On Monday 12 January 2004 20:45, kilopascal wrote:
> > > 1.) You don't have the infinite range you have with a decimal
> > > number.
> >
> > Wrong. All decimal numbers can be expressed as fractions, but not all
> > fractions can be expressed as decimal numbers (1/3, 2/3, 1/7, etc.)
>
> You have it backwards. Any fraction can be expressed as a decimal, but not
> every decimal can be expressed as a fraction with integer numbers in the
> numerator or denominator.
Is there something I'm missing? Decimals are equivalent to fractions where
the denominator is a positive integral power of 10. A decimal number X with
N digits past the decimal is the fraction
X*10^N/10^N
For example, X=23.4821, then N=4. So X is the fraction
234821/10000
On the other hand, fractions like 1/3, 1/6, 1/7, 1/9, etc. repeat infinitely
when written as decimals.
John
