For example, dimensional analysis could be used to determine the number of nickels in 3432.35 dollars. n dla • To begin, write down the starting value, 3432.35 dollars. 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. • Finaly. convert cents to nickels. This conversion also involves a simple conversion factor. since it was on top of the previous conversion factor. • Combining these expressions gives us . This time "cents" should be on the bottom of the conversion factor. 3432.35 dollars 100 centsy I dollar I nickel centa • 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. 100 conts 3432.35 dolkari I nickel Sunts 68, 647 nickels skultar • To complete the calulation, multiply everything in the numerator and divide by everything in the denominator (or top and bottom, respectively). Practice with a sample problem You wash dishes for a chemistry laboratory to make quarters/load, extra money for laundry. You earn 12 dollars/hour, and each shift lasts 75 minutes. Your laundry requires 12
For example, dimensional analysis could be used to determine the number of nickels in 3432.35 dollars. n dla • To begin, write down the starting value, 3432.35 dollars. 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. • Finaly. convert cents to nickels. This conversion also involves a simple conversion factor. since it was on top of the previous conversion factor. • Combining these expressions gives us . This time "cents" should be on the bottom of the conversion factor. 3432.35 dollars 100 centsy I dollar I nickel centa • 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. 100 conts 3432.35 dolkari I nickel Sunts 68, 647 nickels skultar • To complete the calulation, multiply everything in the numerator and divide by everything in the denominator (or top and bottom, respectively). Practice with a sample problem You wash dishes for a chemistry laboratory to make quarters/load, extra money for laundry. You earn 12 dollars/hour, and each shift lasts 75 minutes. Your laundry requires 12
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