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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 85}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,05  ~ \(\times\)  ~ 1 000
\item   0,236  ~ \(\times\)  ~ 1 000
\item   0,088  ~ \(\times\)  ~ 10
\item   0,08  ~ \(\times\)  ~ 1 000
\item   0,594  ~ \(\times\)  ~ 1 000
\item   450  ~ \(\times\)  ~ 10
\item   0,071  ~ \(\times\)  ~ 10
\item   0,45  ~ \(\times\)  ~ 1 000
\item   0,708  ~ \(\times\)  ~ 100
\item   70,9  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   371,2  ~ : ~ 100
\item   18,98  ~ : ~ 10
\item   0,286  ~ : ~ 1 000
\item   245,8  ~ : ~ 10
\item   75,97  ~ : ~ 10
\item   10,44  ~ : ~ 10
\item   691,5  ~ : ~ 10
\item   6,036  ~ : ~ 1 000
\item   284,1  ~ : ~ 10
\item   602,3  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,159  ~ \(\times\)  ~ ... ~ = ~ 15,9
\item   11,3  ~ \(\times\)  ~ ... ~ = ~ 113
\item   7,64  ~ \(\times\)  ~ ... ~ = ~ 764
\item   21,5  ~ \(\times\)  ~ ... ~ = ~ 21 500
\item   912  ~ \(\times\)  ~ ... ~ = ~ 91 200
\item   0,04  ~ \(\times\)  ~ ... ~ = ~ 40
\item   14,9  ~ \(\times\)  ~ ... ~ = ~ 149
\item   0,014  ~ \(\times\)  ~ ... ~ = ~ 1,4
\item   3,87  ~ \(\times\)  ~ ... ~ = ~ 38,7
\item   5,54  ~ \(\times\)  ~ ... ~ = ~ 55,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 617  ~ \(\times\)  ~ 0,001
\item   840,2  ~ \(\times\)  ~ 0,001
\item   85,01  ~ \(\times\)  ~ 0,1
\item   9,441  ~ \(\times\)  ~ 0,001
\item   73,6  ~ \(\times\)  ~ 0,001
\item   419,6  ~ \(\times\)  ~ 0,001
\item   6,985  ~ \(\times\)  ~ 0,01
\item   41,61  ~ \(\times\)  ~ 0,01
\item   5,819  ~ \(\times\)  ~ 0,1
\item   78,11  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   357,3  ~ \(\times\)  ~ ... ~ = ~  35,73
\item   82,85  ~ \(\times\)  ~ ... ~ = ~  8,285
\item   5 670  ~ \(\times\)  ~ ... ~ = ~  567
\item   32,96  ~ \(\times\)  ~ ... ~ = ~  3,296
\item   796  ~ \(\times\)  ~ ... ~ = ~  0,796
\item   2,3  ~ \(\times\)  ~ ... ~ = ~  0,23
\item   1 115  ~ \(\times\)  ~ ... ~ = ~  111,5
\item   65,27  ~ \(\times\)  ~ ... ~ = ~  0,065 27
\item   8 197  ~ \(\times\)  ~ ... ~ = ~  8,197
\item   442  ~ \(\times\)  ~ ... ~ = ~  44,2
\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~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   764,19 ~daL~ = ...~mL
\item   794,35 ~cm~ = ...~m
\item   922,87 ~dm~ = ...~cm
\item   1 980,3 ~dg~ = ...~hg
\item   4 711,4 ~cg~ = ...~g
\item   387,21 ~mL~ = ...~cL
\item   968,01 ~kg~ = ...~dg
\item   1 800,3 ~mm~ = ...~dam
\item   561,42 ~daL~ = ...~cL
\item   613,62 ~cL~ = ...~mL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{5200}{100}\) = \(\dfrac{520}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{390}{100}\)
\item   \(\dfrac{70}{100}\) = \(\dfrac{700}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,05  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 050}
\item   0,236  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 236}
\item   0,088  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,88}
\item   0,08  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 80}
\item   0,594  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 594}
\item   450  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 500}
\item   0,071  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,71}
\item   0,45  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 450}
\item   0,708  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 70,8}
\item   70,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 70 900}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   371,2 ~ : ~ 100 ~ = ~{\color{red} 3,712}
\item   18,98 ~ : ~ 10 ~ = ~{\color{red} 1,898}
\item   0,286 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 286}
\item   245,8 ~ : ~ 10 ~ = ~{\color{red} 24,58}
\item   75,97 ~ : ~ 10 ~ = ~{\color{red} 7,597}
\item   10,44 ~ : ~ 10 ~ = ~{\color{red} 1,044}
\item   691,5 ~ : ~ 10 ~ = ~{\color{red} 69,15}
\item   6,036 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 036}
\item   284,1 ~ : ~ 10 ~ = ~{\color{red} 28,41}
\item   602,3 ~ : ~ 100 ~ = ~{\color{red} 6,023}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,159 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~15,9
\item   11,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~113
\item   7,64 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~764
\item   21,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~21 500
\item   912 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~91 200
\item   0,04 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~40
\item   14,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~149
\item   0,014 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,4
\item   3,87 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~38,7
\item   5,54 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~55,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 617 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,617
}\item   840,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,840 2
}\item   85,01 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,501
}\item   9,441 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 441
}\item   73,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,073 6
}\item   419,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,419 6
}\item   6,985 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,069 85
}\item   41,61 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,416 1
}\item   5,819 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,581 9
}\item   78,11 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,781 1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   357,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 35,73
\item   82,85 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,285
\item   5 670 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 567
\item   32,96 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,296
\item   796 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,796
\item   2,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,23
\item   1 115 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 111,5
\item   65,27 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,065 27
\item   8 197 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,197
\item   442 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 44,2
\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~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   764,19 ~daL~ = {\color{red}  7 641 900 }~mL
\item   794,35 ~cm~ = {\color{red}  7,943 5 }~m
\item   922,87 ~dm~ = {\color{red}  9 228,7 }~cm
\item   1 980,3 ~dg~ = {\color{red}  1,980 3 }~hg
\item   4 711,4 ~cg~ = {\color{red}  47,114 }~g
\item   387,21 ~mL~ = {\color{red}  38,721 }~cL
\item   968,01 ~kg~ = {\color{red}  9 680 100 }~dg
\item   1 800,3 ~mm~ = {\color{red}  0,180 03 }~dam
\item   561,42 ~daL~ = {\color{red}  561 420 }~cL
\item   613,62 ~cL~ = {\color{red}  6 136,2 }~mL
\end{itemize}
\end{multicols}
\end{document}
