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Scientific Notation

Scientific Notation. Remember how?. Rules of Scientific Notation. 4.23 x 10 5 coefficient base exponent . The coefficient must be greater than or equal to 1 and less than 10. Must be base 10

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Scientific Notation

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  1. Scientific Notation Remember how?

  2. Rules of Scientific Notation 4.23x105 coefficientbaseexponent 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)

  3. BAD EXAMPLES These are all BAD EXAMPLES of scientific notation. DON’T DO THESE!!

  4. Scientific Notation  Standard • 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 105 367000 • If the exponent is NEGATIVE, move the decimal LEFT • Add place-holder zeroes as needed • EX: 7.25 x 10-3 0.00725

  5. Example 1 6 9 0 0 x 10 4 1 0 3 2 Once you get to 100, you’re at the standard number. When recording an answer, DO NOT put the 100. Leave it out. Remember: x100 means x1 Write 1.69 x 104 as a standard number

  6. Example 0 0 0 4 2 3 x 10 -3 -1 -2 0 Once you get to 100, you’re at the standard number. When recording an answer, DO NOT put the 100. Leave it out. Remember: x100 means x1 Also, for neatness, it’s best to include the leading zero before the decimal. Write 4.23 x 10-3 as a standard number

  7. Standard  Scientific Notation • 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 103 • If you move the decimal RIGHT, the exponent is NEGATIVE • EX: 0.00058  5.8 x 10-4

  8. Example 0 1 2 3 4 5 7 8 0 3 7 4 2 x 10 7. Is a number between 1 and 10. We needed to move the decimal 5 times to the left, so the exponent became 105. Write 780374.2 in scientific notation.

  9. Example 0 -1 -2 -3 0 0 0 6 2 3 5 x 10 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. Write 0.006235 in scientific notation.

  10. Multiplying in Scientific Notation • Example: 3.2 x 104 x 8.7 x 105 • Rules: • MULTIPLY the coefficients together like usual • 3.2 x 8.7 = 27.84 • ADD the exponents together • 104 x 105 = 109 • Readjust for proper scientific notation, if needed • 27.84 x 109 2.784 x 1010

  11. Multiplication Practice Problems

  12. Dividing in Scientific Notation • Example: • DIVIDE the coefficients like usual (top divided by bottom) • SUBTRACT the exponents (top # – bottom #) • Readjust for proper scientific notation, if needed • 0.573 x 104  5.73 x 103

  13. Division Practice Problems

  14. Scientific Method with Units • 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.

  15. Practice Problems with Units

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