Bell Work How many significant figures

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Bell WorkHow many significant figures?

• 1.) 4.0 cm
• 2.) 7.05 cm
• 3.) .033 m
• 4.) .01
• 5.) 78.21g
• 6.) 5.40 g
• 7.) 225 cm
• 8.) 0.930 m

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Uncertainty in Measuring
When measuring an object with a uncalibrated
meter stick the actual length of the object can
only be estimated and only to the nearest 10th of
a meter (one significant figure)
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Uncertainty in Measuring
The meter stick in the example above is
calibrated in tenths of a meter. We can easily
see that the red object is greater than .2
meters, but less than .3 meters. In this
situation it is necessary to estimate to the
nearest hundredth of a meter. The object is
somewhere between .21 meters and .24 meters, so
.23 meters seems to be a reasonable estimate of
the objects length. How many significant figures
does this estimate contain? Which measurement
(the one measured with the uncalibrated meter
stick or this one is more accurate? Explain
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Significant Digits in Measurement

• Rule The digits in a measurement that are
  considered significant are the ones that
  represent marked calibrations on the meter stick
  or measuring device PLUS one additional digit to
  represent the estimated digit.

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Rules for Zero

• The zero in the following measurement is
  considered significant because it has a digit
  before and after it 303 meters. How many
  significant figures are in this measurement?
• When a decimal point is involved, all zeros that
  follow a number are considered significant. How
  many significant figures are in 74.00 gram?

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Rules for Zero Contd

• If there is no decimal point, any zero that
  follows a number is merely a placeholder and not
  significant. How many significant figures are
  included in the following measurement 180 mL?
• Zeros that appear to the right of the decimal
  point, before a number are not significant (they
  are also considered place holders). How many
  significant figures would be included in the
  following number - .00830 meters?

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Multiplying and Dividing Measured Numbers

• Rule of Thumb The result should have as many
  digits as the measured number with the fewest
  digits.
• Calculate one additional number so you can round
  your answer

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Division

• 1.) 125
• 23.7
• 2.) 20.5
• 51.0
• 3.) 0.065
• 32.5
• 4.) 1.23
• 0.72

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Multiplication

• 1.) 4.72 X 0.52
• 2.) 6.3 X 10.08
• 3.) 3.01 X 5.00 X 25.62
• 4.) 1.55 X 2.61 X 5.3

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Addition and Subtraction of Measured Numbers

• Rule of Thumb
• Make sure that all of the measurements are in
  the same units (mm, cm, degrees, etc.)
• The sum or difference may have no more decimal
  places than the least number in the measurements

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• Write one addition and one subtraction problem
  keeping this rule in mind.
• Switch with the student across from you and solve!