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Dimensional Analysis Reference SheetConversion Factors-3810045021500In order to use dimensional analysis, you must know the conversion factor between the two units of interest. For example, if you need to know how many centimeters are in 3 inches, then you need to know how many centimeters are in 1 inch. This conversion factor is 1 inch = 2.54 cm, and therefore 3 inches = 7.62 cm. You are not expected to memorize all of the conversion factors, but you are required to create a reference sheet of the most commonly used conversion factors. You will be permitted to use this reference sheet on all quizzes, tests, and exams.Metric/English ConversionsLength Conversions Volume Conversions Mass/Weight Conversions 1 inch (in.) = 2.54 centimeter 1 Liter = 0.264 gallons (gal.) 1 ounce (oz.) = 28.35 grams1 mile (mi.) = 5,280 feet (ft.) 1 gallon (gal.) = 4 quarts (qt.) 1 pound (lb.) = 453.59 grams1 meter = 3.281 feet (ft.) 1 mL = 1 cm3 1 pound (lb.) = 16 ounces (oz.)1 mile (mi.) = 1.609 kilometers 1 Liter = 4.226 cups (c.) 1 ton = 2000 lbs.Metric PrefixesPrefixAbbrevFactor = 1 base unitMega-M(0.000001) 10-6 kilo-k(0.001) 10-3hecto-h(0.01) 10-2BASE UNITg, L, m1deci-d101centi-c102milli-m103micro-?(1000000) 106nano-n(1000000000) 109pico-p(1000000000000) 1012You may add any additional conversion factors you find you need throughout our course below:Dimensional AnalysisThe technique of dimensional analysis is used to convert between units anytime you have the appropriate conversion factor. It is critical that you include units throughout all of you work, as units guide each step of the process. Although ratios and other techniques can be used for conversions, you will be required to use dimensional analysis. This is because we have upcoming units (mole and stoichiometry) where it is the only technique that will work.Steps and Example Let’s say that you needed to know how many feet were in 674 meters.To use dimensional analysis, here are the steps involved.Step #1: Write the number and units given. 674 mStep #2: Write a multiplication (x) sign and a fraction bar. 674 m x __________Step #3: Copy the units (not the number) given to the bottom on this fraction bar. 674 m x __________ Notice that I have not filled in a number yet in front of “m” on bottom. mStep #4:Write the units asked for on the top of the fraction bar. 674 m x ft. Notice that I have still not filled in a number in front of “ft” or “m”. mStep #5:Use the conversion factor, 1 meter = 3.281 feet (ft.), to fill in your fraction. 674 m x 3.281 ft. Notice that the 1 stays with meter and the 3.281 stays with feet. 1 mNever switch which number goes with which unit from the conversion factor.Step #6:Cancel the units that are diagonal from one another (m). 674 m x 3.281 ft.You are now left with units of feet (ft.). 1 mStep #7:Solve for the final answer by multiplying the numbers on top and (674 x 3.281) / 1dividing by any numbers on the bottom. 2,211.394 (unrounded)Step #8:Round final answer to match the number of sig. figs. in given number. 2,210 (3 sig. figs. like 674) Step #9: Remember to include units with your final answer. 2,210 ft. ................
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