Accuracy, Precision, Signficant Digits and Scientific Notation

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Accuracy, Precision, Signficant Digits and
Scientific Notation
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Accuracy and Precision

• Accuracy refers to how close a given quantity
  is to an accepted or expected value (page 19)
• Precision refers to how exact a measurement is.
  It also refers to how close measurements are to
  each other (see page 16 and 19)

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Example
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Watch the following video clip

• video

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Rules for Significant Digits

• Digits from 1-9 are always significant.
• Zeros between two other significant digits are
  always significant
• One or more additional zeros to the right of both
  the decimal place and another significant digit
  are significant.
• 4. Zeros used solely for spacing the decimal
  point (placeholders) are not significant.

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Examples of Significant Digits
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Multiplying and Dividing

• RULE When multiplying or dividing, your answer
  may only show as many significant digits as the
  multiplied or divided measurement showing the
  least number of significant digits

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Example When multiplying 22.37 cm x 3.10 cm x
85.75 cm 5946.50525 cm3We look to the
original problem and check the number of
significant digits in each of the original
measurements 22.37 shows 4 significant
digits.3.10 shows 3 significant digits.85.75
shows 4 significant digits.Our answer can only
show 3 significant digits because that is the
least number of significant digits in the
original problem. 5946.50525 shows 9 significant
digits, we must round to the tens place in order
to show only 3 significant digits. Our final
answer becomes 5.95 x 103 cm3.
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Scientific Notation

• Use this method to express large numbers and
  doing calculations by using powers of 10
• To do this, count the number of places you have
  to move the decimal point to yield a value
  between 1 and 10. This counted number is the
  exponent. The exponent is positive if the
  original number is greater than 10 and negative
  if the original number is less than 10
• Examples
• 150 000 000 000 is 1.5 x 1011m
• 0.000 000 000 050 is 5.0 x 10-11m

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Adding and Subtracting

• RULE When adding or subtracting your answer can
  only show as many decimal places as the
  measurement having the fewest number of decimal
  places.

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Example When we add 3.76 g 14.83 g 2.1 g
20.69 gWe look to the original problem to see
the number of decimal places shown in each of the
original measurements. 2.1 shows the least
number of decimal places. We must round our
answer, 20.69, to one decimal place (the tenth
place). Our final answer is 20.7 g
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Practice sig figs
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Practice Adding and substracting
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Practice Multiplying and dividing
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Rounding Rules

• If your answer ends in a number greater than 5,
  increase the preceding digit by 1.
• Example 2.346 can be rounded to 2.35
• 2. If your answer end with a number that is less
  than 5, leave the preceding number unchanged
• Example 5.73 can be rounded as 5.7

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Rounding rules continued

• 3. If you answer ends with 5, increase the
  preceding number by 1 if it is odd. Leave the
  preceding number unchanged if it is even.
• For example, 18.35 can be round to 18.4, but
  18.25 is rounded to 18.2