Title: Review on Unit Conversion
1Review on Unit Conversion
- C. Yau
- Spring 2009
- (Roughly based on Chap.1 Sec. 7 8
- from Brady Senese, 5th edition)
2Unit 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
3Unit 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
4Unit 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.)
5Unit 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
- 1 qt 0.946 L
- You should memorize the conversions within the
English system, such as - 1 ft 12 in 1 yd 3 ft
- 1 lb 16 oz
6Conversion 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.
7Dimensional 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.
8Steps in Dimensional Analysis
I am insisting you use these steps at this point
of the semester 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).
9Steps 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.
10Tips 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. - Example 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
11Tips 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. - Example Density is 3g/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.
12Tips 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. - 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