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SCIENTIFIC NOTATION

SCIENTIFIC NOTATION. A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS. Mathematicians are Lazy!!!. They decided that by using powers of 10, they can create short versions of long numbers.

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SCIENTIFIC NOTATION

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  1. SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALLNUMBERS.

  2. Mathematicians are Lazy!!! They decided that by using powers of 10, they can create short versions of long numbers.

  3. Scientific Notation is used to express the very large and the very small numbers so that problem solving will be made easier. Examples: The mass of one gold atom is .000 000 000 000 000 000 000 327 grams. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms. Scientists can work with very large and very small numbers more more easily if the numbers are written in scientific notation.

  4. Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 105 is not in proper scientific notation. Why?

  5. How to Use Scientific Notation • In scientific notation, a number is written as the product of two numbers….. …..a coefficient and 10 raised to a power.

  6. For example: 4.5 x 103 The number 4,500 is written in scientific notation as ________________. The coefficient is _________. 4.5 The coefficient must be a number greater than or equal to 1 and smaller than 10. The power of 10 or exponent in this example is ______. 3 The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

  7. Rules to Remember! If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. positive left

  8. Rules to Remember! If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. negative right

  9. A number will have an exponent of zero if: ….the number is equal to or greater than 1, but less than 10.

  10. To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive.

  11. Soooo 137,000,000 can be rewritten as 1.37 X 108

  12. Now You Try Using scientific notation, rewrite the following numbers. 347,000. 3.47 X 105 902,000,000. 9.02 X 108 61,400. 6.14 X 104

  13. Convert these: 1.23 X 105 123,000 6.806 X 106 6,806,000

  14. Try These 4,000 4 X 103 2.48 X 103 2,480 6.123 X 106 6,123,000 306,000,000 3.06 X 108

  15. In the United States, 15,000,000 households use private wells for their water supply. Write this number in scientific notation. 1.5 X 107

  16. The U.S. has a total of 1.2916 X 107 acres of land reserved for state parks. Write this in standard form. 12,916,000 acres

  17. Why does a Negative Exponent give us a small number? 10000 = 10 x 10 x 10 x 10 = 104 1000 = 10 x 10 x 10 = 103 100 = 10 x 10 = 102 10 = 101 1 = 100 Do you see a pattern?

  18. Sooooo = 10-1 = = 10-2 = = 10-3 == 10-4

  19. Your Turn Using Scientific Notation, rewrite the following numbers. 0.000882 8.82 X 10-4 0.00000059 5.9 X 10-7 0.00004 4 X 10-5

  20. More Examples 1) 0.0004 4 X 10-4 2) 1.248 X 10-6 .000001248 3) 6.123 X 10-5 .00006123 4) 0.00000306 3.06 X 10-6 5) 0.000892 8.92 X 10-4

  21. The nucleus of a human cell is about 7 X 10-6 meters in diameter. What is the length in standard notation? .000007

  22. A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation. 3 X 10-9

  23. Put these numbers in scientific notation. ANSWERS PROBLEMS • 1.2 x 10-4 • 1 x 103 • 1 x 10-2 • 1.2 x 101 • 9.87 x 10-1 • 5.96 x 102 • 7.0 x 10-7 • 1.0 x 106 • 1.26 x 10-3 • 9.88 x 1011 • 8 x 100 • .00012 • 1000 • 0.01 • 12 • .987 • 596 • .000 000 7 • 1,000,000 • .001257 • 987,653,000,000 • 8

  24. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMS ANSWERS • 4.9 X 102 • 3.75 X 10-2 • 5.95 X 10-4 • 9.46 X 103 • 3.87 X 101 • 7.10 X 100 • 8.2 X 10-5 • 490 • .0375 • .000595 • 9460 • 38.7 • 7.10 • .000082

  25. Addition and Subtraction To add or subtract numbers written in scientific notation, you must….express them with the same power of ten. Sample Problem: Add (5.8 x 103) and (2.16 x 104) Solution: Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5.8 x 103 = .58 x 104 so .58 x 104 + 2.16 x 104 =? Answer: 2.74 x 104

  26. Multiplication When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105) Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5 Answer: 6.7 x 102

  27. Division Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6.4 x 106) by (1.7 x 102) Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2 Answer: 3.8 x 104

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