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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 359}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{48}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,778  ~ \(\times\)  ~ 10
\item   521  ~ \(\times\)  ~ 1 000
\item   839  ~ \(\times\)  ~ 10
\item   43  ~ \(\times\)  ~ 1 000
\item   0,901  ~ \(\times\)  ~ 10
\item   0,007  ~ \(\times\)  ~ 1 000
\item   55,9  ~ \(\times\)  ~ 100
\item   25,6  ~ \(\times\)  ~ 1 000
\item   0,082  ~ \(\times\)  ~ 1 000
\item   4,41  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,561  ~ : ~ 10
\item   860,8  ~ : ~ 100
\item   581  ~ : ~ 100
\item   155  ~ : ~ 100
\item   2,22  ~ : ~ 10
\item   3,042  ~ : ~ 100
\item   72,63  ~ : ~ 1 000
\item   5 453  ~ : ~ 100
\item   80,42  ~ : ~ 100
\item   6 296  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   224  ~ \(\times\)  ~ ... ~ = ~ 22 400
\item   3,58  ~ \(\times\)  ~ ... ~ = ~ 358
\item   0,057  ~ \(\times\)  ~ ... ~ = ~ 57
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 4
\item   0,546  ~ \(\times\)  ~ ... ~ = ~ 5,46
\item   174  ~ \(\times\)  ~ ... ~ = ~ 174 000
\item   927  ~ \(\times\)  ~ ... ~ = ~ 92 700
\item   391  ~ \(\times\)  ~ ... ~ = ~ 391 000
\item   39,3  ~ \(\times\)  ~ ... ~ = ~ 39 300
\item   684  ~ \(\times\)  ~ ... ~ = ~ 684 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,668  ~ \(\times\)  ~ 0,001
\item   46  ~ \(\times\)  ~ 0,1
\item   3,72  ~ \(\times\)  ~ 0,01
\item   3 747  ~ \(\times\)  ~ 0,001
\item   2,089  ~ \(\times\)  ~ 0,001
\item   946,6  ~ \(\times\)  ~ 0,001
\item   4,153  ~ \(\times\)  ~ 0,01
\item   802,6  ~ \(\times\)  ~ 0,1
\item   38,52  ~ \(\times\)  ~ 0,01
\item   45,61  ~ \(\times\)  ~ 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   175,5  ~ \(\times\)  ~ ... ~ = ~  1,755
\item   7 715  ~ \(\times\)  ~ ... ~ = ~  771,5
\item   5 718  ~ \(\times\)  ~ ... ~ = ~  5,718
\item   5,79  ~ \(\times\)  ~ ... ~ = ~  0,005 79
\item   2,727  ~ \(\times\)  ~ ... ~ = ~  0,002 727
\item   1 492  ~ \(\times\)  ~ ... ~ = ~  149,2
\item   0,32  ~ \(\times\)  ~ ... ~ = ~  0,032
\item   4,183  ~ \(\times\)  ~ ... ~ = ~  0,418 3
\item   9 528  ~ \(\times\)  ~ ... ~ = ~  952,8
\item   5,153  ~ \(\times\)  ~ ... ~ = ~  0,051 53
\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 ~cm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   738,61 ~dg~ = ...~dag
\item   483,04 ~mg~ = ...~kg
\item   381,34 ~dm~ = ...~km
\item   9 184,4 ~L~ = ...~kL
\item   604,7 ~dL~ = ...~daL
\item   4 331,9 ~daL~ = ...~kL
\item   409,28 ~dm~ = ...~cm
\item   1 337,7 ~L~ = ...~cL
\item   6 297,7 ~cL~ = ...~dL
\item   386,69 ~g~ = ...~kg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{8500}{100}\) = \(\dfrac{850}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{48}{100}\) = \(\dfrac{480}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,778  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,78}
\item   521  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 521 000}
\item   839  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 390}
\item   43  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 43 000}
\item   0,901  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,01}
\item   0,007  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7}
\item   55,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 590}
\item   25,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 25 600}
\item   0,082  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 82}
\item   4,41  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 410}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,561 ~ : ~ 10 ~ = ~{\color{red} 0,156 1}
\item   860,8 ~ : ~ 100 ~ = ~{\color{red} 8,608}
\item   581 ~ : ~ 100 ~ = ~{\color{red} 5,81}
\item   155 ~ : ~ 100 ~ = ~{\color{red} 1,55}
\item   2,22 ~ : ~ 10 ~ = ~{\color{red} 0,222}
\item   3,042 ~ : ~ 100 ~ = ~{\color{red} 0,030 42}
\item   72,63 ~ : ~ 1 000 ~ = ~{\color{red} 0,072 63}
\item   5 453 ~ : ~ 100 ~ = ~{\color{red} 54,53}
\item   80,42 ~ : ~ 100 ~ = ~{\color{red} 0,804 2}
\item   6 296 ~ : ~ 10 ~ = ~{\color{red} 629,6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   224 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22 400
\item   3,58 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~358
\item   0,057 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~57
\item   0,004 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4
\item   0,546 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,46
\item   174 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~174 000
\item   927 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~92 700
\item   391 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~391 000
\item   39,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~39 300
\item   684 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~684 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,668 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 668
}\item   46 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,6
}\item   3,72 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,037 2
}\item   3 747 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,747
}\item   2,089 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 089
}\item   946,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,946 6
}\item   4,153 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,041 53
}\item   802,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 80,26
}\item   38,52 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,385 2
}\item   45,61 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,045 61
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   175,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,755
\item   7 715 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 771,5
\item   5 718 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,718
\item   5,79 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 79
\item   2,727 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 727
\item   1 492 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 149,2
\item   0,32 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,032
\item   4,183 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,418 3
\item   9 528 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 952,8
\item   5,153 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,051 53
\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 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   738,61 ~dg~ = {\color{red}  7,386 1 }~dag
\item   483,04 ~mg~ = {\color{red}  0,000 483 04 }~kg
\item   381,34 ~dm~ = {\color{red}  0,038 134 }~km
\item   9 184,4 ~L~ = {\color{red}  9,184 4 }~kL
\item   604,7 ~dL~ = {\color{red}  6,047 }~daL
\item   4 331,9 ~daL~ = {\color{red}  43,319 }~kL
\item   409,28 ~dm~ = {\color{red}  4 092,8 }~cm
\item   1 337,7 ~L~ = {\color{red}  133 770 }~cL
\item   6 297,7 ~cL~ = {\color{red}  629,77 }~dL
\item   386,69 ~g~ = {\color{red}  0,386 69 }~kg
\end{itemize}
\end{multicols}
\end{document}
