Proceed as before to determine the largestnumber that can be added as a digit to the divisor90 and used as a multiplier which, when multipliedby the increased divisor, will produce a resultcontainable in the remainder, 901. This numberis obviously 1. The increased divisor is 901, andthis figure, multiplied by the 1, gives a resultexactly equal to the remainder 901.The figure 1 is therefore the third and finaldigit in the answer, The square root of 2,034.01is therefore 45.1Your completed computation appears thus:Fractional and Negative ExponentsIn some formulas, like the velocity (V) ofliquids in pipes, which you will encounter laterin Engineering Aid 1 & C, it is more convenientto use FRACTIONAL EXPONENTS instead ofradicals.It is readily observed that the index of the rootin the above examples is the denominator of thefractional exponent. When an exponent occurs inthe radicand,this exponent becomes thenumerator of the fractional exponent. Roots ofnumbers not found in tables may be easilycomputed by proper treatment of the radical used.Examples:Very small or very large numbers usedin science are expressed in the form 5.832 x 10-4or 8.143 x 106 to simplify computation. To writeout any of these numbers in full, just movethe decimal point to either left or right, thenumber of places equal to the exponent,supplying a sufficient number of zeros dependingupon the sign of the exponent, as shown below:RECIPROCALSThe reciprocal of a number is 1 divided by thenumber. The reciprocal of 2, for example, is 1/2,and the reciprocal of 2/3 is 1 divided by 2/3,which amounts to 1 x 3/2, or 3/2. The reciprocalof a whole number, then, equals 1 over thenumber, while the reciprocal of a fraction equalsthe fraction inverted.In problems containing the power of 10,generally, it is more convenient to use reciprocalsrather than write out lengthy decimals or wholenumbers.Example:1-6
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