Measurements

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Measurements Calculations
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Objectives

1. To learn the English, metric, and SI systems of
   measurement
2. To use the metric system to measure length,
   volume and mass
3. To learn the three temperature scales
4. To define density and its units.

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B. Units

• There are 3 commonly used unit systems.

• English (used in the United States)
• Metric (uses prefixes to change the size of the
  unit)
• SI (uses prefixes to change the size of the unit)

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Metric System

• Prefixes convert the base units into units that
  are appropriate for the item being measured.

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SI Units

• Système International dUnités
• A different base unit is used for each quantity.
• Units provide a scale on which to represent the
  results of a measurement.

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• Measurement

• A quantitative observation
• Consists of 2 parts
• Number
• Unit tells the scale being used

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C. Measurements of Length, Volume and Mass

• Length
• Fundamental unit is meter
• 1 meter 39.37 inches
• Comparing English and metric systems

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C. Measurements of Length, Volume and Mass
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C. Measurements of Length, Volume and Mass

• Volume
• Amount of 3-D space occupied by a substance
• Fundamental unit is meter3 (m3)

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Volume

• The most commonly used metric units for volume
  are the liter (L) and the milliliter (mL).
• A liter is a cube 1 dm long on each side.
• A milliliter is a cube 1 cm long on each side.

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C. Measurements of Length, Volume and Mass

• Mass
• Quantity of matter in an object
• Fundamental unit is kilogram

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C. Measurements of Length, Volume and Mass
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Temperature

• By definition temperature is a measure of the
  average kinetic energy of the particles in a
  sample.

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Temperature

• In scientific measurements, the Celsius and
  Kelvin scales are most often used.
• The Celsius scale is based on the properties of
  water.
• 0?C is the freezing point of water.
• 100?C is the boiling point of water.

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Temperature

• The Kelvin is the SI unit of temperature.
• It is based on the properties of gases.
• There are no negative Kelvin temperatures.
• K ?C 273.15

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Temperature

• The Fahrenheit scale is not used in scientific
  measurements.
• ?F 9/5(?C) 32
• ?C 5/9(?F - 32)

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C. Density

• Density is the amount of matter present in a
  given volume of substance.
• Physical Property

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C. Density
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Objectives

1. To learn how uncertainty in a measurement arises
2. To learn to indicate a measurements uncertainty
   by using significant figures
3. To learn to determine the number of significant
   figures in a calculated result
4. To show how very large or very small numbers ca
   be expressed in scientific notation

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Uncertainty in Measurement

• A digit that must be estimated is called
  uncertain.
• A measurement always has some degree of
  uncertainty.

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Measurement of Volume Using a Buret
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A. Uncertainty in Measurement

• A measurement always has some degree of
  uncertainty.

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Accuracy versus Precision

• Accuracy refers to the proximity of a
  measurement to the true value of a quantity.
• Precision refers to the proximity of several
  measurements to each other.

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Uncertainty in Measurements

• Different measuring devices have different uses
  and different degrees of accuracy.

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A. Uncertainty in Measurement

• Different people estimate differently.

• Record all certain numbers and one estimated
  number.

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B. Significant Figures

• Numbers recorded in a measurement.
• All the certain numbers plus first estimated
  number

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Significant Figures

• The term significant figures refers to digits
  that were measured.
• When rounding calculated numbers, we pay
  attention to significant figures so we do not
  overstate the accuracy of our answers.

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Significant Figures

1. All nonzero digits are significant.
2. Zeroes between two significant figures are
   themselves significant.
3. Zeroes at the beginning of a number are never
   significant.
4. Zeroes at the end of a number are significant if
   a decimal point is written in the number.

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B. Significant Figures

• Rules for Counting Significant Figures

1. Nonzero integers always count as significant
   figures. 1457 4 significant figures

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B. Significant Figures

• Rules for Counting Significant Figures

1. Zeros

1. Leading zeros - never count0.0025 2
   significant figures
2. Captive zeros - always count 1.008 4
   significant figures
3. Trailing zeros - count only if the number is
   written with a decimal point 100 1
   significant figure 100. 3 significant
   figures 120.0 4 significant figures

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B. Significant Figures

• Rules for Counting Significant Figures

1. Exact numbers - unlimited significant figures

• Not obtained by measurement
• Determined by counting3 apples
• Determined by definition1 in. 2.54 cm

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B. Significant Figures
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B. Significant Figures

• Rules for Addition and Subtraction

• The number of significant figures in the result
  is the same as in the measurement with the
  smallest number of decimal places.

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B. Significant Figures

• Rules for Multiplication and Division

• The number of significant figures in the result
  is the same as in the measurement with the
  smallest number of significant figures.

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Significant Figures Summay

• When addition or subtraction is performed,
  answers are rounded to the least significant
  decimal place.
• When multiplication or division is performed,
  answers are rounded to the number of digits that
  corresponds to the least number of significant
  figures in any of the numbers used in the
  calculation.

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A. Scientific Notation

• Very large or very small numbers can be expressed
  using scientific notation
• The number is written as a number between 1 and
  10 multiplied by 10 raised to a power.
• The power of 10 depends on
• The number of places the decimal point is moved.
• The direction the decimal point is moved.

Left ? Positive exponent Right ? Negative
exponent
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A. Scientific Notation

• Representing Large Numbers

• Representing Small Numbers
• 0.000167 To obtain a number between 1 and 10 we
  must move the decimal point.

0.000167 1.67 ?10-4
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Objectives 5.3

• To learn how dimensional analysis can be used to
  solve problems
• To learn to convert from one temperature scale to
  another
• To practice using problem solving techniques

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A. Tools for Problem Solving

• Be systematic
• Ask yourself these questions
• Where do we want to go?
• What do we know?
• How do we get there?
• Does it make sense?

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A. Tools for Problem Solving
Converting Units of Measurement

• We can convert from one system of units to
  another by a method called dimensional analysis
  using conversion factors.
• Unit1 ? conversion factor Unit2

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A. Tools for Problem Solving
Converting Units of Measurement

• Conversion factors are built from an equivalence
  statement which shows the relationship between
  the units in different systems.
• Conversion factors are ratios of the two parts of
  the equivalence statement that relate the two
  units.

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A. Tools for Problem Solving
Converting Units of Measure

• 2.85 cm ? in.2.85 cm ? conversion factor
  ? in. Equivalence statement 2.54 cm 1
  in. Possible conversion factors

Does this answer make sense?
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A. Tools for Problem Solving
Tools for Converting from One Unit to Another
Step 1 Find an equivalence statement that
relates the 2 units.Step 2
Choose the conversion factor by looking at the
direction of the required change (cancel
the unwanted units).Step 3 Multiply
the original quantity by the conversion
factor. Step 4 Make sure you have the correct
number of significant figures.
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B. Temperature Conversions

• There are three commonly used temperature scales,
  Fahrenheit, Celsius and Kelvin.

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B. Temperature Conversions
Converting Between the Kelvin and Celsius Scales

• Note that
• The temperature unit is the same size.
• The zero points are different.
• To convert from Celsius to Kelvin we need to
  adjust for the difference in zero points.

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B. Temperature Conversions
Converting Between the Kelvin and Celsius Scales

• 70. oC ? K
• TC 273 TK

70. 273 343 K
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B. Temperature Conversions
Converting Between the Fahrenheit and Celsius
Scales

• Note

• The different size units
• The different zero points
• To convert between Fahrenheit and Celsius we need
  to make 2 adjustments.