Know constant
 

[QUOTE=R. Gerbicz;85918]This is a known constant. See: [URL="http://mathworld.wolfram.com/ChampernowneConstant.html"]http://mathworld.wolfram.com/ChampernowneConstant.html[/URL][/QUOTE]
:bow:
Thank you R. Gerbicz for hitting the nail on the head by pinning down the Chempernowne constant which is normal for base 10 and also transcendental which I gave as an example.
This was a revelation for me and with your URL for Math World I went on to the 'binary' and ternary 'Champ' and also the Copeland-Erdos constant for the concatenation of the primes which is a normal number.

Particular examples of quadratic irrationals are (a + sq.rt. b) where a =0 and b is a non square natural number (or greater than 1 :) like
Sq roots of 2 ,3, 5, e tc..

The continued fraction representation of such a number is striking.
The sequence of natural numbers that defines it as a continued fraction has a curious characteristic.
It starts with some number A, t hen it is immediately followed by a 'palindromic sewquence ( that is one which reads the same backwards) like B, C, D,.... D,C,B, followed by 2A repeats itself indefinitely.
Take the number sq.rt. 14 as an example for which the sequence is
3,1,2,1,6,1,2.1,6,1,2,1,6,.1,2,1,6........
Here A = 3 and the palindromic sequence D,C,B is just the three term sequence 1,2,1,.

For converting decimal to its rational fraction I give an example for the method.
Eg: Say we have 1.42857 142857 142857.
Let x = 1.42857 repeating
Get rid of the decimal by multiplying
So 100000x = 142857
Subtract the two eqn.s
We get 99999x = 142857
x = 142857/99999 = 1/7

Try it out for x = .01 01 01 01....
You should get 1/99
Mally :coffee: