#!/usr/bin/env lua
-- file: fractions.lua
-- Exercise 2.3: The number 12.7 is equal to the fraction
-- 127/10, where the denominator is a power of ten. Can 
-- you express it as a common fraction where the denominator
-- is a power of two? What about the number 5.5?

-- Just like some numbers like one third (0.333...) cannot
-- be expressesed in the decimal system with a denominator
-- that is a denominator of ten, some numbers can't be
-- represented in the binary system.

-- 12.7 is one of these numbers. It can be exactly represented
-- with 127/10, but not if the denominator has to be a
-- power of two. In this case, the choice of the denominator
-- determines the accuracy of the representation (if the
-- nominator is truncated to an integer)
function represent(number, tries)
    print("Trying to represent "..number)
    denominator = 1
    for i = 1, tries do
        denominator = 2 * denominator
        print((number*denominator) .. '/' .. denominator)
    end
end
represent(12.7, 10)

-- The number 5.5 can, however, easily be represented:
-- already the first attempt of the represent() function
-- works out (using 2 as the denominator)
represent(5.5, 5)