Significant Figures

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Significant Figures
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Sig Figs

• The term Significant Figures aka Significant
  Digits refers to the digits that tell how
  accurately a measurement has been made.
• The more significant figures, the more precise
  your measurement becomes.

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Significant Figures

• The precision of the instrument determines the
  number of significant figures in the measurement.
• The number of significant figures is all the
  digits that can be known for certain 1 more
  that is estimated

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Significant Figures

• A ruler with centimeter divisions would not give
  us as accurate a measure of length as a ruler
  with millimeter divisions

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Sample metersticks
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Sample metersticks
Most precision
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Significant Figures cont.

• A meterstick is used to measure a pen and the
  measurement is recorded as 14.3 cm.
• This measurement has three valid digits two you
  are sure of, and one you estimated.
• The valid digits in a measurement are called
  significant figures aka digits.
• However, the last digit given for any measurement
  is the uncertain digit.

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Significant Figures cont.

• RULES you need to know
• All nonzero digits in a measurement are
  significant.
• Consider a measurement such as 25.68 m. It has 4
  significant figures and 7.93 would have 3.
• Leading zeros aka zeros to the left of the first
  nonzero are NEVER significant
  i.e. 0.389 3 sig figs, 0.0064
  cm 2 sig figs, 0.905 3 sig figs.

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Significant Figures cont.

• RULES you need to know
• Zeros between nonzeros Captives Zeros are
  significant. i.e. 205 3 sig. figures
• Trailing zeros, zeros after nonzeros at the end
  of a number are significant IF after a decimal.
  i.e. 63400 3 sig figs 0.63400 5 sig figs,
  800.00 5 sig figs.

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Significant Figures cont.

• RULES you need to know
• Scientific Notation - ALL digits are significant
  i.e. 2.500 x 103 4 sig. figures

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Significant Figures cont.

• When you perform any arithmetic operation, it is
  important to remember that the answer cannot have
  more sig. figs than the original measurement.
• To add or subtract measurements, first perform
  the operation, then round off the result to
  correspond to the least-precise value involved.

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Significant Figures cont.

• In addition and subtraction, the of sig. figs
  past the decimal in the answer cannot exceed the
  of sig. figs past the decimal in the LEAST
  precise measurement.
• 2.03 4.6 10.0925 16.7
• 18.073 - 5.21 12.86

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Remember

• When doing math operations, the answer cannot
  have more sig. figs than the original
  measurements.
• i.e. A room is 5.4 m x 12.9 m. The area is
  calculated at 69.66 m2 which is more sig. figs
  than the measurements, so round to 70 m2.

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Rounding

• Rounding look at the digit after the last sig.
  fig, if 5, add one to the last sig. fig, then
  drop, if 0-4, drop.

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Significant Figures cont.

• To multiply or divide measurements, perform the
  calculation and then round to the same number of
  significant digits as the least-precise
  measurement.
• i.e. 409.2 km / 11.4 L 35.9 km/L
• the least precise measure has 3
  significant figures
• Note that significant digits are considered only
  when calculating with measurements.

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Significant Figures cont.

• In multiplication and division, the total of
  sig. figs in the answer cannot exceed the TOTAL
  of sig. figs in the LEAST precise measurement.
• 8.05 x 1.3 11
• 23.07 / 4.93 4.68

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 23.30 cm 1843.02 L 2.00012 km
• 3.65 kg 8.701 oC 0.5 mL
• 365 kg 2000.12 mm 704000 hrs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 23.30 cm
• 4 sig figs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 1843.02 L
• 6 sig figs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 2.00012 km
• 6 sig figs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 3.65 kg
• 3 sig figs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 8.701 oC
• 4 sig figs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 0.5 mL
• 1 sig fig

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 365 kg
• 3 sig figs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 2000.12 mm
• 6 sig figs

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Practice

• Determine the number of significant figures in
  each of the following measurements
• 704000 hrs
• 3 sig figs

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A Story

• Marcus needed a cube of metal which had to have a
  mass of 83 g. He knew the density of metal was
  8.67 g/mL, which told him the cubes volume.
• He calculated the volume to be 9.573 mL and
  determined that the edge of the cube had to be
  2.097 cm.

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A Story

• Marcus took his plans to a machine shop to have
  his metal cube made. The foreman said, We can
  make this cube for you, but it will be
  expensive.
• Thats OK, Marcus replied, Its really
  important. After all, he had 50 he could spend.

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A Story

• Marcus returned to the machine shop the next day,
  expecting the job to be done. Sorry, said the
  foreman. Were still working on it. Stop by
  next week.
• So Marcus left.

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A Story

• Finally the day came, and foreman handed Marcus
  his cube. It looked very smooth and shiny and
  beautiful in its velvet case. Marcus said,
  Its perfect!
• Thatll be 500, the foreman said, We had a
  difficult job getting it right - we had to make
  three before we got it to your specifications.

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A Story

• But my friend only paid 25 for the same thing,
  Marcus said.
• The foreman responded, No. He wanted a cube 2.1
  cm on an edge, and your specifications called for
  2.097 cm. We had yours roughed out to 2.1 cm but
  it was the precision grinding to get it down to
  2.097 cm which took so long and increased the
  cost so dramatically.

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A Story

• The foreman continued, The first one we made was
  2.089 cm on one edge when we got finished, so we
  had to scrap it. The second was closer, but
  still not what you specified. Thats why the
  three tries.
• Marcus sadly replied, Oh.

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So

• Is Marcus responsible for the 500 bill?

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Assignment

• Significant Figures W/S