Need explanation on reverse scientific notation function in Lisp

Question

Here's the function i have and understand to go from 1) your coefficient and 2) your exponent to then extract the number out of the scientific notation.

Example:

coefficient 7, 
exponent 3 

7 * 10^3 = 7000

(define (scientific coeffiecent exponent) (* coefficient (expt 10 exponent)))

Here's what im struggling with: The function to go the other way around, From 7000 to the coeffiecent and exponent used to get it into the scientific notation. I've got a working function through networking, but really struggle understanding it entirely.

(define (sci-exponent number)
  (floor (/ (log number) (log 10))))

(define (sci-coefficient number)
  (/ number (expt 10 (sci-exponent number))))

if anyone could help me understand, It'll be greatly appreciated! Thanks for reading either way!

Answer 1

Look at the body of sci-exponent, it takes the floor of log(number)/log(10). As you might remember from math class: log_a(n1)/log_a(n2) = log_n2(n1). So what you're getting there is log₁₀(number), the floor of which gives you the number of digits of number minus 1, which would be the exponent for the scientific notation.

The coefficient is then easily derived from the exponent. Since, as you wrote, coeff * exp = number, then number / exp = coeff, which is exactly what sci-coefficient is implementing.