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Scientific Notation Definition: A method of expressing numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10. Example: The Scientific Notation for 10,492 is 1.0492 X 10 . Show You Tube Video How it works • 10 x 10 = 100 or 10 • Working the other way • 100. • Now move the decimal to the left two places so you have • 1. X 10 or 1 X 10 x10 Going the other way. • Lets say you have a very small number for example • .000005 • Move the decimal to the right and then count the number of time you moved it. 5. X 10 What is happening is 5. x 1 10 x 10 x 10 x 10 x10 x 10 x 10 Application • Scientific Notation is used to easily describe very large and very small things. Most of the time it is used by Scientists. For example if you are studying the size of the planets in the solar system it may be easier to communicate with Scientific Notation. If you are studying Chemistry and are trying to describe atomic mass it is easier to communicate in Scientific Notation. Example • Chemistry (Avogadro’s number) • A Mole = 6.02 X 10 This is the number of atoms or one mole of atoms per 12 grams of carbon 12. The circle represents one Mole and contains many atoms inside of it. Show Khan Video Things to consider • In Avogadro’s number are there a lot or little atoms inside of a Mole? • How do you know? • Is a mole large or small? Example 2 Covert to Scientific Notation • • • • • • • • • • Planet Distance (from Sun) Diameter Mercury 57,910,000 km...0.39 A.U. 4,800 km Venus 108,200,000 km...0.72 A.U. 12,100 km Earth 149,600,000 km...1.00 A.U. 12,750 km Mars 227,940,000 km...1.50 A.U. 6,800 km Jupiter 778,330,000 km...5.20 A.U. 142,800 km Saturn 1,429,400,000 km...9.50 A.U. 120,660 km Uranus 2,870,990,000 km...19.20 A.U. 51,800 km Neptune 4,504,300,000 km...30.10 A.U. 49,500 km Pluto 5,913,520,000 km...39.50 A.U. 3,000 km • Definition: Astronomical Unit (AU) : The average distance from the Earth to the Sun. One AU = 93 million miles or 149.6 million km. At 100 mph (160 kph) it would take more than 100 years to go 1 AU. Converted • • • • • • • • • • Solution: Mercury 5.7x107 4.8x103 Venus 1.082x108 1.21x104 Earth 1.496x108 1.275x104 Mars 2.2794x108 6.8x103 Jupiter 7.7833x108 1.428x105 Saturn 1.4294x109 1.2066x105 Uranus 2.87099x109 5.18x104 Neptune 4.5043x109 4.95x104 Pluto 5.91352x109 3x103 Practice Convert to Scientific notation 1) 45,321 3) .0000256 2) .000083 4) 89,627,235