SIGNIFICANT FIGURES

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SIGNIFICANT FIGURES

• A measurement always has some degree of
  uncertainty. The uncertainty of a measurement
  depends on the measuring device.

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• The numbers recorded in a measurement (all the
  certain numbers plus the first uncertain number)
  are called significant figures. The first
  uncertain number is an estimated number. Only one
  uncertain number is allowed in a measurement. The
  uncertainty in the last number is assumed to be
  1 unless otherwise indicated. For example 1.86
  grams can be interpreted as 1.86 0.01 grams.

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RULES FOR COUNTINGSIGNIFICANT FIGURES

• 1. Nonzero integers or the numbers 1-9. Nonzero
  integers always count as significant figures.

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• 2. Zeros. There are three classes of zeros
• a. Leading zeros are zeros that precede all of
  the nonzero digits. They never count as
  significant figures.
• b. Captive zeros are zeros that fall between
  nonzero digits. They always count as significant
  figures.

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• c. Trailing zeros are zeros at the right end of
  the number. They are significant only if the
  number contains a decimal.

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• 3. Exact numbers. Often calculations involve
  numbers that were not obtained using measuring
  devices but were determined by counting 12 eggs,
  3 oranges. Such numbers are exact numbers. They
  have an unlimited number of significant figures.
  Exact numbers can also arise from definitions.
  For example, 1 inch is defined as exactly 2.54
  centimeters.

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RULES FOR ROUNDING OFF

• 1. Use only the first number to the right of the
  last significant figure.

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• 2. Follow regular rounding off rules for numbers
  from 1-4 and 6-9. 1-4 leave significant figure
  the same and 6-9 increase significant figure by
  one.

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• 3. For rounding off 5's, round up to make the
  number is even.

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• 4. In a series of calculations, carry the extra
  digits through to the final result and then round
  off. This means that you should carry all of the
  digits that show on your calculator until you
  arrive at the final number and then round off,
  using the procedures in rules 1 and 2.

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RULES FOR USINGSIGNIFICANT FIGURES IN
CALCULATIONS

• For multiplication or division, the number of
  significant figures in the result is the same as
  that in the measurement with the smallest number
  of significant figures. We say this measurement
  is limiting because it limited the number of
  significant figures in the result.

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• 2. For addition or subtraction, the limiting term
  is the one with the smallest number of decimal
  places.

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• NOTE For multiplication and division,
  significant figures are counted. For addition and
  subtraction, the decimal places are important.