XXXVlii RECIPROCALS. 



RECIPROCALS. 



This table, page 34, coutains the reciprocals to four places of 

 numbers from i. to 9.99. ami by interpolation from i. to 9.999. Tin* 

 reciprocal to four places of any number from zero to infinity is, 

 of course, one of these tabular values multiplied by a suitable 

 pi'wrr of 10. In this table, the reciprocals of numbers from i. to 

 i.ioo are given directly in the first ten lines to avoid interpolation 

 in finding the reciprocals of terms of the form (i -f a), where a is 

 a small decimal fraction. 



N.l>. The approximation i/(i + ) = (i ) approx., is frequently em- 

 ployed in computations to avoid dividing by (i + a). This useful approxima- 

 tion, however, must be used with caution. The error from its employment is 

 a' 2 ; that is, if a = 0.1, the error from multiplying by (i a) instead of divid- 

 ing by (i -f a) is o. i 2 = o.oi, or i per cent; if a = 0.03, the error is 0.032 

 = 0.0009, or nearly o. i per cent, and so on. 



To find the reciprocal of a number, factor it by the " Notation by 

 Powers of 10," page xv. Find the reciprocal of the first factor by 

 the table and multiply this by the second factor io n with the alge- 

 braic sign of its exponent reversed, i.e. by lo^". 



Example. Desired 1/4486, i.e. (4486)" 1 . 



(4486.)- 1 =(4.486- 1 3 )- 1 =(4.486. )-! I O- 3 . 



In table, line 4.4, col. 8, (4.48) -1 = 0.2232 



By difference table, 0.6 difference = 3 



Reciprocal of 4.486 = 0.2229 



(4486.)" 1 = (4.486)~ 1 -io~ 3 = o.2229*io~ 3 = 0.0002229. 



Example. Desired i/o.oo 327 5. 



(0.00327 5)~i =(3-275)- 1 -(io-3)-i = 0.3054-103 = 305.4. 



NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS. 



It is frequently convenient to have a table giving rough values 

 of the natural trigonometric functions for use in preliminary, check, 

 or approximate computations. The four-place tables of the above 

 four functions cover all ordinary needs. Interpolation can be 

 made in these tables to o.oi by the interpolation tables, or to i' 

 by mental computation, since the step between successive columns is 

 o.i, or 6'. 



