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{
\bf Attendance Quiz \# 24 for Dr. Z.'s Number Theory
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{\bf NAME:} (print!) $\underline
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{\bf E-MAIL ADDRESS:} (print!) 
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{\bf 1.} Convert  the $\frac{27}{23}$ into a simple continued fraction.

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{\bf 2.} Find a representation in the form $a+b\sqrt{Q}$ for rational numbers $a$ and $b$ and positive integer $Q$, for
the following infinite, ultimately periodic, continued fractions $x$.
$$
x=[3,1,2,1,2,1,2,1,2, \dots \quad ] \quad,
$$
where $1,2$ repeat for ever.


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