10 MATHEMATICS 



significant figures are 44668; the number of ciphers follow- 

 ing the decimal point is 3X0 = 0; and 7.64423 = 446.68, correct 

 to five significant figures, 



(c) 3.2425 falls between 3.24278=^10X3.41 and 3.23961 

 = ^10X3.40- The first difference is 317; the second difference 

 is 289; 289 -=-317 = . 911 + , or .91. Hence, the first five sig- 

 nificant figures are 34091; the number of ciphers following the 

 decimal point is 3X1 + 1=4; and .0324253 = .000034091, cor- 

 rect to five significant figures. 



RECIPROCALS 



The reciprocal of any number is equal to 1 divided by that 

 number; thus, the reciprocal of 6 is , because 1-4-6= |. The 

 product of a number and its reciprocal is always 1; thus, J is 

 the reciprocal of 8, and 8X J = 1. 



The last column of the following table gives the reciprocals 

 of all numbers expressed by three significant figures correct to 

 six significant figures. The number of ciphers following the 

 decimal point in the reciprocal of a number is 1 less than the 

 number of figures in the integral part of the number; and if 

 the number is entirely decimal, the number of figures in the 

 integral part of the reciprocal is 1 greater than the number 

 of ciphers following the decimal point in the number. 



EXAMPLE. Find the reciprocal of the following: 



(a) 379.426; (b) .0004692 j 



SOLUTION. (a) .379426 falls between .378788 = and 



1 -'.lit 



.380228 = -. The first difference is 380,228-: 



= 1,440; the second difference is 380,228-379, 12(1 = SOL'; 

 802-=-l,440=.o">7, or .56. Hence, the first five significant 

 figures are 26356, and the reciprocal of 379.426 is .002- ;:;:,(, 

 to five significant figures. j 



(b) .469200 falls between .469484 = and .H,72!i 



1 2 - 13 



= . The first difference is 2,194; the second difference is 



2.14 ! 



284; 284-=- 2,194 = .129 + , or .13. Hence, = 2,131.3, 



.0004692 



correct to five significant figures. 



