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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 361}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{65}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   75,9  ~ \(\times\)  ~ 1 000
\item   0,018  ~ \(\times\)  ~ 1 000
\item   0,379  ~ \(\times\)  ~ 1 000
\item   0,324  ~ \(\times\)  ~ 10
\item   0,049  ~ \(\times\)  ~ 1 000
\item   0,078  ~ \(\times\)  ~ 100
\item   57  ~ \(\times\)  ~ 10
\item   0,031  ~ \(\times\)  ~ 1 000
\item   4,22  ~ \(\times\)  ~ 1 000
\item   0,864  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   621,4  ~ : ~ 1 000
\item   3 205  ~ : ~ 1 000
\item   6,428  ~ : ~ 10
\item   3,243  ~ : ~ 10
\item   6 646  ~ : ~ 1 000
\item   37,92  ~ : ~ 10
\item   5 429  ~ : ~ 1 000
\item   137,5  ~ : ~ 10
\item   54,8  ~ : ~ 100
\item   3,553  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,5  ~ \(\times\)  ~ ... ~ = ~ 80 500
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 0,27
\item   567  ~ \(\times\)  ~ ... ~ = ~ 5 670
\item   3,14  ~ \(\times\)  ~ ... ~ = ~ 31,4
\item   931  ~ \(\times\)  ~ ... ~ = ~ 9 310
\item   4,4  ~ \(\times\)  ~ ... ~ = ~ 440
\item   32,2  ~ \(\times\)  ~ ... ~ = ~ 322
\item   195  ~ \(\times\)  ~ ... ~ = ~ 19 500
\item   0,233  ~ \(\times\)  ~ ... ~ = ~ 2,33
\item   0,066  ~ \(\times\)  ~ ... ~ = ~ 6,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   67,15  ~ \(\times\)  ~ 0,01
\item   215  ~ \(\times\)  ~ 0,01
\item   6,631  ~ \(\times\)  ~ 0,001
\item   1,758  ~ \(\times\)  ~ 0,1
\item   44,04  ~ \(\times\)  ~ 0,001
\item   46,77  ~ \(\times\)  ~ 0,01
\item   4,09  ~ \(\times\)  ~ 0,001
\item   5 753  ~ \(\times\)  ~ 0,1
\item   72,72  ~ \(\times\)  ~ 0,01
\item   9,55  ~ \(\times\)  ~ 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   445,1  ~ \(\times\)  ~ ... ~ = ~  44,51
\item   738,2  ~ \(\times\)  ~ ... ~ = ~  7,382
\item   6,011  ~ \(\times\)  ~ ... ~ = ~  0,006 011
\item   64,81  ~ \(\times\)  ~ ... ~ = ~  6,481
\item   7 635  ~ \(\times\)  ~ ... ~ = ~  76,35
\item   6 433  ~ \(\times\)  ~ ... ~ = ~  64,33
\item   914,3  ~ \(\times\)  ~ ... ~ = ~  91,43
\item   82,98  ~ \(\times\)  ~ ... ~ = ~  0,082 98
\item   5 100  ~ \(\times\)  ~ ... ~ = ~  5,1
\item   926,4  ~ \(\times\)  ~ ... ~ = ~  92,64
\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 ~km~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 492 ~dL~ = ...~cL
\item   318,06 ~hm~ = ...~m
\item   876,61 ~mm~ = ...~hm
\item   7 282,9 ~cL~ = ...~dL
\item   174,61 ~cL~ = ...~L
\item   1 112,8 ~cL~ = ...~kL
\item   399,3 ~dg~ = ...~kg
\item   351,57 ~daL~ = ...~dL
\item   4 242 ~mL~ = ...~kL
\item   7 301,6 ~dam~ = ...~m
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{620}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{130}{100}\)
\item   \(\dfrac{65}{100}\) = \(\dfrac{650}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   75,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 75 900}
\item   0,018  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 18}
\item   0,379  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 379}
\item   0,324  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,24}
\item   0,049  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 49}
\item   0,078  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,8}
\item   57  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 570}
\item   0,031  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 31}
\item   4,22  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 220}
\item   0,864  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 864}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   621,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,621 4}
\item   3 205 ~ : ~ 1 000 ~ = ~{\color{red} 3,205}
\item   6,428 ~ : ~ 10 ~ = ~{\color{red} 0,642 8}
\item   3,243 ~ : ~ 10 ~ = ~{\color{red} 0,324 3}
\item   6 646 ~ : ~ 1 000 ~ = ~{\color{red} 6,646}
\item   37,92 ~ : ~ 10 ~ = ~{\color{red} 3,792}
\item   5 429 ~ : ~ 1 000 ~ = ~{\color{red} 5,429}
\item   137,5 ~ : ~ 10 ~ = ~{\color{red} 13,75}
\item   54,8 ~ : ~ 100 ~ = ~{\color{red} 0,548}
\item   3,553 ~ : ~ 10 ~ = ~{\color{red} 0,355 3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~80 500
\item   0,027 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,27
\item   567 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 670
\item   3,14 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~31,4
\item   931 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 310
\item   4,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~440
\item   32,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~322
\item   195 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~19 500
\item   0,233 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,33
\item   0,066 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   67,15 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,671 5
}\item   215 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,15
}\item   6,631 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 631
}\item   1,758 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,175 8
}\item   44,04 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,044 04
}\item   46,77 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,467 7
}\item   4,09 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 09
}\item   5 753 ~ \(\times\)  0,1 ~ = ~{\color{red} 575,3
}\item   72,72 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,727 2
}\item   9,55 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 55
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   445,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 44,51
\item   738,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,382
\item   6,011 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 011
\item   64,81 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,481
\item   7 635 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 76,35
\item   6 433 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 64,33
\item   914,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 91,43
\item   82,98 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,082 98
\item   5 100 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,1
\item   926,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 92,64
\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 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 492 ~dL~ = {\color{red}  74 920 }~cL
\item   318,06 ~hm~ = {\color{red}  31 806 }~m
\item   876,61 ~mm~ = {\color{red}  0,008 766 1 }~hm
\item   7 282,9 ~cL~ = {\color{red}  728,29 }~dL
\item   174,61 ~cL~ = {\color{red}  1,746 1 }~L
\item   1 112,8 ~cL~ = {\color{red}  0,011 128 }~kL
\item   399,3 ~dg~ = {\color{red}  0,039 93 }~kg
\item   351,57 ~daL~ = {\color{red}  35 157 }~dL
\item   4 242 ~mL~ = {\color{red}  0,004 242 }~kL
\item   7 301,6 ~dam~ = {\color{red}  73 016 }~m
\end{itemize}
\end{multicols}
\end{document}
