NAUI Master Scuba Diver 72 Diving Physics are related by factors of ten. Sizes of units can be made bigger or smaller by using an appropriate prefix. With computers we have become used to these prefixes, using bytes, kilobytes, megabytes, gigabytes, and even terrabytes to designate amounts of information. Common prefixes you may see in this chapter are: mega M x 1,000,000 kilo k x 1,000 hecta h x 100 deca da x 10 unit deci d x 1/10 centi c x 1/100 milli m x 1/1,000 micro μ x 1/1,000,000 The other system in common use is found in the United States. The U.S. Customary System is derived from the English or Imperial System, and it is often called by these names although the systems are not everywhere equivalent. (Most notably, the English imperial gallon is significantly larger than the U.S. gallon, which itself differs for liquid and dry measure.) The U.S./Imperial System is a traditional system, evolved from a mixture of Roman and customary units of measurement, many based on measurements of the human body, usually the king’s. Units are not decimalized, and users must memorize the relationships between them (12 inches to the foot, 3 feet to the yard, 6 feet to the fathom, 5.5 yards to the rod, 40 rods to the furlong, 5,280 feet to the statute mile). Efforts have been made to convert the United States to use of the SI system, but progress is slow. Most U.S. customary units are now defined by law in terms of SI/metric units. A Note on Conversions and Formulas You can convert measurements in one system to the equivalent amount in the other system with the help of conversion factors. Actually, there are very few such equivalencies or formulas that you will have to know. You may have to make conversions within a system of measurement or between systems of measurement, such as changing one way of measuring a distance, size, temperature, or force into another way of measuring the same thing. It is very easy to move around within the SI/metric system if you know the meaning of unit prefixes. Working within the U.S./Imperial system requires more knowledge of the relationship between units and could be very confusing, but most of the equivalents are familiar to those who were raised using the system. Some helpful hints for those who dislike math: 1. If you are having difficulty, do your calculations one step at a time. Don’t try to jump immediately from the problem to the answer through a single, complicated formula that you could never hope to remember. 2. When changing an ordinary language statement to a mathematical statement, remember that “is” becomes “equals,” “of” becomes “times,” and “per” becomes “divided by.” 3. It will help if you include the unit’s names in your written calculations. When you solve the problem, the extra units should cancel out, except for the desired solution. If the units are wrong, the numeric answer is wrong. For example, If you are converting from 12 atmospheres of pressure to pounds per square inch in a U.S./Imperial problem, write: 12 atm x 14.7 psi/atm = 176.4 psi. The “atm’s” cancel out, and you are left with psi. 4. Many problems can be set up as ratios if you are converting from one set of measurements to another. The above problem could be stated and written, “What is 12 atmospheres in pounds per square inch if 14.7 psi is one atmosphere,” or (what) = 12 atm 14.7 psi 1 atm The “is”s become “equals;” the “if” indicates you are working with a ratio. 5. Don’t develop a “decimal fetish.” Answers can be no more accurate than their least accurate contributing number. 1.73 x 3.1415926536 = 5.43, not 5.4349552907, unless you know that “1.73” is an exact number. It may also be that the “exact” answer is not what is needed for the purpose. If someone wants to swim 200 meters, a U.S./Imperial distance of 219 or even 220 yards may be a more useful equivalent than “218 yards 2 feet 2 inches.”
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