Warm Up Simplify.

8-2 Scientific Notation Objective: Express numbers in scientific notation and standard notation. Find products and quotients of numbers expressed in scientific notation. January 27, 2010

Answers to Homework ; c

When dealing with very large and small numbers, we use scientific notation.

A number is expressed in scientific notation when it is written as a product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10. A number in scientific notation is written as, where and n is an integer.

Steps in writing in standard form: 1. Determine whether n is positive or negative. 2. If n is positive, move the decimal point to the right n places. If n is negative, move the decimal point to the left n places. 3. Add zeros, decimal point, and/or commas as needed.

Examples: Write in standard form x x 10 5

x x 10 7

10^2 - HundredHundred 10^3 - ThousandThousand 10^6 - MillionMillion 10^9 - BillionBillion 10^12 -TrillionTrillion 10^15 - QuadrillionQuadrillion 10^18 - QuintillionQuintillion 10^21 - SextillionSextillion 10^24 - SeptillionSeptillion 10^27 - OctillionOctillion 10^30 - NonillionNonillion 10^100 - GoogolGoogol

Little Known Facts: 1. The number of grains of sand on the beach at Coney Island is about 10^20.sandConey Island 2. A googol is 10^100. The number of raindrops that has fallen on New York City in a century is much less than a googol.raindropsNew York Citycentury 3. The number of snow crystals needed to form the Ice Age was probably around 10^30snow crystalsIce Age 4. If the entire universe was filled with protons and electrons, the total number would be like 10^110.universeprotons and electrons 5. Assuming that you could count to 200 in one minute, that you deside to count for 12 hours a day at this rate, and that you don't have anything better to do, it would take you 19,024 years, 68 days, 10 hours, and 40 minutes to count to 1 billion (10^9).don't have anything betterbillion

Situations giving Rise to Scientific Notation Numerals.Scientific Notation Situation Scientific Notation X-RayX-Ray frequencies 1 x 10^16 (vibrations/second) Bottles of Champagne consumed by the x 10^8Champagne FrenchFrench yearly Number of toothbrushes purchased by 2.8 x 10^8toothbrushes Americans yearly Number of candles it would take to reproduce 3.01 x 10^27candles Sunlight

Grains of sand on Miami Beach 1.7 x 10^14Miami Beach Weight (in tons) of all the water on Earth 1.97 x 10^18waterEarth Number of people in the world who speak 6.5 x 10^8 Mandarin Mandarin Length of a Hemoglobin molecule 6.8 x 10^-6Hemoglobin molecule The mass of the hydrogen atom (in grams) 1.66 x 10^- 24hydrogen Number of ways to arrange 52 ordinary x 10^67 playing cards

Steps in writing in Scientific Notation: 1. Move the decimal so that it is to the right of the first nonzero digit. 2. Make note of how many places n and the direction you moved the decimal. 3. If moved to the left, write with positive exponent. If moved to the right, write with negative exponent.

Write in scientific notation ,022,000,000,000

, 592,039

Scientific Notation on the calculator: 2nd then comma (EE) USE PARENTHESES ALWAYS!!!

Examples: Simplify. 1. 2(7 x ) (6.4 x 10 4 )

Classwork – Workbook page 98 # 2-44 even, #46-51 Homework - page even