. Text Book Example #1b The U.S. Federal Debt as of 1:00 pm (EST) on Jan 21, 2011 was $14,060,657,049,248. Write this number in scientific notation. 1.4061  1013 trillion dollars The national debt for the United States in 1992 was listed as 4064.6 billion dollars. Write this number in scientific notation. 4.0646  1012 How much has the National Debt increased over the 19 years? About 10 trillion dollars (9.9964 x 1012)

  9. The speed of light is 186,282 miles per second or 186,300 miles/sec as seen in some text books . Convert the second value for the speed of light into both feet/second and miles per hour. ft/second: 186,300 miles 983,664,000 ft 5280 feet • = per 1 second 1 second 1 mile miles per hour: 186,300 miles 60 min 60 seconds • • per 1 second 1 hour 1 min 670,680,000 mil = 1 hour

  10. Text Book Example #3 Write each number in decimal notation: 3.67 x 104 = 36,700 = 0.00004103 4.103 x 10-5 = 367,700,000,000 3.677 x 1011 = 0.000000436 4.36 x 10-7 = 672,500 6.725 x 105 = 0.000302 3.02 x 10-4

  11. 8.5 Scientific Notation Text Book Example #4 Express the product and quotient in scientific notation (6 x 1015) (6 x 1015) = = (6 x 1012) (1000) (103) = 1.2 x 10-1 (3 x 103)(4 x 10-5) = 12 x 10-2 (2.5 x 106) = 5 x 103 = 0.5 x 104 (5 x 102)

  12. 8.5 Scientific Notation Additional Ex #4 Express the product and quotient in scientific notation (3 x 1028) = 3 x 1024 (1 x 104) (2.5 x 105)(1.56 x 10-3) = 3.9 x 102 (3.6 x 105) = 6 x 101 (6 x 103)

  13. Text Book Example #5 The speed of light is about 2.98 x 105 kilometers per second (km/sec). If the sun is about 1.49 x 108 km from the Earth, how long does it take sunlight to reach the Earth? (1.49 x 108) = 8.333…, min = 500 sec (2.98 x 105) One astronomical unit (AU) is the Earth’s avg distance from the sun, which is about 93 million miles. What is the distance of Neptune from the sun, if it is about 30 AU from the sun? = 279,0000,000miles = 2.79 billion miles

  14. Guided Practice Write each number in scientific notation: = 4.63 x 108 463,000,000 25,000 = 2.5 x 104 = 5.97 x 10-4 0.000597 = 1.65 x 10-7 0.000000165 = 4.57 x 10-6 0.00000457

  15. Guided Practice Write decimal notation: 3.677 x 108 = 367,700,000 = 0.0000528 5.28 x 10-5 Write scientific notation: (6 x 1014) = (6 x 1012) (102) (3.5 x 103)(2.67 x 10-5) = 9.345 x 10-2 (2.4 x 104) = 4 x 102 (6 x 101)

  16. Guided Practice The speed of light is about 2.98 x 105 kilometers per second. If a certain star is about 2.36 x 1014 km from the Earth, how long does it take sunlight to reach the Earth (sec/min/hr/days/yrs)? (2.36 x 1014) = 7.919463087 x 108 sec (2.98 x 105) = 1.319910515 x 107 min = 2.199850858 x 105 hrs = 9.16604524 x 103 days = 2.511245271 x 101 yrs = about 25.1 yrs

  17. AWE Factor Listen carefully during the presentation and try to record all 13 of the distance references. 10 quadrillion KM 10 KM 1 light year (a light year is the distance light travels in one year which is 5.87 X 1012 miles) 100 KM 100,000 KM 1 million KM 10 light years 100 million KM 1000 light years 93 million miles 10 million light years 10 trillion KM 100 million light years

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