MATHEMATICS 29 



is applied to the integral part only; if the number is wholly 

 decimal, there will be twice as many ciphers following the 

 decimal in the square or twice as many plus one as in the 

 number squared, depending on whether VTbn or "Vn column 

 is used. For example, 273. 42 2 will contain five figures 

 in the integral part; 4516.2 2 will contain eight figures in the 

 integral part, all after the fifth being denoted by ciphers; 

 .00294532 2 will have five ciphers following the decimal point; 

 .052436 2 will have two ciphers following the decimal point. 



EXAMPLE. (a) 273.42 2 =? (6) .052436 2 =? 



SOLUTION. (a) Placing the decimal point between the first 

 and second significant figures, the result is 2.7342; this 

 number occurs between 2.73313= ^7A7 and 2.73496= V7.48 

 in the column headed Vn. The first difference is 2.73496 

 -2.73313 = 183; the second difference is 2.73420-2.73313 

 = 107; and 107 -J- 183 = . 584 + , or .58. Hence, 273.42 2 

 = 74,758, correct to five significant figures. 



(b) Shifting the decimal .point to between the first and 

 second significant figures, the number 5.2436 is obtained. 

 This falls between 5.23450 - \27.4 and 5.24404 = \27.5. The 

 first difference is 954; the second difference is 910; 910-5-954 

 = .953 + , or .95. Hence, .052436 2 =. 0027495, to five sig- 

 nificant figures. 



A number is cubed in exactly the same manner, using the 

 column headed ^n, "^lOn, or "^lOOn, according to whether 

 the first period of the significant part of the number contains 

 one, two, or three figures, respe tively. If the number con- 

 tains an integral part, the number of figures in the integral 

 part of the cube will be three Jtimes as many as in the given 

 number if column headed "VlOOn is used; it will be three 

 times as many less 1 if the column headed "VlOn is used; 

 and it will be three times as many less 2 if the column 

 headed ^n is used. If the given number is wholly decimal, 

 the cube will have either three times, three time's plus 

 one, or three times plus two, as many ciphers following the 

 decimal as there are ciphers following the decimal point in 

 the given number. 



EXAMPLE. (o) 129.6843= ? (6) .764423= ? (c) .0324253= ? 



SOLUTION. (a) Placing the decimal point between the 



