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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 391}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,175  ~ \(\times\)  ~ 10
\item   0,705  ~ \(\times\)  ~ 1 000
\item   725  ~ \(\times\)  ~ 10
\item   0,242  ~ \(\times\)  ~ 1 000
\item   407  ~ \(\times\)  ~ 10
\item   666  ~ \(\times\)  ~ 100
\item   4,25  ~ \(\times\)  ~ 100
\item   6,49  ~ \(\times\)  ~ 1 000
\item   0,214  ~ \(\times\)  ~ 100
\item   0,052  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,24  ~ : ~ 1 000
\item   67,45  ~ : ~ 1 000
\item   8,523  ~ : ~ 1 000
\item   4,528  ~ : ~ 10
\item   3,762  ~ : ~ 1 000
\item   3,503  ~ : ~ 1 000
\item   77,71  ~ : ~ 100
\item   9 118  ~ : ~ 1 000
\item   399,8  ~ : ~ 100
\item   16,15  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   81  ~ \(\times\)  ~ ... ~ = ~ 81 000
\item   7,11  ~ \(\times\)  ~ ... ~ = ~ 711
\item   7,62  ~ \(\times\)  ~ ... ~ = ~ 762
\item   0,892  ~ \(\times\)  ~ ... ~ = ~ 8,92
\item   0,044  ~ \(\times\)  ~ ... ~ = ~ 0,44
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 62
\item   565  ~ \(\times\)  ~ ... ~ = ~ 56 500
\item   5,92  ~ \(\times\)  ~ ... ~ = ~ 5 920
\item   0,631  ~ \(\times\)  ~ ... ~ = ~ 631
\item   0,874  ~ \(\times\)  ~ ... ~ = ~ 87,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 186  ~ \(\times\)  ~ 0,1
\item   407,9  ~ \(\times\)  ~ 0,001
\item   599,4  ~ \(\times\)  ~ 0,01
\item   7 013  ~ \(\times\)  ~ 0,01
\item   63,08  ~ \(\times\)  ~ 0,001
\item   636,1  ~ \(\times\)  ~ 0,1
\item   528,8  ~ \(\times\)  ~ 0,001
\item   4 119  ~ \(\times\)  ~ 0,001
\item   2 333  ~ \(\times\)  ~ 0,01
\item   619,2  ~ \(\times\)  ~ 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   9 207  ~ \(\times\)  ~ ... ~ = ~  9,207
\item   26,32  ~ \(\times\)  ~ ... ~ = ~  0,026 32
\item   148,9  ~ \(\times\)  ~ ... ~ = ~  14,89
\item   3,517  ~ \(\times\)  ~ ... ~ = ~  0,351 7
\item   239  ~ \(\times\)  ~ ... ~ = ~  23,9
\item   466,5  ~ \(\times\)  ~ ... ~ = ~  0,466 5
\item   0,817  ~ \(\times\)  ~ ... ~ = ~  0,081 7
\item   517,2  ~ \(\times\)  ~ ... ~ = ~  51,72
\item   247  ~ \(\times\)  ~ ... ~ = ~  24,7
\item   7 356  ~ \(\times\)  ~ ... ~ = ~  735,6
\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~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~dm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 591,1 ~kg~ = ...~g
\item   482,27 ~dm~ = ...~cm
\item   2 041,4 ~cL~ = ...~dL
\item   167,17 ~dL~ = ...~daL
\item   9 300,4 ~kL~ = ...~L
\item   242,82 ~km~ = ...~mm
\item   3 686 ~hL~ = ...~daL
\item   2 471,8 ~m~ = ...~hm
\item   984,56 ~m~ = ...~mm
\item   182,72 ~hL~ = ...~L
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{9200}{100}\) = \(\dfrac{920}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{960}{100}\)
\item   \(\dfrac{29}{100}\) = \(\dfrac{290}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,175  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,75}
\item   0,705  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 705}
\item   725  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 250}
\item   0,242  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 242}
\item   407  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 070}
\item   666  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66 600}
\item   4,25  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 425}
\item   6,49  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 490}
\item   0,214  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 21,4}
\item   0,052  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,52}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,24 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 24}
\item   67,45 ~ : ~ 1 000 ~ = ~{\color{red} 0,067 45}
\item   8,523 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 523}
\item   4,528 ~ : ~ 10 ~ = ~{\color{red} 0,452 8}
\item   3,762 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 762}
\item   3,503 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 503}
\item   77,71 ~ : ~ 100 ~ = ~{\color{red} 0,777 1}
\item   9 118 ~ : ~ 1 000 ~ = ~{\color{red} 9,118}
\item   399,8 ~ : ~ 100 ~ = ~{\color{red} 3,998}
\item   16,15 ~ : ~ 100 ~ = ~{\color{red} 0,161 5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   81 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~81 000
\item   7,11 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~711
\item   7,62 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~762
\item   0,892 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,92
\item   0,044 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,44
\item   0,062 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~62
\item   565 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~56 500
\item   5,92 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 920
\item   0,631 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~631
\item   0,874 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~87,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 186 ~ \(\times\)  0,1 ~ = ~{\color{red} 118,6
}\item   407,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,407 9
}\item   599,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,994
}\item   7 013 ~ \(\times\)  0,01 ~ = ~{\color{red} 70,13
}\item   63,08 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,063 08
}\item   636,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 63,61
}\item   528,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,528 8
}\item   4 119 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,119
}\item   2 333 ~ \(\times\)  0,01 ~ = ~{\color{red} 23,33
}\item   619,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 61,92
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 207 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,207
\item   26,32 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,026 32
\item   148,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 14,89
\item   3,517 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,351 7
\item   239 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 23,9
\item   466,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,466 5
\item   0,817 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,081 7
\item   517,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 51,72
\item   247 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 24,7
\item   7 356 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 735,6
\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~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 591,1 ~kg~ = {\color{red}  1 591 100 }~g
\item   482,27 ~dm~ = {\color{red}  4 822,7 }~cm
\item   2 041,4 ~cL~ = {\color{red}  204,14 }~dL
\item   167,17 ~dL~ = {\color{red}  1,671 7 }~daL
\item   9 300,4 ~kL~ = {\color{red}  9 300 400 }~L
\item   242,82 ~km~ = {\color{red}  242 820 000 }~mm
\item   3 686 ~hL~ = {\color{red}  36 860 }~daL
\item   2 471,8 ~m~ = {\color{red}  24,718 }~hm
\item   984,56 ~m~ = {\color{red}  984 560 }~mm
\item   182,72 ~hL~ = {\color{red}  18 272 }~L
\end{itemize}
\end{multicols}
\end{document}
