Re: 0.1010010001...

Dear Debra,
the article

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?
view=body&id=pdf_1&handle=euclid.pja/1195510210

contains a complete answer on your question. The main theorem claims the
algebraic independence of numbers \theta_2(q), \theta_2'(q), \theta_2''(q)
for any algebraic q, 0<|q|<1. Consequently the number \theta_2(q) should
be transcendental. In your case q=10^{-1/2} is an algebraic number.
With best regards,
Yuri Nesterenko