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{\huge  \sc   Homework 4} \\
\smallskip
{ Due Date: 10/19/2021}\\
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{Name:  }\\
{\large  }
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\begin{enumerate}

\item[3.1] Express the decimal $1.\overline{813}$ as a fraction $\frac{m}{n}$ (where $m$ and $n$ are integers).
\newpage
 \item[3.3] Which of the following numbers are rational, and which are irrational?
 Express those which are rational in the form $\frac{m}{n}$ with $m,n\in \mathbb{Z}$.
 
 \begin{enumerate}
 
     \item $0.a_1a_2a_3\ldots$ where $n\in\mathbb{N}$ the value of $a_n$ is the number 0,1,2,3 or 4 which is the remainder on dividing $n$ by 5.
     
     \item 0.101001000100001000001\ldots
     
     \item $1.b_1b_2b_3\ldots$ where $b_i=1$ if $i$ is a square, and $b_i=0$ if $i$ is not a square. 
 \end{enumerate}
\newpage
    \item[3.4] Without using a calculator, find the cube root of $2$ , correct to $1$ decimal place.
    \newpage
    \item[3.6] Show that for an integer $n\geq 2$, the period of the decimal expression for the rational number $\frac{1}{n}$ is at most $n-1$. 
   
\end{enumerate}

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