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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.

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Presentation on theme: "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."— Presentation transcript:

1 Scientific Notation Remember how?

2  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

3  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 x x Coefficient is not between 1 and x x 2 8 Not base 10 (we won’t be solving for these) 4.74 x 256 = = x 10 3

4  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   If the exponent is NEGATIVE, move the decimal LEFT  Add place-holder zeroes as needed  EX: 7.25 x  Scientific Notation  Standard

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

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

7  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  x 10 3  If you move the decimal RIGHT, the exponent is NEGATIVE  EX:  5.8 x Standard  Scientific Notation

8  Write in scientific notation. Example x Is a number between 1 and 10. We needed to move the decimal 5 times to the left, so the exponent became 10 5.

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

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

11 Multiplication Practice Problems ProblemWorkTemp AnswerFINAL Answer 4.8 x x = = 10 (3 + 12) = x Can’t leave x x x = = 10 (-4 + 3) = x The 7 is ok 7.56 x x x = = 10 ( ) = x Can’t leave x x x = = 10 (6 + -4) = x10 2 Can’t leave x x x = = 10 ( ) = x Can’t leave x

12 Dividing in Scientific Notation

13 Division Practice Problems ProblemWork (coeff)Work (exp)Temp AnswerFINAL Answer 1.36 x x x x x x x x 10 15

14  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 kg6.27 x 10 3 g6270 g mega MHz2.3 x 10 6 Hz Hz nano nm7.4 x m m

15 Practice Problems with Units ProblemEquivalentWork (coeff)Work (exp)Answer 12 x 10 3  1.2 x 10 4 g 4.42 x m (or 4.42 mm) 2.3 ks 16 s = = x 10 3  3.68 x kHz 98 mHz 0.4 x x = = x 10 0  3.92 x 10 1 Hz


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