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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 62}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{50}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{96}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   37,3  ~ \(\times\)  ~ 1 000
\item   20  ~ \(\times\)  ~ 10
\item   27,5  ~ \(\times\)  ~ 10
\item   0,039  ~ \(\times\)  ~ 100
\item   540  ~ \(\times\)  ~ 100
\item   0,098  ~ \(\times\)  ~ 1 000
\item   17,3  ~ \(\times\)  ~ 1 000
\item   0,89  ~ \(\times\)  ~ 1 000
\item   0,047  ~ \(\times\)  ~ 10
\item   0,64  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   57,14  ~ : ~ 100
\item   3,55  ~ : ~ 100
\item   709,2  ~ : ~ 1 000
\item   468,2  ~ : ~ 10
\item   60  ~ : ~ 10
\item   252,3  ~ : ~ 10
\item   17,67  ~ : ~ 100
\item   81,09  ~ : ~ 10
\item   615,6  ~ : ~ 100
\item   2,438  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,74  ~ \(\times\)  ~ ... ~ = ~ 74
\item   0,419  ~ \(\times\)  ~ ... ~ = ~ 4,19
\item   0,038  ~ \(\times\)  ~ ... ~ = ~ 38
\item   82  ~ \(\times\)  ~ ... ~ = ~ 820
\item   0,77  ~ \(\times\)  ~ ... ~ = ~ 7,7
\item   74,6  ~ \(\times\)  ~ ... ~ = ~ 74 600
\item   5,52  ~ \(\times\)  ~ ... ~ = ~ 552
\item   70,9  ~ \(\times\)  ~ ... ~ = ~ 7 090
\item   1,15  ~ \(\times\)  ~ ... ~ = ~ 115
\item   0,132  ~ \(\times\)  ~ ... ~ = ~ 13,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,53  ~ \(\times\)  ~ 0,1
\item   6 751  ~ \(\times\)  ~ 0,01
\item   4,326  ~ \(\times\)  ~ 0,01
\item   394,1  ~ \(\times\)  ~ 0,1
\item   9 286  ~ \(\times\)  ~ 0,001
\item   67,07  ~ \(\times\)  ~ 0,01
\item   80,64  ~ \(\times\)  ~ 0,1
\item   655  ~ \(\times\)  ~ 0,1
\item   5 141  ~ \(\times\)  ~ 0,01
\item   40,12  ~ \(\times\)  ~ 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   29,19  ~ \(\times\)  ~ ... ~ = ~  2,919
\item   80,41  ~ \(\times\)  ~ ... ~ = ~  0,080 41
\item   66,56  ~ \(\times\)  ~ ... ~ = ~  0,665 6
\item   86,71  ~ \(\times\)  ~ ... ~ = ~  8,671
\item   8,644  ~ \(\times\)  ~ ... ~ = ~  0,008 644
\item   4,358  ~ \(\times\)  ~ ... ~ = ~  0,435 8
\item   5,67  ~ \(\times\)  ~ ... ~ = ~  0,056 7
\item   8 483  ~ \(\times\)  ~ ... ~ = ~  848,3
\item   6 196  ~ \(\times\)  ~ ... ~ = ~  61,96
\item   2,321  ~ \(\times\)  ~ ... ~ = ~  0,002 321
\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 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~hm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 430,1 ~dam~ = ...~cm
\item   491,84 ~km~ = ...~m
\item   8 905,2 ~dg~ = ...~hg
\item   587,06 ~hg~ = ...~dag
\item   629,8 ~hm~ = ...~km
\item   2 048 ~dam~ = ...~m
\item   963,19 ~dm~ = ...~cm
\item   3 744,4 ~dg~ = ...~kg
\item   626,84 ~kL~ = ...~L
\item   435,4 ~cL~ = ...~kL
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{410}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{50}{10}\) = \(\dfrac{500}{100}\)
\item   \(\dfrac{96}{100}\) = \(\dfrac{960}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   37,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 37 300}
\item   20  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 200}
\item   27,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 275}
\item   0,039  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,9}
\item   540  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 54 000}
\item   0,098  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 98}
\item   17,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 17 300}
\item   0,89  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 890}
\item   0,047  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,47}
\item   0,64  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 64}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   57,14 ~ : ~ 100 ~ = ~{\color{red} 0,571 4}
\item   3,55 ~ : ~ 100 ~ = ~{\color{red} 0,035 5}
\item   709,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,709 2}
\item   468,2 ~ : ~ 10 ~ = ~{\color{red} 46,82}
\item   60 ~ : ~ 10 ~ = ~{\color{red} 6}
\item   252,3 ~ : ~ 10 ~ = ~{\color{red} 25,23}
\item   17,67 ~ : ~ 100 ~ = ~{\color{red} 0,176 7}
\item   81,09 ~ : ~ 10 ~ = ~{\color{red} 8,109}
\item   615,6 ~ : ~ 100 ~ = ~{\color{red} 6,156}
\item   2,438 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 438}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,74 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74
\item   0,419 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,19
\item   0,038 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~38
\item   82 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~820
\item   0,77 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,7
\item   74,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~74 600
\item   5,52 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~552
\item   70,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 090
\item   1,15 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~115
\item   0,132 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~13,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,53 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,053
}\item   6 751 ~ \(\times\)  0,01 ~ = ~{\color{red} 67,51
}\item   4,326 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,043 26
}\item   394,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 39,41
}\item   9 286 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,286
}\item   67,07 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,670 7
}\item   80,64 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,064
}\item   655 ~ \(\times\)  0,1 ~ = ~{\color{red} 65,5
}\item   5 141 ~ \(\times\)  0,01 ~ = ~{\color{red} 51,41
}\item   40,12 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,012
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   29,19 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,919
\item   80,41 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,080 41
\item   66,56 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,665 6
\item   86,71 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,671
\item   8,644 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 644
\item   4,358 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,435 8
\item   5,67 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,056 7
\item   8 483 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 848,3
\item   6 196 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 61,96
\item   2,321 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 321
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\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   5 430,1 ~dam~ = {\color{red}  5 430 100 }~cm
\item   491,84 ~km~ = {\color{red}  491 840 }~m
\item   8 905,2 ~dg~ = {\color{red}  8,905 2 }~hg
\item   587,06 ~hg~ = {\color{red}  5 870,6 }~dag
\item   629,8 ~hm~ = {\color{red}  62,98 }~km
\item   2 048 ~dam~ = {\color{red}  20 480 }~m
\item   963,19 ~dm~ = {\color{red}  9 631,9 }~cm
\item   3 744,4 ~dg~ = {\color{red}  0,374 44 }~kg
\item   626,84 ~kL~ = {\color{red}  626 840 }~L
\item   435,4 ~cL~ = {\color{red}  0,004 354 }~kL
\end{itemize}
\end{multicols}
\end{document}
