Measurement Unit Notes 2

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Measurement Unit Notes 2

• Foundations of Chemistry

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Scientific Notation Continued

• When multiplying values, multiply the M values
  and add the exponents.
• Example (2.0 x 105)(3.0 x 10-3) 6.0 x 102
• When dividing values, divide the M values and
  subtract the exponents.

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Volume

• the three-dimensional space an object occupies
• 1 cm3 is equal to 1 milliliter.
• 1 dm3 is equal to 1 liter.

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Density

• the ratio of mass to volume the compactness of
  a substance
• D m / V
• The units of density are usually reported as
  g/cm3 (solids) or g/mL. (liquids)

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Reporting Measured Quantities

•  Accuracy how well a measurement agrees with
  an accepted value (the smaller the difference
  between them, the more accurate).
•  
• Precision how well a measurement can be
  reproduced
• (this is limited to how well the measuring device
  is designed and constructed).

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Tip Take the measurement and guess the last
digit. (This does not apply to measuring mass
using an electric balance you must trust the
balance.)
Accurate
Precise
Both
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Precision Measurement
We can tell that the crayon is just over 2
inches, so we would guess the next digit in the
tenths spot 2.3 inches.   We could not guess
numbers past this point, because the ruler is not
constructed with more graduations.
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Significant figures (or significant digits)

• digits that are part of any valid measurement (a
  result of the number of divisions, or
  graduations, on the measuring device).
• We take the measurement using the graduations we
  are given and then guess the final digit. Your
  measurement will only be as good as the measuring
  device.
• Lets look at different pieces of instruments
  that measure volume

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Beaker

• The smallest graduations are in 10 mL increments.
  We will guess the ones place for this
  measurement.
• _________ mL

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Graduated cylinder

• The smallest graduations are in 1 mL increments.
  We will guess the tenths place for this
  measurement.
• __________ mL

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Buret

• The smallest graduations are in 0.1 mL
  increments. We will guess the
  hundredths place for this measurement.
• __________ mL

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Determining Significant Figures

• 1. All digits other than 0 are significant (1
  through 9).
• Ex. 283.5
• 2. Place-holder zeros in decimals are not
  significant (they would disappear if the number
  was in scientific notation)
• Ex. 0.00036
• 3. Terminating zeros to the left of decimal
  points are not significant unless the decimal
  point is shown.
• Ex. 2000 Ex. 2000.

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• 4. Trailing zeros are significant if they trail a
  decimal to show precision.
• Ex. 0.000360
• 5. Trapped zeros between two digits (1 through 9)
  are significant.
• Ex. 1,000,006
• Examples
• 100.20
• 0.000 000 521
• 1002
• 2,000,500
• 1020.

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Adding Subtracting with Sig Figs

• The number of sig figs is determined by how many
  decimal places are noted in the problem. The
  quantity with the least number of decimal places
  decides how many decimal places appear in the
  answer.

Ex. 53.263 Ex. 1.2 Ex. 1000
12.51 12.521
2  
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Multiplying Dividing with Sig Figs

• The number of sig figs is determined by the
  quantity with the least number of sig figs.
• Ex. 3.626 x 5.2
• Ex. 892 x 2

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Percent Error

• how closely a measurement agrees with the
  accepted value.
• error experimental value accepted value
  x 100
• accepted value
•  
• Example Working in the laboratory, a student
  find the density of a piece of pure aluminum to
  be 2.85 g/cm3.  The accepted value for the
  density of aluminum is 2.699 g/cm3.  What is the
  student's percent error?

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Factor-Label Method (FLM)

• solving conversion problems with fractions called
  conversion factors.
• We use equivalent values as conversion factors
  and set them up in order so that the units cancel
  out. ALWAYS start with the number the problem
  gives you.
• Example How many seconds are there in six years
  (average years, not leap years)?
• We know that 60 sec 1 min, 60 min 1 hr, 24 hr
  1 day, 365 days 1 year. These are our
  conversion factors (we will set them up as
  fractions).

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• Start with what we were given 6 years.
• 6 yr x 365 days x 24 hr x 60 min x 60 sec
  
• 1 yr 1 day 1 hr
  1 min
• Notice that the UNITS CANCEL. Thats the whole
  idea to this method of problem-solving!

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Graphing Skills Exercise

• Follow the directions given in your packet.
• Work In Pencil!!!
• Work Neatly