28 MATHEMATICS 



SOLUTION. (a) Pointed off into periods, the number 

 appears as 000'006'241'700, and by moving the decimal 

 point the number appears as 6.2417. The number falls 

 between 6.22950 = 1.843 and 6.33163 = 1.853; the first differ- 

 ence is 10213; the second difference is 6.24170-6.22950 

 = 1220; 1220-*- 10213 = .! 19 + , or .12, the fourth and fifth 

 figures of the root. The decimal point is located by the rule 

 previousjyjgiven^jhence, ^.0000062417 = .018412. 



(6) ^50932676=? As the number contains more than 

 six significant figures, reduce it to six significant figures by 

 replacing all after the sixth figure with ciphers, increasing 

 the sixth figure by 1 when the seventh is 5 or a greater 

 digit. In other words, the first five figures of ^50932700 and 

 of ^50932676 are the same. Pointed off into periods, the 

 number appears as 50'932'700, and by moving the decimal 

 point, the number appears as 50.9327, which falls between 

 60.6530 = 3.703 and 51.0648 = 3.713; the first difference 

 is 4118; the second difference is 2797; 2797-^4118 = . 679 + , 

 or .68. The integral part of the root evidently contains 

 three figures; hence "^50932676 = 370.68, correct to five 

 figures. 



Squares and Cubes. If the given number contains but 

 three (or less) significant figures, the square or cube is found 

 in the column headed n 2 or n 3 , opposite the given number in 

 the column headed n. If the given number contains more 

 than three significant figures, proceed in a manner similar to 

 that described for extracting roots. To square a number, 

 place the decimal point between the first and second signifi- 

 cant figures and find in the column headed "Vn or "VlOn two 

 consecutive numbers, one of which shall be a little greater 

 and the other a little less than the given number. The 

 remainder of the work is exactly as heretofore described. To 

 locate the decimal point, employ the principle that the square 

 of any number contains either twice as many figures as the 

 number squared or twice as many less one. If the column 

 headed VTOn is used, the square wil contain twice as many 

 figures, while if the column headed Vn is used, the square will 

 contain twice as many figures as the number squared, less 

 one. If the number contains an integral part, the principle 



