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Review on Unit Conversion

Review on Unit Conversion. Dr. C. Yau Spring 2015 (Very loosely based on Lecture Handout, and Chap.1 Sec. 4 & 6 from Jespersen, 7 th edition). Unit Conversion. This topic is presented mainly on the blackboard during the lecture and not as a PowerPoint. Refer to your lecture notes.

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Review on Unit Conversion

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  1. Review on Unit Conversion Dr. C. Yau Spring 2015 (Very loosely based on Lecture Handout, and Chap.1 Sec. 4 & 6 from Jespersen, 7th edition)

  2. Unit Conversion • This topic is presented mainly on the blackboard during the lecture 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.

  3. 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

  4. 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 Tables 1.4 and 1.5 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.

  7. 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 cm-3 • 35 mph • $5 per person

  8. 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.

  9. Steps in Dimensional Analysis I am insisting you use these steps at this point of the semester. Later you can use whatever steps are 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).

  10. 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.

  11. 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 30000.0 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

  12. 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 3.0 g/mL. What is the mass of 5.0 mL of the liquid? x g = 5.0 mL not x g = 3.0 g/mL (because g/mL is a fractional unit, and g is not. You cannot equate g with g/mL.

  13. 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

  14. 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 ans. etc. IMPORTANT: Do not leave the “slash” in your unit. Translate it into a fraction:See next slide.

  15. 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 the 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. • Numerator: m  cm  in  ft  mi • Denominator: s  min  h

  16. 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. If you missed the lecture & need help, see me! (Check sig. fig. & units?) (Should be in sci. notation?) (Final Answer)

  17. 6. A glass bead with a mass of 5.96 g is dropped into a beaker of water containing 10.2 mL. If the resulting volume is 12.3 mL, what is the density of the bead? Can you solve this problem using dimensional analysis? What is the first question you ask yourself in dimensional analysis?

  18. 7. Acetone, the solvent in some nail polish removers, has a density of 7.90 g/mL. What is the volume of 14.8 g of acetone? What is it in pints? Set up the problem using dimensional analysis.

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