Dimensional Analysis Learning Goal: To understand how to use dimensional analysis to solve problems. Dimensional analysis is a useful tool for solving problems that involve unit conversions. By carefully tracking units and conversion factors, you can avoid many of the errors commonly encountered in chemistry problems. Dimensional analysis can also help you work through problems when you are not sure where to begin. Dimensional analysis involves multiplying a given value by a conversion factor. This results in a value in the new units. The conversion factor can be the ratio of any two quantities, as long as the ratio is equal to one. For example, dimensional analysis could be used to determine the number of nickels in 3432.35 . • To begin, write down the starting value, 3432.35 . This can also be written as a fraction: . • Next, convert dollars to cents. This conversion involves a simple conversion factor: . Note that the "dollar" unit should appear on the bottom of this conversion factor, since "dollars" appears on the top of the starting value. • Finally, convert cents to nickels. This conversion also involves a simple conversion factor: . This time "cents" should be on the bottom of the conversion factor, since it was on top of the previous conversion factor. • Combining these expressions gives us • Finally, cancel units. Since dollars are divided by dollars, and cents are divided by cents, both of these units can be canceled. Multiplying through gives the final result: You wash dishes for a chemistry laboratory to make extra money for laundry. You earn 6 , and each shift lasts 75 . Your laundry requires 6 .
Part A How many shifts must you work if you wish to wash 10 of laundry? Hint A.1 How to approac h the problem Hint not displaye d Hint A.2 Find the number of quarters require d Hint not displaye d Hint A.3 Find the number of dollars require d Hint not displaye d
Scientific Notation Scientific notation can be used to express very large or very small numbers more easily. For example, In MasteringChemistry, you may enter answers in scientific notation in the following format: 2.998*10^8 5.09*10^-6
Part A Convert the number 0.000127 to scientific notation, then enter the answer using the Masterin gChemis try format . Express your answer numerica lly. ANSWER: 1 . 2 7 × 10 − 4 C o r r e c t Entering scientific notation on a calculator It is important, especially for exams, that you be able to enter scientific notation in your calculator. All calculators are different, but look for a button such as E , EE , or EXP . If this button exists on your calculator,
it means "times ten to the" and so you never actually type the number 10 . For example, would be entered on a calculator as 2.998 E 8 For entering negative exponents, some calculators require the sign to be entered after the exponent. For example, might be entered on a calculator as 5.09 E -6 or as 5.09 E 6- Also note that many calculators have a "change sign" button ( +/-) that should be used for exponents instead
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