I know that a continued fraction can be converted to a decimal fraction by condensing it to a simple fraction and then performing long division to produce a decimal fraction.
I am wondering how the decimal fraction can be discovered "natively," meaning without condensing it first.
It seems to me the whole benefit of the continued fraction is that the value has been reduced to a series of terms which provide utility and that potential utility is thrown away if the continued fraction is condensed and terms disposed of. I would think that there probably is some way to convert the terms directly into decimal place values.