MATHEMATICS 9 



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

 and second significant figures, the number is 2.7342, which 

 occurs between 2.73313= VrTi? and 2.73496=^7748, found 

 under \. The first three figures of the square are 747. The 

 second difference 107 -^ the first difference 183 = .584, or .58. 

 Hence, 273.422 = 74,758. 



(&) With the position of the decimal point changed, the 

 number is 5.2436, which is between 5.23450 = \2.74 and 

 5.24404 = V2.75, both under "VlOn. The first three significant 

 figures of the root are 2.74, and the second difference 910-;- 

 the first difference 954 = .953, or .95, the next two figures. The 

 number has one cipher following the decimal point, and the 

 column headed VlOn is used; hence, .0524362 = .0027495. 



CUBES 



To cube a number, proceed in the same way, but use a 

 column headed ^n, ^lOn, or ^lOOw. If the number contains 

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

 of the cube will be three times as many as in the given num- 

 ber if the column headed ^100 is used; it will be three times 

 as many less 1 if the column headed A/lOn is used; and it will 

 be three times as many less 2 if the column headed 3jn is used. 

 If the number is wholly decimal, the number of ciphers fol- 

 lowing the decimal point in the cube will be three times, three 

 times plus 1, or three times plus 2, as many as in the given 

 number, depending on whether the >/100w, "VtlOn, or 3ln column 

 is used. 



EXAMPLE. Find the results of the following: 



(a) 129.6843 = ? (b) 7.6442 3 = ? (c) .032425' = ? 



SOLUTION. (a) With the position of the decimal 

 changed, the number 1.29684 is between 1.29664 = 

 and 1.29862= "fe.19, found under -%. The second difference 

 20 -r- the first difference 198 = . 101 + , or .10. Hence, the first 

 five significant figures are 21810; the number of figures in 

 the integral part of the cube is 3X3 2 = 7; and 129.684 s 

 = 2,181,000, correct to five significant figures. 



(6) 7.64420 occurs between 7.64032=^446 and 7.64603 

 = ^447. The first difference is 571; the second difference is 

 388; and 388 -4- 571 = .679 + , or .68. Hence, the first five 



