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Scientific Notation Learning Targets: 12. I can determine which numbers in a measurement are significant and use these rules to make precise calculations. 13. I am able to convert values from standard form into scientific notation and vise-versa How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation. 2.1 x 1023 When using Scientific Notation, there are two kinds of exponents: positive and negative Positive Exponent: 2.35 x 108 Negative Exponent: 3.97 x 10-7 An easy way to remember this is: • If an exponent is positive, the number gets larger, so move the decimal to the right. • If an exponent is negative, the number gets smaller, so move the decimal to the left. When changing scientific notation to standard notation, the exponent tells you how you should move the decimal: With a positive exponent, move the decimal to the right: 4.08 x 103 = 4 0 8 Don’t forget to fill in your zeroes! The exponent also tells how many spaces to move the decimal: 4.08 x 103 = 4 0 8 In this problem, the exponent is +3, so the decimal moves 3 spaces to the right. When changing scientific notation to standard notation, the exponent tells you how you should move the decimal: With a negative exponent, move the decimal to the left: 4.08 x 10-3 = 408 Don’t forget to fill in your zeroes! The exponent also tells how many spaces to move the decimal: 4.08 x 10-3 = 408 In this problem, the exponent is -3, so the decimal moves 3 spaces to the left. Try changing these numbers from Scientific Notation to Standard Notation: 1) 9.678 x 104 96780 2) 7.4521 x 10-3 .0074521 3) 8.51 x 107 85,100,000 4) 4.09 x 10-5 .0000409 When changing from Standard Notation to Scientific Notation: 1) First, write only the sig figs in the number. Move the decimal after the first sig fig: 3258 2) Second, add your multiplication sign and your base (10). 3 . 2 5 8 x 10 3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10 3 3 2 1 When changing from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one. – If the number is greater than one, the exponent will be positive. 348943 = 3.48943 x 105 – If the number is less than one, the exponent will be negative. .0000000672 = 6.72 x 10-8 Try changing these numbers from Standard Notation to Scientific Notation: 1) 9,070,000 9.07 x 106 2) .0000345 3.45 x 10-5 3) .08376 8.376 x 10-2 4) 5,670 5.67 x 103 Scientific Notation Math Multiplication - multiply the numbers, add the indices 1.2 x 104 multiplied by 5 x 106 = Division - divide the numbers, subtract the indices 5.5 x 108 divided by 1.1 x 102 = Convert the following numbers between standard form and scientific notation: 329 1.7 x 103 700,000 2.4503 x 105 20090 0.000034 0.01023 123.4 45.607 7.9 x 1011 2.8 x 10-3 7.45 x 10-1 2.3 x 10-7 Convert the following numbers/sums into correct scientific notation: 3.59 x 103 3,590 5.56 x 106 5,560,000 2.2 x 10-3 0.0022 3.48 x 10-4 0.000348 1.805 x 105 180,500 3.04 x 10-7 0.000000304 On a Calculator 10X • Locate these buttons: ^ , 2nd , LOG , • Scientific Standard given 1.2 x 105 – 1.2 x 10 5 = 120,000 ^ 10X – 1.2 2nd LOG 5 = 120,000 • Standard Scientific given 120,000 Sci/Eng – 120,000 = DRG select Sci = Sci/Eng – To undo: DRG select Flo = Sci/Eng DRG