30 MATHEMATICS 



first and second significant figures, the number 1.29684 is 

 found between 1.29664=^2.18 and 1.29862=^2.19. The 

 first difference is 198; the second difference is 20; and 20 -H 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 129.6843 = 2,181,000, correct to five sig- 

 nificant figures. 



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

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

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

 significant figures are 44668 ; the number of ciphers following 

 the decimal point is 3X0 = 0; and .76442 3 = .44866, correct to 

 five significant figures. 



(c) 3.2425 falls between 3.24278= ^341 and 3.23961 



= "^34.0. The first difference is 317; the second difference 

 is 289; 289 H- 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 .032425 3 = .000034091, 

 correct to five significant figures. 



Reciprocals. The reciprocal of a number is 1 divided by 

 the number. By using reciprocals, division is changed into 



multiplication, since a-4-& = r = aXr. The table gives the 



reciprocals of all numbers expressed by three significant 

 figures correct to six significant figures. By proceeding in a 

 manner similar to that just described for powers and roots, 

 the reciprocal of any number correct to five significant 

 figures may be obtained. The decimal point in the result 

 may be located as follows: If the given number has an 

 integral part, the number of ciphers following the decimal 

 point in the reciprocal will be one less than the number of 

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

 given number is entirely decimal, the number of figures in 

 the integral part of the reciprocal will be one greater than 

 the number of ciphers following the decimal point in the 

 given number. For example, the reciprocal of 3370 = .00029- 

 6736 and of .00348 = 287.356. 



When the number whose reciprocal is desired contains 

 more than three significant figures, express the number to 



