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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 317}

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\begin{document}

\begin{center}
    \small Fractions décimales, multiplication/division par 10, 100, 1 000, conversions d'unités.
\end{center}
\vspace{0.5em}
\sloppy

\needspace{5\baselineskip}
\section*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,579  ~ \(\times\)  ~ 1 000
\item   0,494  ~ \(\times\)  ~ 1 000
\item   3,01  ~ \(\times\)  ~ 100
\item   0,273  ~ \(\times\)  ~ 100
\item   8,75  ~ \(\times\)  ~ 1 000
\item   945  ~ \(\times\)  ~ 10
\item   0,521  ~ \(\times\)  ~ 1 000
\item   386  ~ \(\times\)  ~ 100
\item   20,8  ~ \(\times\)  ~ 10
\item   0,11  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   7 483  ~ : ~ 1 000
\item   69,4  ~ : ~ 1 000
\item   9,847  ~ : ~ 1 000
\item   76,12  ~ : ~ 10
\item   17,63  ~ : ~ 1 000
\item   3 247  ~ : ~ 10
\item   43,54  ~ : ~ 10
\item   11,36  ~ : ~ 10
\item   7,895  ~ : ~ 10
\item   66,29  ~ : ~ 100
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   79  ~ \(\times\)  ~ ... ~ = ~ 79 000
\item   448  ~ \(\times\)  ~ ... ~ = ~ 4 480
\item   0,037  ~ \(\times\)  ~ ... ~ = ~ 37
\item   17  ~ \(\times\)  ~ ... ~ = ~ 170
\item   0,223  ~ \(\times\)  ~ ... ~ = ~ 223
\item   63,6  ~ \(\times\)  ~ ... ~ = ~ 63 600
\item   0,099  ~ \(\times\)  ~ ... ~ = ~ 0,99
\item   0,037  ~ \(\times\)  ~ ... ~ = ~ 37
\item   0,576  ~ \(\times\)  ~ ... ~ = ~ 5,76
\item   2,44  ~ \(\times\)  ~ ... ~ = ~ 244
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   500,6  ~ \(\times\)  ~ 0,01
\item   8 528  ~ \(\times\)  ~ 0,001
\item   4 204  ~ \(\times\)  ~ 0,001
\item   8 277  ~ \(\times\)  ~ 0,1
\item   5 176  ~ \(\times\)  ~ 0,01
\item   58,38  ~ \(\times\)  ~ 0,01
\item   827  ~ \(\times\)  ~ 0,01
\item   5 073  ~ \(\times\)  ~ 0,001
\item   668,7  ~ \(\times\)  ~ 0,1
\item   591,2  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   311,8  ~ \(\times\)  ~ ... ~ = ~  3,118
\item   37,34  ~ \(\times\)  ~ ... ~ = ~  3,734
\item   84,75  ~ \(\times\)  ~ ... ~ = ~  0,847 5
\item   55,81  ~ \(\times\)  ~ ... ~ = ~  5,581
\item   1,914  ~ \(\times\)  ~ ... ~ = ~  0,019 14
\item   9 522  ~ \(\times\)  ~ ... ~ = ~  95,22
\item   455,6  ~ \(\times\)  ~ ... ~ = ~  0,455 6
\item   959  ~ \(\times\)  ~ ... ~ = ~  9,59
\item   54,7  ~ \(\times\)  ~ ... ~ = ~  0,547
\item   56,26  ~ \(\times\)  ~ ... ~ = ~  0,056 26
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\section*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   878,75 ~cm~ = ...~hm
\item   2 544,4 ~hg~ = ...~dag
\item   389,49 ~mm~ = ...~hm
\item   9 244,2 ~m~ = ...~dm
\item   307,18 ~dag~ = ...~cg
\item   774,69 ~km~ = ...~hm
\item   296,96 ~m~ = ...~dam
\item   1 828,4 ~mL~ = ...~L
\item   819,25 ~daL~ = ...~mL
\item   7 826,4 ~dg~ = ...~cg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

\needspace{5\baselineskip}
\subsection*{Exercice 1 : Recopie et complète :}

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{6000}{100}\) = \(\dfrac{600}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{360}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{420}{1\,000}\)
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 2 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   0,579  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 579}
\item   0,494  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 494}
\item   3,01  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 301}
\item   0,273  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 27,3}
\item   8,75  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 750}
\item   945  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9 450}
\item   0,521  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 521}
\item   386  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 38 600}
\item   20,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 208}
\item   0,11  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,1}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 3 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   7 483 ~ : ~ 1 000 ~ = ~{\color{red} 7,483}
\item   69,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,069 4}
\item   9,847 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 847}
\item   76,12 ~ : ~ 10 ~ = ~{\color{red} 7,612}
\item   17,63 ~ : ~ 1 000 ~ = ~{\color{red} 0,017 63}
\item   3 247 ~ : ~ 10 ~ = ~{\color{red} 324,7}
\item   43,54 ~ : ~ 10 ~ = ~{\color{red} 4,354}
\item   11,36 ~ : ~ 10 ~ = ~{\color{red} 1,136}
\item   7,895 ~ : ~ 10 ~ = ~{\color{red} 0,789 5}
\item   66,29 ~ : ~ 100 ~ = ~{\color{red} 0,662 9}
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 4 : Complète par 10, 100, 1000... :}

\begin{multicols}{2}
\begin{itemize}
\item   79 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~79 000
\item   448 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 480
\item   0,037 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~37
\item   17 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~170
\item   0,223 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~223
\item   63,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~63 600
\item   0,099 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,99
\item   0,037 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~37
\item   0,576 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,76
\item   2,44 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~244
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 5 : Calcule mentalement :}

\begin{multicols}{2}
\begin{itemize}
\item   500,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,006
}\item   8 528 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,528
}\item   4 204 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,204
}\item   8 277 ~ \(\times\)  0,1 ~ = ~{\color{red} 827,7
}\item   5 176 ~ \(\times\)  0,01 ~ = ~{\color{red} 51,76
}\item   58,38 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,583 8
}\item   827 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,27
}\item   5 073 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,073
}\item   668,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 66,87
}\item   591,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 59,12
}\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 6 : Complète par 0,1 ~ 0,01 ~  0,001 ... }

\begin{multicols}{2}
\begin{itemize}
\item   311,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,118
\item   37,34 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,734
\item   84,75 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,847 5
\item   55,81 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,581
\item   1,914 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,019 14
\item   9 522 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 95,22
\item   455,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,455 6
\item   959 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,59
\item   54,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,547
\item   56,26 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,056 26
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 7 : Complète par 10,100 1 000... ou une fraction décimale : }

\begin{multicols}{2}
\begin{itemize}
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

\needspace{5\baselineskip}
\subsection*{Exercice 8 : Complète : }

\begin{multicols}{2}
\begin{itemize}
\item   878,75 ~cm~ = {\color{red}  0,087 875 }~hm
\item   2 544,4 ~hg~ = {\color{red}  25 444 }~dag
\item   389,49 ~mm~ = {\color{red}  0,003 894 9 }~hm
\item   9 244,2 ~m~ = {\color{red}  92 442 }~dm
\item   307,18 ~dag~ = {\color{red}  307 180 }~cg
\item   774,69 ~km~ = {\color{red}  7 746,9 }~hm
\item   296,96 ~m~ = {\color{red}  29,696 }~dam
\item   1 828,4 ~mL~ = {\color{red}  1,828 4 }~L
\item   819,25 ~daL~ = {\color{red}  8 192 500 }~mL
\item   7 826,4 ~dg~ = {\color{red}  78 264 }~cg
\end{itemize}
\end{multicols}
\end{document}
