(Racket/Scheme) Subtraction yields result off by i

Question

I'm currently messing around with "How To Design Programs" - using Scheme/Racket; I've come across a really peculiar feature in the R5RS version of Scheme.

When conducting a simple subtraction, albeit using values with decimal point accurace, answers are minutely off what would be expected.

For example; given the following subtraction operation:

(- 5.00 4.90)
=> 0.09999999999999965

When one should surely be expecting a clean 0.10? Whole number subtraction works as expected;

> (- 5 4)
 => 1
> (- 5 4.9)
 => 0.09999999999999965

Take for example, Exercise 3.1.1:

The next step is to make up examples for each of the functions. Determine how many attendees can afford a show at a ticket price of $3.00, $4.00, and $5.00. Use the examples to formulate a general rule that shows how to compute the number of attendees from the ticket price. Make up more examples if needed.

The rule in the example that was for every $0.10 taken off of the ticket prices, 15 more people would attend. So a quick function like this would work..

(define (attendees ticket-price)
  (+ 120 (* (/ (- 5.00 ticket-price) 0.10) 15)))

However, this returns the (rather annoying)..

> (attendance 4.90)
 => 134.99999999999994

So after trying the (pretty much identical) solution from the text book..

(define (attendance price)
  (+ (* (/ 15 .10) (- 5.00 price))
    120))

I got exactly the same error. Is this something specific with my local system? I'm pretty curious - in reality I could simply use some form of rounding to correct this; but I'd rather know why it's occurring first!

Apart from that, I advise anyone interested in Lisp to look at HTDP. It appears to be quite a gentle text from skimming it, very hands on. I do like SICP - but thats more of a long term thing; I seem to spend a good few days doing the reading, then the exercises, then catching up with lectures online. HTDP seems to be a bit more like 'Oh, I've got 15 minutes spare - I'll look at HTDP'.

Answer 1

In addition to the prior (correct) answer: the question you really should be asking is: "why doesn't this happen in other language levels?" To which the answer is: many of the other language levels interpret 5.03 as being an exact number (five and three hundredths) rather than as a floating-point number.

JFYI!

Answer 2

Floating-point numbers are not always stored as the exact values you expect. See e.g. The Perils of Floating Point.

If you want exact calculations, you could use integer arithmetic in your case by storing the values in cents instead of dollars.

(define (attendees ticket-price-cents)
  (+ 12000 (* (/ (- 500 ticket-price-cents) 10) 1500)))