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\module{Scientific notation}{01}{AP05}{1 period}

\prereq{\begin{itemize}
	\item Positive and negative powers of ten.
	\end{itemize}}

\object{\begin{itemize}
        \item Discover the scientific notation, the E notation used by the calculators and the engineering notation.
	\item Switch from one notation to another.
        \end{itemize}}

\mater{\begin{itemize}
	\item Fact sheets about the three notations (36 copies).
	\item Test paper with 16numbers (36 copies).
	\item Matching cards with different notations of the same numbers (20 cards).
	\end{itemize}}

\modpart{Matching game}{10 mins}

Students are handed out cards with numbers written in ordinary decimal notation, scien-
tific notation, E notation or engineering notation. They commit their numbers to memory
and mingle to find the students with equal numbers.

\modpart{Team work}{20 mins}

Working in the same teams as in the first part on a lesson handed-out by the teacher, students have to undersand the
three notations and how to switch from one to another.

\modpart{Test}{Remaining time}

Still working in teams, students have to convert numbers from one notation to the others, including the ordinary
notation.

\pagebreak
\newcommand{\E}{\textrm{E}}

\moddocdis{Scientific notation}{01}{AP05}{Lesson}

\defi{Scientific notation}{A decimal number $x$ is said to be in scientific notation if there exist two numbers $k$ and $n$
such as $$x=a \times 10^n,$$
where $a$ is a decimal number such that $1\leq |a|<10$, and $n$ is an integer (positive or negative).}

{\sl Examples :}
\begin{itemize}
\itemb $158$ ; $-45.8$ and $3.7$ are not in scientific notation.
\itemb $-2.58749 \times 10^5$ is in scientific notation, as $1\leq 2.58749 < 10$ and $5$ is an integer.
\itemb $7.451 \times 10^{-4}$ is the scientific notation of the number $0.0007451$.
\itemb $12 \times 10^{-8}$ is not a scientific notation because $12$ is greater than $10$.
\itemb $0.587 \times 10^2$ is not a scientific notation because $0.587$ is lower than $1$.
\end{itemize}

\bigskip

\defi{E notation}{An alternative notation used by calculators is the ``E'' notation. It's basically the scientific
notation, with the letter E standing for $\times 10$\^{}.}

{\sl Examples :}
\begin{itemize}
\itemb The E notation of the number $-2.58749 \times 10^5$ is $-2.58749\E5$.
\itemb The E notation of the number $0.0007451$ is $7.451\E-4$.
\end{itemize}

\bigskip

\defi{Engineering notation}{Engineering notation differs from normalized scientific notation in that the exponent $n$ is
restricted to multiples of $3$. Consequently, the absolute value of $a$ is in the range $1\leq |a|<1000$, rather than
$1\leq |a|<10$.}

{\sl Examples :}
\begin{itemize}
\itemb The engineering notation of the number $-2.58749 \times 10^5$ is $-258.749 \times 10^3$.
\itemb The engineering notation of the number $0.0007451$ is $745.1 \times 10^{-6}$.
\end{itemize}

\pagebreak

\moddocdis{Scientific notation}{01}{AP05}{Test}

\begin{center}
\begin{tabularx}{16cm}{c|X|>{\columncolor{lightgray}} c|X|>{\columncolor{lightgray}} c|X|>{\columncolor{lightgray}} c|X|>{\columncolor{lightgray}} c}
 &\centering Ordinary &&\centering Scientific &&\centering Calculator &&\centering Engineering & \\ \hline
1 &\centering $45$ && && && & \rule{0pt}{20pt}\\[5pt] \hline
2 & &&\centering $-3.8405 \times 10^5$ && && & \rule{0pt}{20pt}\\[5pt] \hline
3 & && &&\centering $1.15\E-2$ && & \rule{0pt}{20pt}\\[5pt] \hline
4 & && && &&\centering $458.7 \times 10^0$ & \rule{0pt}{20pt}\\[5pt] \hline
5 &\centering $-4879$ && && && & \rule{0pt}{20pt}\\[5pt] \hline
6 & &&\centering $7.7484 \times 10^{-4}$ && && & \rule{0pt}{20pt}\\[5pt] \hline
7 & && &&\centering $2.951\E0$ && & \rule{0pt}{20pt}\\[5pt] \hline
8 & && && &&\centering $55.0002 \times 10^{-3}$ & \rule{0pt}{20pt}\\[5pt] \hline
9 &\centering $0.258$ && && && & \rule{0pt}{20pt}\\[5pt] \hline
10 & &&\centering $-3.7 \times 10^{-4}$ && && & \rule{0pt}{20pt}\\[5pt] \hline
11 & && &&\centering $2.3548792\E7$ && & \rule{0pt}{20pt}\\[5pt] \hline
12 & && && &&\centering $-80 \times 10^{-6}$ & \rule{0pt}{20pt}\\[5pt] \hline
13 &\centering $100000$ && && && & \rule{0pt}{20pt}\\[5pt] \hline
14 & &&\centering $1 \times 10^{-5}$ && && & \rule{0pt}{20pt}\\[5pt] \hline 
15 & && &&\centering $4.01\E4$ && & \rule{0pt}{20pt}\\[5pt] \hline
16 & && && &&\centering $510 \times 10^{-6}$ & \rule{0pt}{20pt}\\[5pt] \hline
\end{tabularx}
\end{center}
\pagebreak

\moddocdis{Scientific notation}{01}{AP05}{Correction}

\begin{center}
\begin{tabularx}{16cm}{c|X|>{\columncolor{lightgray}} c|X|>{\columncolor{lightgray}} c|X|>{\columncolor{lightgray}} c|X|>{\columncolor{lightgray}} c}
 &\centering Ordinary &&\centering Scientific &&\centering Calculator &&\centering Engineering & \\ \hline
1 &\centering $45$ && \centering $4.5\times10^1$&& \centering $4.5\E1$ && \centering $45\times10^0$& \rule{0pt}{20pt}\\[5pt] \hline
2 &\centering $-384050$ &&\centering $-3.8405 \times 10^5$ && \centering $-3.8405\E5$&& $-384.05 \times 10^3$& \rule{0pt}{20pt}\\[5pt] \hline
3 &\centering $0.0115$ &&\centering $1.15\times 10^{-2}$ &&\centering $1.15\E-2$ &&\centering $11.5\times 10^{-3}$&\rule{0pt}{20pt}\\[5pt] \hline
4 &\centering $458.7$ &&\centering $4.587 \times 10^{2}$ &&\centering $4.587 \E2$ &&\centering $458.7(\times 10^0)$ & \rule{0pt}{20pt}\\[5pt] \hline
5 &\centering $-4879$ &&\centering $-4.879 \times 10^{3}$ &&\centering $-4.879 \E3$ &&\centering $-4.879 \times 10^{3}$ & \rule{0pt}{20pt}\\[5pt] \hline
6 &\centering $0.00077484$ &&\centering $7.7484 \times 10^{-4}$ &&\centering $7.7484 \E-4$ && \centering $774.84 \times 10^{-6}$& \rule{0pt}{20pt}\\[5pt] \hline
7 & \centering $2.951$&&\centering $2.951\times 10^{0}$ &&\centering $2.951\E0$ &&\centering $2.951\times 10^{0}$ & \rule{0pt}{20pt}\\[5pt] \hline
8 & \centering $0.0550002$&&\centering $5.50002 \times 10^{-2}$ &&\centering $5.50002\E-2$ &&\centering $55.0002 \times 10^{-3}$ & \rule{0pt}{20pt}\\[5pt] \hline
9 &\centering $0.258$ &&\centering $2.58\times 10^{-1}$  && \centering $2.58\E-1$&& \centering $258\times 10^{-3}$& \rule{0pt}{20pt}\\[5pt] \hline
10 &\centering $-0.00037$ &&\centering $-3.7 \times 10^{-4}$ &&\centering $-3.7 \E-4$ && \centering $-370 \times 10^{-6}$& \rule{0pt}{20pt}\\[5pt] \hline
11 &\centering$23548792$ &&\centering $2.3548792\times 10^{7}$ &&\centering $2.3548792\E7$ &&\centering$23.548792\times 10^{6}$ & \rule{0pt}{20pt}\\[5pt] \hline
12 &\centering $-0.00008$ &&\centering$-8 \times 10^{-5}$ &&\centering $-8 \E-5$&&\centering $-80 \times 10^{-6}$ & \rule{0pt}{20pt}\\[5pt] \hline
13 &\centering $100000$ && \centering $(1\times)10^{5}$&& \centering $1\E5$ && \centering  $100\times10^{3}$ & \rule{0pt}{20pt}\\[5pt] \hline
14 &\centering $0.00001$ &&\centering $1 \times 10^{-5}$ &&\centering$1 \E-5$ &&\centering $10 \times 10^{-6}$ & \rule{0pt}{20pt}\\[5pt] \hline 
15 &\centering $40100$ &&\centering $4.01 \times 10^{4}$ &&\centering $4.01\E4$ &&\centering $40.1 \times 10^{3}$ & \rule{0pt}{20pt}\\[5pt] \hline
16 &\centering $0.00051$ &&\centering $5.1 \times 10^{-4}$ &&\centering $5.1\E-4$ &&\centering $510 \times 10^{-6}$ & \rule{0pt}{20pt}\\[5pt] \hline
\end{tabularx}
\end{center}

\pagebreak

\moddoc{Matching cards with various notations of the same numbers}

\begin{center}
\includegraphics[scale=0.8]{Euro.s01AP05.eps}
\end{center}

 

\end{document}
