# [Tutor] while loop ends prematurly

Walter Prins wprins at gmail.com
Mon Jan 2 11:51:01 CET 2012

```Hi Steven,

On 2 January 2012 06:28, Steven D'Aprano <steve at pearwood.info> wrote:
> That only applies to decimal values which can be represented using a fixed
> number of decimal places. So 1/5 is fine, and is 0.2 exactly, but 1/3 is
> not, since it would require an infinite number of decimal places.

Just a small nit pick with the above:  1/3 is however not a decimal
number.   The word decimal means "tenth part", decimal numbers are
generally defined/understood as numbers that are expressible as
decimal fractions, meaning numbers where the denominator is a power of
10 or is an exact "tenth part".  Understood as such, decimal numbers
are therefore obviously accurately representable by the Decimal class
which is the whole point of calling the class "Decimal".

To backtrack slightly, numbers like 1/3, 1/5 etc are in general called
common or vulgar fractions, the only requirement being that they have
an integer numerator and an integer non-zero denominator.  The class
of numbers representible like this is called rational numbers and the
test for whether a number can be called rational is whether it can be
written as such.

The set of numbers we refer to as decimal numbers then, are a subset
of rational numbers, the test for whether they can be called decimal
being whether they can be written as a rational number with the
additional requirement that the denominator be a power of ten.
Addtionally, any rational number with a denominator of which the prime
factors are 2 and 5 may therefore be rewritten as a decimal number,
thus we know that 2/5 can also be accurately represented by a decimal
number (since the prime factors of 5 is 5), as can 1/50 (since the
prime factors of 50 are 2,5,5), but 1/3 can not, since 3 has only 3 as
its prime factor (and not 2 or 5), and neither 1/24 (since the prime
factors are 2,2,2,3).  So an additional test for whether a given
rational number can be accurately rewritten as a decimal (tenth part)
number, is to inspect the prime factors of the denominator.  If this
consists solely of 2's and 5's it can be expressed as a decimal, if
any other factors are present then it cannot be accurately expressed
as a decimal.

A happy and prosperous 2012 to all,

Walter
```