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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 242}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{73}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   53,4  ~ \(\times\)  ~ 10
\item   2,16  ~ \(\times\)  ~ 1 000
\item   22,3  ~ \(\times\)  ~ 1 000
\item   0,75  ~ \(\times\)  ~ 10
\item   0,087  ~ \(\times\)  ~ 100
\item   0,93  ~ \(\times\)  ~ 100
\item   235  ~ \(\times\)  ~ 10
\item   0,571  ~ \(\times\)  ~ 100
\item   4,94  ~ \(\times\)  ~ 100
\item   7,5  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 828  ~ : ~ 10
\item   226,8  ~ : ~ 100
\item   891,1  ~ : ~ 100
\item   461,2  ~ : ~ 10
\item   2 885  ~ : ~ 10
\item   343,2  ~ : ~ 10
\item   55,59  ~ : ~ 100
\item   833,1  ~ : ~ 1 000
\item   762,8  ~ : ~ 1 000
\item   66,69  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,083  ~ \(\times\)  ~ ... ~ = ~ 0,83
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 0,89
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 6,4
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 33
\item   0,55  ~ \(\times\)  ~ ... ~ = ~ 5,5
\item   35,9  ~ \(\times\)  ~ ... ~ = ~ 3 590
\item   742  ~ \(\times\)  ~ ... ~ = ~ 7 420
\item   861  ~ \(\times\)  ~ ... ~ = ~ 861 000
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 61
\item   5,94  ~ \(\times\)  ~ ... ~ = ~ 59,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 061  ~ \(\times\)  ~ 0,001
\item   6,719  ~ \(\times\)  ~ 0,1
\item   822,2  ~ \(\times\)  ~ 0,01
\item   5,79  ~ \(\times\)  ~ 0,1
\item   68,66  ~ \(\times\)  ~ 0,001
\item   6,11  ~ \(\times\)  ~ 0,1
\item   5,84  ~ \(\times\)  ~ 0,1
\item   3,483  ~ \(\times\)  ~ 0,001
\item   491  ~ \(\times\)  ~ 0,1
\item   2,839  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   903,1  ~ \(\times\)  ~ ... ~ = ~  0,903 1
\item   5 664  ~ \(\times\)  ~ ... ~ = ~  56,64
\item   9 500  ~ \(\times\)  ~ ... ~ = ~  9,5
\item   4 537  ~ \(\times\)  ~ ... ~ = ~  453,7
\item   66,7  ~ \(\times\)  ~ ... ~ = ~  0,667
\item   21,54  ~ \(\times\)  ~ ... ~ = ~  0,215 4
\item   8 113  ~ \(\times\)  ~ ... ~ = ~  811,3
\item   9 339  ~ \(\times\)  ~ ... ~ = ~  93,39
\item   51,25  ~ \(\times\)  ~ ... ~ = ~  0,512 5
\item   33,25  ~ \(\times\)  ~ ... ~ = ~  0,332 5
\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~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 243,5 ~dm~ = ...~km
\item   653,52 ~dam~ = ...~m
\item   238,82 ~kL~ = ...~cL
\item   361,05 ~cL~ = ...~hL
\item   4 482,3 ~m~ = ...~dm
\item   670,8 ~cm~ = ...~mm
\item   491,5 ~cg~ = ...~mg
\item   913,65 ~cg~ = ...~dg
\item   8 202,6 ~mm~ = ...~dam
\item   3 888,9 ~hm~ = ...~dam
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{7400}{100}\) = \(\dfrac{740}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{90}{10}\) = \(\dfrac{900}{100}\)
\item   \(\dfrac{73}{100}\) = \(\dfrac{730}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   53,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 534}
\item   2,16  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 160}
\item   22,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 22 300}
\item   0,75  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,5}
\item   0,087  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,7}
\item   0,93  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 93}
\item   235  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 350}
\item   0,571  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 57,1}
\item   4,94  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 494}
\item   7,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 500}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 828 ~ : ~ 10 ~ = ~{\color{red} 382,8}
\item   226,8 ~ : ~ 100 ~ = ~{\color{red} 2,268}
\item   891,1 ~ : ~ 100 ~ = ~{\color{red} 8,911}
\item   461,2 ~ : ~ 10 ~ = ~{\color{red} 46,12}
\item   2 885 ~ : ~ 10 ~ = ~{\color{red} 288,5}
\item   343,2 ~ : ~ 10 ~ = ~{\color{red} 34,32}
\item   55,59 ~ : ~ 100 ~ = ~{\color{red} 0,555 9}
\item   833,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,833 1}
\item   762,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,762 8}
\item   66,69 ~ : ~ 1 000 ~ = ~{\color{red} 0,066 69}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,083 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,83
\item   0,089 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,89
\item   0,064 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,4
\item   0,033 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33
\item   0,55 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,5
\item   35,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 590
\item   742 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 420
\item   861 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~861 000
\item   0,061 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~61
\item   5,94 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~59,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 061 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,061
}\item   6,719 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,671 9
}\item   822,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,222
}\item   5,79 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,579
}\item   68,66 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,068 66
}\item   6,11 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,611
}\item   5,84 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,584
}\item   3,483 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 483
}\item   491 ~ \(\times\)  0,1 ~ = ~{\color{red} 49,1
}\item   2,839 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 839
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   903,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,903 1
\item   5 664 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 56,64
\item   9 500 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,5
\item   4 537 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 453,7
\item   66,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,667
\item   21,54 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,215 4
\item   8 113 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 811,3
\item   9 339 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 93,39
\item   51,25 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,512 5
\item   33,25 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,332 5
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 243,5 ~dm~ = {\color{red}  0,724 35 }~km
\item   653,52 ~dam~ = {\color{red}  6 535,2 }~m
\item   238,82 ~kL~ = {\color{red}  23 882 000 }~cL
\item   361,05 ~cL~ = {\color{red}  0,036 105 }~hL
\item   4 482,3 ~m~ = {\color{red}  44 823 }~dm
\item   670,8 ~cm~ = {\color{red}  6 708 }~mm
\item   491,5 ~cg~ = {\color{red}  4 915 }~mg
\item   913,65 ~cg~ = {\color{red}  91,365 }~dg
\item   8 202,6 ~mm~ = {\color{red}  0,820 26 }~dam
\item   3 888,9 ~hm~ = {\color{red}  38 889 }~dam
\end{itemize}
\end{multicols}
\end{document}
