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1.4 Dimensional Analysis343852553975English EnglishMetric MetricEnglishMetric0English EnglishMetric MetricEnglishMetricThis section is all about conversions.We are going to be using conversion facts to make conversion “chains.”552450020764500We will be working with different units in terms of: 428498082550019050147320Linear – measuring distance, 1 dimensional (ft, m)Area – 2 dimensional (sq ft or ft2, m2)Volume – 3 dimensional (cu ft or ft3, m3)0Linear – measuring distance, 1 dimensional (ft, m)Area – 2 dimensional (sq ft or ft2, m2)Volume – 3 dimensional (cu ft or ft3, m3)You will need to make use of some formulas. Pretty much, all the info you need, can be found in the appendix. You are going to be using this information A LOT. I strongly suggest you make a copy and maybe laminate it so it lasts longer. This way you don’t have to keep flipping back and forth in your text.The best way for me to teach you conversions is through lots of examples. But first:Rounding: I need to give you a quick tutorial on the type of rounding we will be doing in this class. You might consider it the “conventional” method as opposed to rounding used in an engineering sense.1)Rounding decimals. You need to know place value. If you don’t, you will likely get most of your answers wrong; so, please learn it.Once you can find the place value, look one digit to the right.If it is 5 or more, round up.If it is less than 5, round down.326707511557000138112586169500If you need practice, click on the picture to the right. It will take you to where you can practice some problems.Great website for tons of math stuff you need to know “Adapted Mind”.Practice on Rounding: Round each value as directed.124.89903Nearest whole number ___________________Nearest hundred___________________Nearest hundredth___________________Nearest ten___________________Nearest tenth___________________Nearest thousandth___________________Nearest ten thousandth___________________0.0908277Nearest whole number ___________________Nearest hundred___________________Nearest hundredth___________________Nearest ten___________________Nearest tenth___________________Nearest thousandth___________________Nearest ten thousandth___________________2)Changing decimals to fractions (to the nearest 1/2, 1/4, 1/8, 1/16, 1/32, etc.). We discussed this once before, but let’s review.Once you have the decimal -Multiply the decimal portion of the number by the denominator of the fraction you want. This gives you the numerator. If necessary, round to the nearest whole number.Demonstration: The length of a piece of metal is 18.6349 inches. Give this dimension to the nearest 16th of an inch.18.6349 inches = 18 whole inches plus ???? 16ths more. So forget about the 18 and concentrate on the decimal portion.Multiply 0.6349 times 16 = 10.1584 This is how many 16ths there are in 0.6349 in.Now, round to the nearest whole number (the nearest whole 16th). 10.1584 ≈10Final Answer: 18.6349 ≈ 18-10/16 in But, are we done?...Probably not. Simplifying further makes sense. Final answer 18-5/8 inThis process works EVERY TIME!You will need the appendix in the back of your text for the following examples.397002015557500Example 1A circuit board measures 15” wide by 11” tall. Convert the dimensions into centimeters rounded to one decimal place. 5057775-28575000Example 2Usain Bolt's 9.58sec at world championships shatters 100-meter record ...Aug 16, 2009 Berlin Germany ... Lightning Bolt captures another world record ... Convert Usain Bolt’s speed to MPH (miles per hour) for his time of 9.58 seconds in the 100 meter dash.311467520066000Example 3Find the weight of the beam cut from a Douglas fir tree weighing 36 lbs/ft3 (pounds per cubic foot). Be careful with the units!48101255715000Example 5 (1.4.1: Calculating concrete volume, from your text)Find the volume of concrete in yd3 needed for a sidewalk that is4 in deep by 6 ft wide by 100 ft long. Pay close attention to the units.528637514351000Example 6 (1.4.3: Converting from metric to standard weight, from your text)A length of steel tubing is labeled to weigh 8700 grams, convert this weight to pounds to determine how much trouble it will be to lift.Extra Practice: Odd problems from end of section exercises.Homework: Problems 4,10,17,23,24,26,27,28,32,34(10 problems). You must give a complete conversion chain for each problem. The chain must include the correct values and units. Don’t forget to include units on your final answer.Section 1.4:96.5 cm61 13”161295.4 mm29’ 6 5”161.79 miles5 5”8 = 14.3 cm, 4 3”8 = 11.1 cm, 8 1”4 = 21.0 cm, 2 1”2 = 6.4 cm184 mm = 7 1”4, 122 mm = 4 13”16, 30 mm = 1 3”16109.68 cm21.64 ft213,939 ft28.67 yd2.51 m253.82 ft210.8 oz37.4 gallons6.19 yd3946 cm36,912 in33.9 yd34,428 ft3day11.41 ftyr8.0 mileshour39.5 mileshour0.84 gL12.3 mileshour12.1 ms a. 8,951.0 ozft3b. 316.3 gin3c. 49,282.7 gft3d. 490.1 lbsft3e. 4.6 gcm396.9 lbs580 lbs9 grains588 lbs83.4 lbs67.6 lbs368 mg of protein, 883.2 mgday ................
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