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Integrated Algebra NOTES: Scientific Notation Name Let’s review !! Scientific Notation is a short cut for writing very large or very small numbers. Scientific notation is the product of two factors: a decimal greater than or equal to 1 and less than 10: 1 ≤ d < 10 (basically there can only be one nonzero number in front of the decimal place) AND an integer power of 10. ex) 2.3 x 104 1.003 x 108 3 x 10-3 4.124 x 10-5 To write a number greater than 10 in Scientific Notation: - move the decimal point until there is only one non-zero number to the left of it - count how many places you moved the decimal point to the left - write the number of places the decimal moved as the exponent ex) 34,510,000. = 3.451 x 107 To write a number between 0 and 1 in Scientific Notation: - move the decimal point until there is only one non-zero number to the left of it - count how many places you moved the decimal point to the right - write the negative of the number of places the decimal moved as the exponent ex) .000357 = 3.57 x 10-4 To write a number from Scientific Notation to Standard form: - move the decimal place according to the exponent (a) if negative move it that many places to the left (b) if it is positive move it that many places to the right ex) 5.6 x 104 = 56,000 1.78 x 10-4 = .000178 Integrated Algebra More Review……….. When multiplying powers with the same base, keep the base add the exponents. When dividing powers with the same base, keep the base subtract the exponents. ex) 104 x 102 = 106 10-3 x 1012 = 109 10 7 = 102 10 5 105 10 9 Try: 106 x 10-4 = 10-14 10-8 x 10-2 107 102 10 3 105 Now that we’ve reviewed, we should be ready to multiply and divide in scientific notation. Multiplying Numbers in Scientific Notation 310 4 10 = 3 4 10 3 5 = 12 x 108 Try: (2 x x 109) 10-6)(5 3 105 Regroup (associative property) and use the rules for multiplying (6 x 10)(4 x 1012) Let’s see: (3.23 x 103)(3.4 x104) Write answer in scientific notation. 3.23 3.4 103 104 10.982 107 not in scientific notation 10.982 x 107 need to move decimal one more place to the left so need to add another power of ten 1.0982 x 108 Integrated Algebra Dividing Numbers in Scientific Notation 2.8 10 1.4 10 6 3 2.8 10 1.4 10 3 6 = Regroup and use rules for dividing each 2 10 3 Try: 3 10 1.5 10 4.6 10 2.5 10 8 7 2 2 **Don’t forget that if the product or quotient doesn’t end up in scientific notation, then you may need to put it in scientific notation. Read the directions and questions carefully to determine exactly how the question is to be answered. **Graphing Calculator** The Graphing Calculator can be used to put standard numbers into scientific notation and also scientific notation to standard form. Multiplication and Division can also be done with the Graphing Calculator. This is a great tool to check your answers. Remember if a scientific notation question is presented in a part II, III, or IV question on the regents, then your work must be shown. http://mathbits.com/mathbits/TISection/General/ScientificNotation.htm Integrated Algebra HOMEWORK: Scientific Notation Name Write each number in Scientific Notation. 1) 34,500,000 2) 5,004 3) .034 4) .0000056 5) .345 x 106 Write each number in Standard Form. 6) 6.34 x 106 7) 4.002 x 10-5 8) 1.9 x 10-4 9) 5 x 102 Write product or quotient in Scientific Notation. 10) 2 10 3 4 10 3.58 10 2 10 4 12) 2 11) 4.2 10 1.5 10 13) 6.2 10 1.8 10 8 6 3 4 3 14) The human eye blinks about 6.25 x 106 times each year. A 15 year old would have blinked how many times? Write your answer in Scientific Notation. 15) A single-celled organism is about 2 x 10-3 inches long. How many of these organisms would have to be lined up to make a foot?