SICP Exercise 3.58 expand

Exercise 3.58.  Give an interpretation of the stream computed by the following procedure:

(define (expand num den radix)
  (cons-stream
   (quotient (* num radix) den)
   (expand (remainder (* num radix) den) den radix)))

(Quotient is a primitive that returns the integer quotient of two integers.) What are the successive elements produced by (expand 1 7 10) ? What is produced by (expand 3 8 10) ?

SOLUTION

 The code and tests are here.

 EXPLANATION

 (expand 1 7 10) produces:

 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4 ...

 (expand 3 8 10) produces
3, 7, 5, 0, 0, 0, 0 ...

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