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Measurements

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Title: Measurements


1
Measurements Calculations
2
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.

3
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)

4
Metric System
  • Prefixes convert the base units into units that
    are appropriate for the item being measured.

5
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.

6
  • Measurement
  • A quantitative observation
  • Consists of 2 parts
  • Number
  • Unit tells the scale being used

7
C. Measurements of Length, Volume and Mass
  • Length
  • Fundamental unit is meter
  • 1 meter 39.37 inches
  • Comparing English and metric systems

8
C. Measurements of Length, Volume and Mass
9
C. Measurements of Length, Volume and Mass
  • Volume
  • Amount of 3-D space occupied by a substance
  • Fundamental unit is meter3 (m3)

10
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.

11
C. Measurements of Length, Volume and Mass
  • Mass
  • Quantity of matter in an object
  • Fundamental unit is kilogram

12
C. Measurements of Length, Volume and Mass
13
Temperature
  • By definition temperature is a measure of the
    average kinetic energy of the particles in a
    sample.

14
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.

15
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

16
Temperature
  • The Fahrenheit scale is not used in scientific
    measurements.
  • ?F 9/5(?C) 32
  • ?C 5/9(?F - 32)

17
C. Density
  • Density is the amount of matter present in a
    given volume of substance.
  • Physical Property

18
C. Density
19
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

20
Uncertainty in Measurement
  • A digit that must be estimated is called
    uncertain.
  • A measurement always has some degree of
    uncertainty.

21
Measurement of Volume Using a Buret
22
A. Uncertainty in Measurement
  • A measurement always has some degree of
    uncertainty.

23
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.

24
Uncertainty in Measurements
  • Different measuring devices have different uses
    and different degrees of accuracy.

25
A. Uncertainty in Measurement
  • Different people estimate differently.
  • Record all certain numbers and one estimated
    number.

26
B. Significant Figures
  • Numbers recorded in a measurement.
  • All the certain numbers plus first estimated
    number

27
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.

28
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.

29
B. Significant Figures
  • Rules for Counting Significant Figures
  1. Nonzero integers always count as significant
    figures. 1457 4 significant figures

30
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

31
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

32
B. Significant Figures
33
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.

34
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.

35
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.

36
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
37
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
38
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

39
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?

40
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

41
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.

42
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?
43
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.
44
B. Temperature Conversions
  • There are three commonly used temperature scales,
    Fahrenheit, Celsius and Kelvin.

45
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.

46
B. Temperature Conversions
Converting Between the Kelvin and Celsius Scales
  • 70. oC ? K
  • TC 273 TK

70. 273 343 K
47
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.
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