10 PRACTICAL MATHEMATICS 



The second approximations are : 



(1 + a) n -z. 1 + na + -n(n l)a 2 



(1 a) n r 1 na + -n(n l)a 2 



m 



(1 + a)- s 1 - na + -n(n + l)a 2 



m 



(1 - a)~ n z 1 + na + -n(n + l)a 2 



A 



To find the first and second approximations of 



= (125 + 5) 3 = s(l + 

 Since n=i A = |=i 



B-\xli-ix 1. l - 

 2 ~3 X 3 ' 9 



y 1 



Then 



The first approximation is 5\l + J = 5-0667 given to four 



places of decimals. 



The term to be subtracted from the first approximation to give 



5 1 



the second approximation is - x = 0-0009 given to four 



./ O 



places of decimals. 



The second approximation is 5-0658. 



Also 5-066 is the result correct to four significant figures. 



To find the first and second approximations of VlOOO. 

 5/1000 = (1024 - 24)^ = 4( 1 - -|- 



Since n = - A = f = - 

 5 15 



21 J2_ 



5 X 5 = ~ 25 



Then 



^ > 1*^8 



/ 3 



The first approximation is 4(l ^77;) = 3-98125 given to five 



places of decimals. 



