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Scientific Notation Remember how?

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The coefficient must be greater than or equal to 1 and less than 10. Must be base 10 The exponent shows the number of places the decimal must be moved to change the coefficient to a standard number A standard number exists when the exponent is zero (0) Rules of Scientific Notation 4.23 x 10 5 coefficient base exponent

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These are all BAD EXAMPLES of scientific notation. DON’T DO THESE!! BAD EXAMPLES ExampleWhy it’s incorrectCorrected 0.34 x 10 7 Coefficient is not between 1 and 10 3.4 x 10 6 25 x 10 -5 Coefficient is not between 1 and 10 2.5 x 10 -4 4.74 x 2 8 Not base 10 (we won’t be solving for these) 4.74 x 256 = 1213.44 = 1.21344 x 10 3

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When going from scientific notation to standard, do the following If the exponent is POSITIVE, move the decimal RIGHT Add place-holder zeroes as needed EX: 3.67 x 10 5 367000 If the exponent is NEGATIVE, move the decimal LEFT Add place-holder zeroes as needed EX: 7.25 x 10 -3 0.00725 Scientific Notation Standard

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Write 1.69 x 10 4 as a standard number Example 1 6 9 0 0 x 10 4 32 10 Once you get to 10 0, you’re at the standard number. When recording an answer, DO NOT put the 10 0. Leave it out. Remember: x10 0 means x1

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Write 4.23 x 10 -3 as a standard number Example 0 0 0 4 2 3 x 10 -3 -2 0 Once you get to 10 0, you’re at the standard number. When recording an answer, DO NOT put the 10 0. Leave it out. Remember: x10 0 means x1 Also, for neatness, it’s best to include the leading zero before the decimal.

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When going from standard to scientific notation, do the opposite as before, so: If you move the decimal LEFT, the exponent is POSITIVE EX: 8976 8.976 x 10 3 If you move the decimal RIGHT, the exponent is NEGATIVE EX: 0.00058 5.8 x 10 -4 Standard Scientific Notation

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Write 780374.2 in scientific notation. Example 7 8 0 3 7 4 2 x 10 012345 7. Is a number between 1 and 10. We needed to move the decimal 5 times to the left, so the exponent became 10 5.

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Write 0.006235 in scientific notation. Example 0 0 0 6 2 3 5 x 10 0-2-3 6 is a number between 1 and 10. We needed to move the decimal 3 times to the right, so the exponent became 10 -3. Get rid of any leading zeroes.

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Example: 3.2 x 10 4 x 8.7 x 10 5 Rules: MULTIPLY the coefficients together like usual 3.2 x 8.7 = 27.84 ADD the exponents together 10 4 x 10 5 = 10 9 Readjust for proper scientific notation, if needed 27.84 x 10 9 2.784 x 10 10 Multiplying in Scientific Notation

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Multiplication Practice Problems ProblemWorkTemp AnswerFINAL Answer 4.8 x 10 3 2.3 x 10 12 4.8 2.3 = 11.04 10 3 10 12 = 10 (3 + 12) = 10 15 11.04 x 10 15 Can’t leave 11 1.104 x 10 16 3.6 x 10 -4 2.1 x 10 3 3.6 2.1 = 7.56 10 -4 10 3 = 10 (-4 + 3) =10 -1 7.56 x 10 -1 The 7 is ok 7.56 x 10 -1 2.65 x 10 -5 7.3 x 10 -7 2.65 7.3 = 19.345 10 -5 10 -7 = 10 (-5 + -7) = 10 -12 19.345 x10 -12 Can’t leave 19 1.9345 x 10 -11 9.56 x 10 6 9.8 x 10 -4 9.56 9.8 = 93.688 10 6 10 -4 = 10 (6 + -4) = 10 2 93.688 x10 2 Can’t leave 93 9.3688 x 10 3 2.1 x 10 3 7.22 x 10 -19 2.1 7.22 = 15.162 10 3 10 -19 = 10 (3 + -19) = 10 -16 15.162 x10 -16 Can’t leave 15 1.5162 x 10 -15

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Dividing in Scientific Notation

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Division Practice Problems ProblemWork (coeff)Work (exp)Temp AnswerFINAL Answer 1.36 x 10 -5 0.815 x 10 4 8.15 x 10 3 0.385 x 10 -1 3.85 x 10 -2 1.51 x 10 3 0.488 x 10 16 4.88 x 10 15

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Metric units have assigned values. When calculating with those values, replace the unit with its value, then solve. The values are NOT the same as the ones for the factor label conversions This is because they are absolute values, not comparisons to the base unit. Scientific Method with Units UnitValueSampleEquivalent (Scientific) Equivalent (Standard) kilo-10 3 6.27 kg6.27 x 10 3 g6270 g mega-10 6 2.3 MHz2.3 x 10 6 Hz2300 000 Hz nano-10 -9 7.4 nm7.4 x 10 -9 m0.000 000 007 4 m

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Practice Problems with Units ProblemEquivalentWork (coeff)Work (exp)Answer 12 x 10 3 1.2 x 10 4 g 4.42 x 10 -3 m (or 4.42 mm) 2.3 ks 16 s2.3 16 = 36.810 3 10 0 = 10 3 36.8 x 10 3 3.68 x 10 4 0.4 kHz 98 mHz 0.4 x 10 3 98 x 10 -3 0.4 98 = 39.2 10 3 10 -3 = 10 0 39.2 x 10 0 3.92 x 10 1 Hz

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