SCIENTIFIC MATH:

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SCIENTIFIC MATH

• Significant Digits/Standard Notation
• Scientific Notation

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SIGNIFICANT FIGURES

• With development of better measuring devices has
  come better precision.
• Calibration / Training
• Scientists indicate precision of measurements by
  the number of digits they report digits reported
  are significant figures.
• ex value of 3.52 g is more precise than value
  of 3.5 g.

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SIGNIFICANT FIGURES

• DEFINED
• Include all
• Known digits plus
• one estimated digit

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RULES FOR RECOGNIZING SIGNIFICANT FIGURES

• 1. Non-zero numbers always significant
• Ex 72.3 has 3 SF
• 2. Zeros between non-zero numbers always
  significant
• Ex 60.5 has 3 SF
• 3. All final zeros to the right of the decimal
  place are significant
• Ex 6.20

• 4. Zeros that act as placeholders are not
  significant
• -convert quantities to scientific notation to
  remove the placeholder zeros
• Ex 0.0253
• Ex 4320
• 5. Counting numbers and defined constants have an
  infinite number if SF
• Ex 6 molecules 60s 1 min

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SCIENTIFIC NOTATION

• 0.000000000000000000000000000167262 kg
• proton mass OR 1.627 62 X 10-27 kg
• 0.000000000000000000000000000000910939 kg
• electron mass OR 9.109 39 X 10-31 kg
• Extremely small or large numbers are hard to
  handle
• Convert to scientific notation to deal with this
  problem

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SN Examples

• 700 m 7 x 10 2
• 0.0054 kg 5.4 x 10 3
• 38 000 m 3.8 x 10 4
• 0.000 006 87 kg 6.87 x 10 6
• 4 500 000 m 4.5 x 10 6
• 0.000 000 076 kg 7.6 x 10 8
• 0.000 000 000 8 kg 8 x 10 -10
• 685 000 000 000 m 6.85 x 10 11

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SCIENTIFIC NOTATION

• SN expresses numbers as a multiple of two
  factors a number between 1 10 and ten raised
  to a power, or exponent.
• Exponent- tells how many times the first factor
  must be multiplied by ten.

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Precision and Accuracy

• When we make a measurement in the laboratory we
  need to know how good is the measurement. To this
  end, we introduce two concepts Precision and
  Accuracy.
• Precision indicates degree of reproducibility of
  a measured number how close a series of
  measurements are to one another
• Accuracy indicates how close your measurements
  are to the true value how close a measured value
  is to an accepted value
• Let's look at throwing darts and trying to hit
  the bullseye as an illustration of these two
  concepts.

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Precision and Accuracy