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Scientific Notation

Scientific Notation. 9.3 x 10 7 = 93,000,000. 1.0 x 10 -7 = .0000001. Scientific Notation is important to both the Mathematical and Scientific Communities. Scientific Notation is based on the decimal system. (base 10) Scientific Notation is necessary to

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Scientific Notation

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  1. Scientific Notation 9.3 x 107 = 93,000,000 1.0 x 10 -7 = .0000001

  2. Scientific Notation is important to both the Mathematical and Scientific Communities. • Scientific Notation is based on the decimal system. (base 10) • Scientific Notation is necessary to communicate the size of very, very large objects and very, very small.

  3. Imagine…..

  4. You are a astrophysicist and you are studying our Solar System. Here are some of the facts you would be dealing with…….. There is an average distance of 93 million miles (one way) between the Earth and the Sun. **Write 93 million in standard numbers **

  5. Saturn is an average distance of 888million miles from the Sun in one direction! **Write 888 million miles in standard numbers.** Pluto is an average distance of 3 billion 674 million miles from the Sun. ** Write 3 billion 674 million miles in standard numbers.**

  6. The next closest star besides the Sun in our solar system is proximacentauri. This star is 4.24 light years from Earth. 1 light year is approximately 6 trillion miles. Therefore, the next closest star to Earth is about…… • 24, 000,000,000,000 miles away !!! (24 trillion miles away) Proxima Centauri

  7. Those numbers are only discussing our Solar System which is smaller than a drop of water when compared to the rest of the Milky Way Galaxy, not to mention the entire Universe. These distances can get very VERYVERY LARGE!!!!

  8. As a result of such numbers, to avoid errors and to be more efficient, scientists use Scientific Notation. • There are 2 ways to write numbers. • Standard Scientific Notation Notation

  9. Different ways to write numbers • There are several different ways to write numbers. • Standard Notation- This method is just writing a number like 2,500,000 or 0.00912 or 5 • Scientific Notation- This notation is written as a product of a decimal and base 10. For example, 2.2 X 108

  10. Standard Scientific NotationNotation Regular Numbers A product of a decimal mulitiplied by 10 raised to a certain power. For Example: 3,250,000 = 3.25 x 106 “Three million 2 hundred fifty thousand”

  11. Scientific Notation A number written in scientific notation is the product of two factors: a decimal greater than or equal to 1 but less than 10 multiplied by a power of 10. This is the official definition of Scientific Notation.

  12. So what does that mean???? • Practical reasoning is we use base 10 with a power because our decimal number system is based on 10. • The first decimal number has a number in the 1’s place only…. Greater than 0 but less than 10. • Find the decimal point in a number if it is a big number (greater than 10) move the decimal point until a number is in the 1’s place and then use the number of spaces moved as the power for 10.

  13. For example: 3,245, 000 ( three million two hundred forty five thousand) • Find the decimal point: 3,245,000. • Move the decimal point until a number is in the ones place greater than 0 but less than 10. 3,245,000. = 3.245 Count the number of spaces the decimal moved and this is your power on the 10. This decimal moved 6 spaces Resulting in - 3.245 x 106 3,245,000 = 3.245 x 106

  14. Examples : 6,700 = 6.7 x 103 8,200,000,000,000,000 = 8.2 x 1015 2,789,111,000 = 2.789111 x 109 60 = 6.0 x 101

  15. Imagine…..

  16. You are a microbiologist studying cells, viruses and bacteria. • Or you are a chemist studying atoms, molecules, protons, electrons and neutrons. • These things can be very, very, VERY small.

  17. How small is small? • The diameter of a proton is 0.000000000000002 m ( “Two quadrillionths of a meter”) What does that mean????? Take a meter stick and cut it into a quadrillion equal parts and the proton is the same size a two of them. And the proton is the LARGEST of all three charged particles identified in an atom.

  18. An Electron is 0.000000000000000002 m ( 2 quintillionth of a meter…… even smaller than the proton!!!!!!!!) The average Carbon atom is 0.000000000143m (said “One hundred forty three trillionths”)

  19. The average virus… you know like a cold virus…. etc is….. 0.000001m *** you write this one in words*** • A grain of salt is 0.01m *** you write this one in words***

  20. Mycoplasma is so small….. They estimate a 1 billion of them can fit on the head of a pin… A pin head is 0.0001m

  21. Scientific Notation for numbers smaller than 1 • Decimals can be written in scientific notation too. • These numbers are written the same way except the power on the 10 is negative. • For example: 0.003 in standard notation is written 3.0 x 10-3

  22. How to? • Once again find the decimal point first- 0.000021 (said “twenty one millionths”) • Move the decimal point until a number greater than 0 but less than 10 is in the ones place. 0.000021 = 2.1 Count the number of spaces the decimal point moved and this number is your power. In this example, the decimal point moved -5 Final answer- 0.000021 = 2.1 x 10-5

  23. Examples 0.02 = 2.0 x 10-2 0.0000000123 = 1.23 x 10-8 0.00104 = 1.04 x 10-3 0.00000000000000000009 = 9.0 x 10-20

  24. Converting from Scientific to Standard To convert from Scientific Notation to Standard Notation use the following guidelines. • Check the power…. If the power is POSITIVE you have a large number ( greater than or equal to 1). If you have a NEGATIVE power you have a small number ( less than 1).

  25. 2. Move the decimal point the number of spaces indicated by the number of the power…. Moving to the RIGHT for POSITIVE Powers and to the LEFT for NEGATIVE Powers

  26. Examples: 8.16 x 105 ( positive power = big number = move 5 spaces to the right.) 8.16 x 105 = 8.16 = 816,000. Answer? 816,000 (eight hundred sixteen thousand) CHECK: 816,000 is a BIG number.

  27. Examples cont…. 8.16 x 10-5 ( negative power = small number = move 5 spaces to the left.) 8.16 x 10-5 = 8.16 =.0000816 Answer? 0.0000816 (eight hundred sixteen hundred millionths) CHECK: 0.0000816 is a SMALL number.

  28. Now you try……

  29. Name______________________ Date_______ Directions- Complete each section. Rewrite in standard notation. 1. 5.0 x 10 5 2. 5.0 x 10 -3 3. 5.0 x10 -6 4. 5.0 x10 2 Rewrite in scientific notation. 5. 50 6. .0014 7. 246, 000 Order in descending order ( least to greatest). 8. 4.1 x 10 -2 9.5 x 10 -6 8.0 x 10 4 1.1 x 10 10 9. 6.9 x 10 3 6.94 x103 2.1 x 10 5 2.0 x 106 • 1.23 x 10 -4 1.23 x 10 -5 1.23 x10 -2 1.23 Bonus: 8.0 x 100

  30. All finished !!!!!!!!

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