Review on Unit Conversion

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Review on Unit Conversion

• Dr. C. Yau
• Fall 2009
• (Roughly based on Chap.1 Sec. 7 8
• from Brady Senese, 5th edition)

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Unit Conversion

• This topic is presented mainly on the blackboard
  and not as a PowerPoint. Refer to your lecture
  notes.
• This PowerPoint is to serve only as a review of
  some key points involved in Unit Conversion.

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Unit Conversion in the Metric System

• First learn the inter-relationships between the
  prefixes in the metric system. This was presented
  in the lecture. If you missed the lecture, get
  notes from a fellow classmate immediately.
• Mm - - Km - - m dm cm mm - - ?m - - nm - - pm
• Mg - - Kg - - g dg cg mg - - ?g - - ng - - pg
• ML - - KL - - L dL cL mL - - ?L - - nL - - pL

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Unit Conversion in the Metric System
Practise interconverting between the metric units
such as 1 dg ? ng 1 kL ? cL 1 cm ?
?m These conversions do not require dimensional
analysis, and you should be able to do this in
one step. (See handout and answers to in-class
exercise posted.)
5
Unit Conversion in the English System

• Do not rely on the Table 1.4 and 1.6 in your
  textbook. On exams and quizzes you will be given
  ONLY these conversions
• 1 in 2.54 cm (exactly)
• 1 lb 454 g (not exact)
• 1 qt 0.946 L (not exact)
• You should memorize the conversions within the
  English system, such as
• 1 ft 12 in 1 yd 3 ft
• 1 lb 16 oz (These are all exact numbers)

6
Conversion Factors

• Know what is meant by "conversion factor."
• "Conversion factor" in dimensional analysis is a
  fraction with one unit at the top and a different
  unit on the bottom. It is used to multiply with
  a given number to convert the units of that
  number from one to another.
• e.g. 1 in 2.54 cm can be written as
• See handout on practice questions on writing
  conversion factors.

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Conversion Factors

• 1. Write 2 conversion factors for each pair of
  units shown below
• mg and kg
• cm and µm
• lb and oz
• 1.05 g/mL
• 35 mph
• 5 per person

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Dimensional Analysis
This is also known as the Factor-Label
Method. "Dimensional" refers to units. "Analysis"
refers to analyzing a problem. "Dimensional
analysis" refers to solving a problem by
analyzing the units in the problem.
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Steps in Dimensional Analysis
I am insisting you use these steps at this point
of the semester. Later you can use whatever is
easier for you. 1. Read the question and decide
on what units your answer should have. DO NOT
skip this step! 2. Write "x" (the unknown number)
followed by the units your answer should be. 3.
Write "" (the equal sign) followed by the number
and units on which your answer is dependent. 4.
Begin writing one or more conversion factors so
that units cancel properly to give you the unit
you are looking for (unit of x).
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Steps in Dimensional Analysis (cont'd)

• 5. Cancel out the units, checking to make sure
  they do INDEED cancel properly to give the
  desired unit.
• 6. Using chain operation on your calculator,
  calculate the answer.
• 7. Check your sig. fig. and units.
• 8. Check whether you need scientific notation.

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Tips on Dimensional Analysis

• When converting between metric and the English
  system, first write down the link.
• (such as 1 in 2.54 cm).
• Examine the unit you are given and see how that
  can be converted to one of the units in your
  link.
• The link will then take you to the system you are
  looking for (metric or English).
• Finally, look at how you can convert to the unit
  you are looking for.
• 2. How many miles are in 30000 mm?
• The link is 1 in 2.54 cm.
• Chart out your units
• mm must be changed to cm. The link takes you to
  inches.
• From inches you must go to ft and then to miles.
• mm ? cm ?in ?ft ?mi

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Tips on Dimensional Analysis

• If the answer you want is a single unit rather
  than a fraction, you should not begin with a
  fraction on the other side of the equation.
• 3. Density is 3 g/mL. What is the mass of 5 mL
  of the liquid?
• x g 5 mL
• not
• x g 3 g/mL (because g/mL is a fractional unit,
  and g is not. You cannot equate g with g/mL.

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Tips on Dimensional Analysis

• When you see units such as cm, mm, ft, in, you
  know these are measurements of length.
• When you see units such as mL, L, gallons,
  quarts, you know these are measurements of
  volume.
• When you see length units CUBED (such as cm3,
  mm3, cu. ft., in3 or cu. in, you know these are
  ALSO units of volume.
• 4. How do we convert 1 qt to mm3 ?
• The key is 1 mL 1 cm3 (exactly)
• This you must know well!!!!
• Think of the links that lead you to 1 mL 1 cm3.
• 1 qt ?L ?mL ?cm3 ?mm3

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Tips on Dimensional Analysis

• How do we deal with problems where the answer has
  a fractional unit?
• 5. What is the velocity of an electron going at
  2.5x10-4 m/s in mph?
• First you analyze the units of the answer mph
  miles/hour not meters/hour
• You can follow the usual step of writing x
  followed by the desired units of the answeretc.
• IMPORTANT Do not leave the slash in your unit.
  Translate it into a fraction

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• 5. What is the velocity of an electron going at
  2.5x10-4 m/s in mph?
• Note that the dimensions must match
• Length or distance is on top on both sides of
  eqn.
• Time is on the bottom on both sides of eqn.
• Now chart out how to change m to mi in numerator,
  and s to h in the denominator.
• Meter is a metric unit and mile is an English
  unit. The link is 1 in 2.54 cm.
• m ? cm ? in ? ft ? mi
• Denominator s ? min ? h

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• 5. What is the velocity of an electron going at
  2.5x10-4 m/s in mph?
• Numerator m ? cm ? in ? ft ? mi
• Denominator s ? min ? h
• 0.000559234
• 0.00056 mi/h
• 5.6x10-4 mph
• NOTE 5.6x10-4 mi h-1 is a common way of writing
  mi/h with which you should be familiar.

(Check sig. fig. units?)
(Should be in sci. notation?)
(Final Answer)