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Scientific Notation When you are given a number in scientific notation it will always be the number times 10 raised to an exponent This is to help write big numbers in an easier to read way! A. When converting from scientific notation to standard form (the whole entire number) you will: -move the decimal point to the right if the exponent is positive: Ex. 3.25 x 102 = 325 (moved the decimal to the right 2 places since the exponent was a positive 2) Ex. 3.6 x 105 = 360000 (moved the decimal to the right 5 places since the exponent was a positive 5) ***notice since there weren’t any other whole numbers after the 6 I added zeroes for each additional place the decimal was moved -move the decimal point to the left if the exponent is negative: Ex. 4.36-2 = .0436 (moved the decimal to the left 2 places since the exponent was a negative 2) ***notice since there was only one whole number to the left of the decimal, I added a zero for the additional place the decimal was moved. Ex. 5.346-4 = .0005346 B. When converting from standard form to scientific notation you will: - move the decimal point to the left if it is a whole number until the decimal is behind the first digit. Ex. 436 = 4.36 x 102 (moved the decimal point to the left behind the 4 then said that it would be times 10 to the 2nd because I moved the decimal 2 places to the left) ***It is a positive power because you started with a whole number Ex. 5079 = 5.079 x 103 - move the decimal point to the right if it is a decimal (# less than 1) to start with until it is behind the first number other than zero. Ex. .00217 = 2.17 x 10-3 (moved the decimal point to the right behind the 2 then said it would be times 10 to the -3 because I moved the decimal 3 places) *****It is negative because you started with a decimal (# less than 1) Ex. .0000893 = 8.93 x 10-5 NAME ________________________________________ DATE ______________ PERIOD Practice: Skills Scientific Notation Write each number in standard form. 1. 6.7 x 101 2. 1.6 x 103 3. 2.91 x 105 4. 3.35 x 10-1 5. 1.49 x 10-7 6. 5.2277 x 10-3 7. 3.46 x 102 8. 8.651 x 107 9. 7.3 x 10-6 11. 4.0027 x 10-4 12. 8.50284 x 10-2 Write each number in scientific notation. 13. 34 14. 79,700 15. 4,733,800 16. 0.00916 17. 0.00000571 18. 0.0121 19. 273 20. 6,590 21. 2,204,000,000 22. 0.29 23. 0.0008331 24. 0.00000018 _____ Practice: Word Problems Scientific Notation 1. MEASUREMENT There are about 25.4 millimeters in one inch. Write this number in scientific notation. 2. POPULATION In the year 2000, the population of Rahway, New Jersey, was 26,500. Write this number in scientific notation. 3. MEASUREMENT There are 5,280 feet in one mile. Write this number in scientific notation. 4. PHYSICS The speed of light is about 1.86 x 105 miles per second. Write this number in standard notation. 5. COMPUTERS A CD can store about 650,000,000 bytes of data. Write this number in scientific notation. 6. SPACE The diameter of the Sun is about 1.39 x 109 meters. Write this number in standard notation. 7. ECONOMICS The U.S. Gross Domestic Product in the year 2000 was 9.87 x 1012 dollars. Write this number in standard notation. 8. MASS The mass of planet Earth is about 5.98 x 1024 kilograms. Write this number in standard notation.