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\begin{document}

\noindent
{\Large 
Real Numbers Worksheet I \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~201}
\vspace{.25in}


\be 
\item Convert the following fractions to decimals.  Note that the prime
power representations of each denominator contain only $2$'s and/or $5$'s.
	\be
	\item $\bfrac{7}{40}$
	\item $\bfrac{11}{8}$
	\item $\bfrac{23}{25}$
	\ee
\item Classify each decimal according to the following categories
	\be
	\item[\bb] terminating decimal or nonterminating decimals
	\item[\bb] repeating decimal or non-repeating decimal
	\ee
	\be
	\item $123.123$
	\item $45.4545$
	\item $0.101001000100001 \dots $
	\item $0.10101010 \dots $
	\item $0.9999 \dots $
	\item $5.\ol{67}$
	\item $67.1243636 $
	\ee
\item Convert the following decimals to fractions, if possible.
	\be
	\item $123.123$
	\item $45.4545$
	\item $0.101001000100001 \dots $
	\item $0.10101010 \dots $
	\item $0.9999 \dots $
	\item $5.\ol{67}$
	\item $5.\ol{675}$
	\item $5.\ol{67234}$
	\item $67.1243636 $
	\ee
\item Objective number 48 should say: \\
Know that every terminating decimal is a rational number,
that is, every terminating decimal can be expressed as a
fraction.\\
You need to remove the word ``repeating''
\item Know that every nonterminating, repeating decimal is a rational number,
that is, every nonterminating, repeating decimal can be expressed as a
fraction. 
\item Know that every nonterminating, non-repeating decimal is a NOT
rational number, that is, every nonterminating, non-repeating decimal CANNOT
be expressed as a fraction. 
\item Show that $\sqrt{2}$ is irrational.  
\item Show that $3 \sqrt{2}$ is irrational.
\item Show that $5 + \sqrt{2}$ is irrational.
\item Know that there are infinitely many irrational numbers.
\item Know that every position on the number line represents a real number
and every real number is represented by a position on the number line.
\item Know that there are positions on the number line which do not
represent rational numbers.  
\ee
\end {document}
