Figure 1-2.-2-percent grade.In connection with the study of decimalfractions, businessmen as early as the fifteenthcentury made use of certain decimal fractions somuch that they gave them the special designationPERCENT. The word percent is derived fromLatin. It was originally per centum, which means“by the hundredths.” In banking, interest ratesare always expressed in percent; statisticians usepercent; in fact, people in almost all walks of lifeuse percent to indicate increases or decreases inproduction, population, cost of living, and so on.The Engineering Aid uses percent to expresschange in grade (slope), as shown in figure 1-2.Percent is also used in earthwork computations,progress reports, and other graphical representa-tions. Study chapter 6 of NAVEDTRA 1-0069-D1for a clear understanding of percentage.POWERS, ROOTS, EXPONENTS,AND RADICALSAny number is a higher power of a given root.To raise a number to a power means to multiply,using the number as a factor as many times as thepower indicates. A particular power is indicatedby a small numeral called the EXPONENT;for example, the small 2 on 32 is an exponentindicating the power.Many formulas require the power or roots ofa number. When an exponent occurs, it mustalways be written unless its value is 1.A particular ROOT is indicated by the radicalsign (~), together with a small number called theINDEX of the root. The number under the radicalsign is called the RADICAND. When the radicalsign is used alone, it is generally understood tomean a square root, and ~,~, and ~,indicate cube, fifth, and seventh roots, respec-tively. The square root of a number may be either+ or – . The square root of 36 may be writtenthus: G = t6, since 36 could have been theproduct of ( + 6)( + 6) or ( – 6)( – 6). However, inpractice, it is more convenient to disregardthe double sign ( ± ). This example is what wecall the root of a perfect square. Sometimesit is easier to extract part of a root onlyafter separation of the factors of the number, suchas: ~ = ~ = 3~. As you can see, wewere able to extract only the square rootof 9, and 3 remains in the radical becauseit is an irrational factor. This simplificationof the radical makes the solution easier becauseyou will be dealing with perfect squares andsmaller numbers.Examples:Radicals are multiplied or divided directly.Examples:Like fractions, radicals can be added or sub-tracted only if they are similar.Examples:When you encounter a fraction under theradical, you have to RATIONALIZE thedenominator before performing the indicatedoperation. If you multiply the numerator anddenominator by the same number, you can1-4
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