8 MATHEMATICS 



the second difference is 1,220; 1, 220 -5- 10,213 = .119, or .12, 

 which gives the fourth and fifth figures. There is one 

 cipher period after the decimal point in the number; hence, 

 ^00000624 17 = .0184 12. 



(b) Replace all after the sixth figure with ciphers, making 

 the sixth figure 1 greater when the seventh figure is 5 or greater; 

 that is, -^50932700 and %)932676 will be the same. Placing 

 the decimal point between the first and second periods gives 

 50.9327. Under n? find 50.6530 = 3.70* and 5 1.0648 = 3.7 1 3 . 

 The first three figures of the root are 370. The second dif- 

 ference 2^797 4- the first difference 4. 118 = .679 or .68. Hence, 

 ^'50932676 = 370.68. 



SQUARES 



If the given number contains fewer than four significant 

 figures, the significant figures of the square or cube can be 

 found under n 2 or n 3 opposite the given number under n. The 

 decimal point can be located by the fact that if the column 

 headed VlOn is used, the square will contain twice as many 

 figures as the number to be squared, while if the column headed 

 Vn is used, the square will contain twice as many figures as 

 the number to be squared, less 1. If the number contains 

 an integral part, the principle is applied to the integral part 

 only; if the number is wholly decimal, the square will have 

 twice as many ciphers, or twice as many plus 1, following the 

 decimal point as in the number itself, depending on whether 

 ViOn or Vn column is used. 



To square a number containing more than three significant 

 figures, place the decimal point between the first and second 

 significant figures and find in the column headed Vn or \\()n 

 two consecutive numbers, one a little greater and the other 

 a little less than the given number. The remainder of the 

 work is exactly as described for extracting roots. The square 

 will contain twice as many figures as the mfmber itself, or 

 twice as many less 1, according to whether the column headed 

 \10n or Vn is used. The number of ciphers following the 

 decimal point in the square of a number wholly decimal is 

 determined in the same way. 



EXAMPLE. Find the results of the following: 

 (a) 273.42* = ? (b) .052436 2 = ? 





