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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 111}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{61}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{64}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64  ~ \(\times\)  ~ 1 000
\item   0,207  ~ \(\times\)  ~ 1 000
\item   24,4  ~ \(\times\)  ~ 1 000
\item   0,483  ~ \(\times\)  ~ 100
\item   7,4  ~ \(\times\)  ~ 100
\item   2,35  ~ \(\times\)  ~ 100
\item   832  ~ \(\times\)  ~ 100
\item   70,3  ~ \(\times\)  ~ 1 000
\item   0,471  ~ \(\times\)  ~ 10
\item   0,9  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,67  ~ : ~ 10
\item   5,652  ~ : ~ 10
\item   568,3  ~ : ~ 1 000
\item   387  ~ : ~ 100
\item   83,44  ~ : ~ 1 000
\item   8,212  ~ : ~ 100
\item   8 993  ~ : ~ 1 000
\item   2 652  ~ : ~ 10
\item   8,107  ~ : ~ 1 000
\item   9 668  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   71,8  ~ \(\times\)  ~ ... ~ = ~ 7 180
\item   71,5  ~ \(\times\)  ~ ... ~ = ~ 715
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 6
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 6,1
\item   0,001  ~ \(\times\)  ~ ... ~ = ~ 1
\item   71,6  ~ \(\times\)  ~ ... ~ = ~ 716
\item   78,6  ~ \(\times\)  ~ ... ~ = ~ 78 600
\item   6  ~ \(\times\)  ~ ... ~ = ~ 600
\item   0,057  ~ \(\times\)  ~ ... ~ = ~ 0,57
\item   8,99  ~ \(\times\)  ~ ... ~ = ~ 8 990
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 291  ~ \(\times\)  ~ 0,01
\item   604,9  ~ \(\times\)  ~ 0,001
\item   3,316  ~ \(\times\)  ~ 0,1
\item   8,627  ~ \(\times\)  ~ 0,01
\item   3 581  ~ \(\times\)  ~ 0,01
\item   4 311  ~ \(\times\)  ~ 0,01
\item   228,2  ~ \(\times\)  ~ 0,1
\item   7,944  ~ \(\times\)  ~ 0,01
\item   934  ~ \(\times\)  ~ 0,1
\item   3,889  ~ \(\times\)  ~ 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   2 145  ~ \(\times\)  ~ ... ~ = ~  214,5
\item   88,23  ~ \(\times\)  ~ ... ~ = ~  0,882 3
\item   584,3  ~ \(\times\)  ~ ... ~ = ~  0,584 3
\item   95,59  ~ \(\times\)  ~ ... ~ = ~  0,955 9
\item   3,01  ~ \(\times\)  ~ ... ~ = ~  0,030 1
\item   450,1  ~ \(\times\)  ~ ... ~ = ~  4,501
\item   85,11  ~ \(\times\)  ~ ... ~ = ~  0,085 11
\item   7 052  ~ \(\times\)  ~ ... ~ = ~  70,52
\item   881,7  ~ \(\times\)  ~ ... ~ = ~  0,881 7
\item   92,97  ~ \(\times\)  ~ ... ~ = ~  9,297
\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 ~dam~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   862,47 ~dm~ = ...~km
\item   4 761,2 ~cm~ = ...~dam
\item   6 750,7 ~dg~ = ...~kg
\item   448,71 ~hL~ = ...~mL
\item   926,13 ~dm~ = ...~m
\item   709,6 ~dam~ = ...~km
\item   4 116,1 ~m~ = ...~dam
\item   2 167,4 ~daL~ = ...~mL
\item   1 236,1 ~cg~ = ...~g
\item   411 ~dL~ = ...~daL
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{7400}{100}\) = \(\dfrac{740}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{61}{10}\) = \(\dfrac{610}{100}\)
\item   \(\dfrac{64}{100}\) = \(\dfrac{640}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 64 000}
\item   0,207  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 207}
\item   24,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 24 400}
\item   0,483  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 48,3}
\item   7,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 740}
\item   2,35  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 235}
\item   832  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 83 200}
\item   70,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 70 300}
\item   0,471  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,71}
\item   0,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 900}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   18,67 ~ : ~ 10 ~ = ~{\color{red} 1,867}
\item   5,652 ~ : ~ 10 ~ = ~{\color{red} 0,565 2}
\item   568,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,568 3}
\item   387 ~ : ~ 100 ~ = ~{\color{red} 3,87}
\item   83,44 ~ : ~ 1 000 ~ = ~{\color{red} 0,083 44}
\item   8,212 ~ : ~ 100 ~ = ~{\color{red} 0,082 12}
\item   8 993 ~ : ~ 1 000 ~ = ~{\color{red} 8,993}
\item   2 652 ~ : ~ 10 ~ = ~{\color{red} 265,2}
\item   8,107 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 107}
\item   9 668 ~ : ~ 100 ~ = ~{\color{red} 96,68}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   71,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 180
\item   71,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~715
\item   0,06 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6
\item   0,061 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,1
\item   0,001 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1
\item   71,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~716
\item   78,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~78 600
\item   6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~600
\item   0,057 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,57
\item   8,99 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 990
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 291 ~ \(\times\)  0,01 ~ = ~{\color{red} 12,91
}\item   604,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,604 9
}\item   3,316 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,331 6
}\item   8,627 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,086 27
}\item   3 581 ~ \(\times\)  0,01 ~ = ~{\color{red} 35,81
}\item   4 311 ~ \(\times\)  0,01 ~ = ~{\color{red} 43,11
}\item   228,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 22,82
}\item   7,944 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,079 44
}\item   934 ~ \(\times\)  0,1 ~ = ~{\color{red} 93,4
}\item   3,889 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 889
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 145 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 214,5
\item   88,23 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,882 3
\item   584,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,584 3
\item   95,59 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,955 9
\item   3,01 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,030 1
\item   450,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,501
\item   85,11 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,085 11
\item   7 052 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 70,52
\item   881,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,881 7
\item   92,97 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,297
\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 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   862,47 ~dm~ = {\color{red}  0,086 247 }~km
\item   4 761,2 ~cm~ = {\color{red}  4,761 2 }~dam
\item   6 750,7 ~dg~ = {\color{red}  0,675 07 }~kg
\item   448,71 ~hL~ = {\color{red}  44 871 000 }~mL
\item   926,13 ~dm~ = {\color{red}  92,613 }~m
\item   709,6 ~dam~ = {\color{red}  7,096 }~km
\item   4 116,1 ~m~ = {\color{red}  411,61 }~dam
\item   2 167,4 ~daL~ = {\color{red}  21 674 000 }~mL
\item   1 236,1 ~cg~ = {\color{red}  12,361 }~g
\item   411 ~dL~ = {\color{red}  4,11 }~daL
\end{itemize}
\end{multicols}
\end{document}
