1. Scientific Notation Algebra 1

2. What are these numbers? Do you know this number, 300,000,000 m/sec.? It's the speed of light ! Do you recognize this number, 0.000 000 000 753 kg? This is the mass of a dust particle!

3. Which is easier to read? What about the number 145,000,000? The Department of Energy's (DOE) inventory of high level radioactive waste was approximately 145,000,000 pounds. 145,000,000 or 1.45 x 10 8 ?

4. A Shortcut Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific notation is based on powers of the base number 10. Scientists Using Scientific Notation While Studying Dinosaurs Video Size of the Universe Demonstration of Scientific Notation Power of Ten Video – Old but a Classic

5. To Change from Standard Form to Scientific Notation (1)Write decimal one number in from the left so that the number is between 1 and 10. (2)Write “x 10” (3)Negative if the decimal moves left to original location; right is positive. Where is the decimal “implied” if no decimal appears in a number? (example: 195)

6. Scientific Notation Video Lesson Scientific Notation Interactive Practice

7. Examples Given: 4,750,000 Use 4.75 (moved 6 decimal places) Answer: 4.75 X 10 6 The original number was greater than 1 so the exponent is positive. Given: 0.000789 Use 7.89 (moved 4 decimal places) answer: 7.89 x 10 -4 The original number was less than 1 so the exponent is negative.

8. To Change from Scientific Notation to Standard Form (1)Move decimal point right for +. left for -.

9. Examples Given: 1.015 x 10 -8 Answer: 0.00000001015 (8 places to left) Negative exponent move decimal to the left. Given: 5.024 x 10 3 Answer: 5,024 (3 places to right) Positive exponent move decimal to the right.

10. Real Life Examples The Andromeda Galaxy (the closest one to our Milky Way galaxy) contains at least 200,000,000,000 stars. On the other hand, the weight of an alpha particle, which is emitted in the radioactive decay of Plutonium-239, is 0.000,000,000,000,000,000,000,000,006,645 kilograms.

11. Large Numbers the number of bits on a computer hard disk (as of 2006, about 1 x 10 12 GB) the number of cells in the human body (more than 1 x 10 14 ) the number of neuronal connections in the human brain (estimated at 1 x 10 14 ) Avogadro's number (the number of atoms in 12 grams of carbon-12, ~ 6.022 × 10 23 )

12. There are around 8,360,000,000,000,000,000,000,000 molecules in a cup of tea! The current Big Bang model of the Universe suggests that it is 13.7 billion years or (4.3 × 10 17 seconds) old The observable universe is 78 billion light years across (7.4 × 10 26 meters), and contains about 5 × 10 22 stars, organized into around 80 thousand million galaxies.

13. wavelength of green light: 5.5 × 10 -7 m period of a 100 MHz FM radio wave: 1 × 10 -8 s time taken by light to travel one meter: roughly 3 × 10 -9 s radius of a hydrogen atom: 2.5 × 10 -11 m the charge on an electron: roughly 1.6 × 10 -19 C (negative)

14. Between 1980 and 2011, hard disk sizes increased from 10 megabytes (1 × 10 7 ) to over 18 exabytes (1.8 x 10 19 bytes). Earth = 12.76 x 10 6 = 12,760,000 meters wide Plant Cell = 12.76 x 10 -6 =0.00001276 m wide

15. On-Line Practice and More On-line Practice Problems

16. Scientific Notation

17. Interactive Practice Changing Numbers to Scientific Notation http://www.aaamath.com/dec71i-dec2sci.html Changing Numbers from Scientific Notation http://www.aaamath.com/dec71i-dec2sci.html