# Scientific Notation Remember how?.  The coefficient must be greater than or equal to 1 and less than 10.  Must be base 10  The exponent shows the number.

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Scientific Notation Remember how?

 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

 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

 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

 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

 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.

 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

 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.

 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.

 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

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

Dividing in Scientific Notation

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

 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

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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