# SICP Solutions

### Section - The Elements of Programming

#### Exercise 1.7

For small numbers, specially whose square are themselves less than 0.001 the method good-enough is not good enough as it will return true as soon our guess reach close to 0.001 and clearly it wont be correct.

For example: (sqrt 0.00000001) should return 0.0001 but the procedure returns 0.03125106561775382.

For large numbers, generally computers does not support high precision. Thus the difference between two large numbers which are very close will still result there difference more than 0.001, no matter how close they get.

Thus the program will go into infinite recursive calls.

After changing the program with new good-enough we get:

This programs works for small numbers as well as large numbers. Note that in racket I used numbers in decimal form like 100000000000000000.0 or 0.000000001. Using fractional or natural numbers takes program much larger time to finish because racket internally uses rational number which end up generating very large numerators and denominators in the fractions.