Decimals not equalling themselves (e.g. 0.2 = 0.2000000001)

[Tommy Nordgren]

On 3 aug 2008, at 17.16, Edwin.Madari at VerizonWireless.com wrote:

> for nth square root: use math.sqrt n times for example

	Ehum. The OP wants to compute the nth root ( not the nth square root)
>
>>>> import math
>>>> num = 625
>>>> how_many_sqrt = 2
>>>> for i in range(how_many_sqrt):
> ..     num = math.sqrt(num)
> ..
>>>> num
> 5.0
>
> all comparisons work fine for arbitrary floating point numbers...
> For readability print them with required precision. for example
>>>> a = .2
>>>> b = .4
>>>> b = b/2
>>>> a == b
> True
>>>> a, b
> (0.20000000000000001, 0.20000000000000001)
>>>> '%.2f' % a, '%.2f' % b
> ('0.20', '0.20')
>>>>
>
> thx. Edwin
>
> -----Original Message-----
> From: python-list-bounces+edwin.madari=verizonwireless.com at python.org
> [mailto:python-list-bounces+edwin.madari=verizonwireless.com at python.org 
> ]
> On Behalf Of CNiall
> Sent: Sunday, August 03, 2008 10:03 AM
> To: python-list at python.org
> Subject: Decimals not equalling themselves (e.g. 0.2 = 0.2000000001)
>
>
> I am very new to Python (I started learning it just yesterday), but I
> have encountered a problem.
>
> I want to make a simple script that calculates the n-th root of a  
> given
> number (e.g. 4th root of 625--obviously five, but it's just an example
> :P), and because there is no nth-root function in Python I will do  
> this
> with something like x**(1/n).
>
> However, with some, but not all, decimals, they do not seem to 'equal
> themselves'. This is probably a bad way of expressing what I mean, so
> I'll give an example:
>>>> 0.5
> 0.5
>>>> 0.25
> 0.25
>>>> 0.125
> 0.125
>>>> 0.2
> 0.20000000000000001
>>>> 0.33
> 0.33000000000000002
>
> As you can see, the last two decimals are very slightly inaccurate.
> However, it appears that when n in 1/n is a power of two, the decimal
> does not get 'thrown off'. How might I make Python recognise 0.2 as  
> 0.2
> and not 0.20000000000000001?
>
> This discrepancy is very minor, but it makes the whole n-th root
> calculator inaccurate. :\
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------
What is a woman that you forsake her, and the hearth fire and the home  
acre,
to go with the old grey Widow Maker.  --Kipling, harp song of the Dane  
women
Tommy Nordgren
tommy.nordgren at comhem.se