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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 241}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{87}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,067  ~ \(\times\)  ~ 10
\item   6,53  ~ \(\times\)  ~ 100
\item   7,65  ~ \(\times\)  ~ 1 000
\item   150  ~ \(\times\)  ~ 10
\item   0,072  ~ \(\times\)  ~ 10
\item   0,053  ~ \(\times\)  ~ 1 000
\item   0,024  ~ \(\times\)  ~ 100
\item   174  ~ \(\times\)  ~ 1 000
\item   679  ~ \(\times\)  ~ 10
\item   77,4  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   591,7  ~ : ~ 1 000
\item   570,2  ~ : ~ 1 000
\item   643  ~ : ~ 100
\item   893  ~ : ~ 10
\item   83,51  ~ : ~ 1 000
\item   92,48  ~ : ~ 1 000
\item   3,033  ~ : ~ 10
\item   9,485  ~ : ~ 1 000
\item   1,3  ~ : ~ 10
\item   5,877  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,306  ~ \(\times\)  ~ ... ~ = ~ 3,06
\item   0,65  ~ \(\times\)  ~ ... ~ = ~ 650
\item   0,349  ~ \(\times\)  ~ ... ~ = ~ 34,9
\item   8,8  ~ \(\times\)  ~ ... ~ = ~ 8 800
\item   0,577  ~ \(\times\)  ~ ... ~ = ~ 57,7
\item   133  ~ \(\times\)  ~ ... ~ = ~ 1 330
\item   331  ~ \(\times\)  ~ ... ~ = ~ 33 100
\item   0,968  ~ \(\times\)  ~ ... ~ = ~ 968
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 7,7
\item   0,736  ~ \(\times\)  ~ ... ~ = ~ 736
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 155  ~ \(\times\)  ~ 0,1
\item   1,176  ~ \(\times\)  ~ 0,1
\item   37,5  ~ \(\times\)  ~ 0,1
\item   6,027  ~ \(\times\)  ~ 0,1
\item   6 226  ~ \(\times\)  ~ 0,01
\item   7,093  ~ \(\times\)  ~ 0,01
\item   746,1  ~ \(\times\)  ~ 0,001
\item   3 859  ~ \(\times\)  ~ 0,01
\item   6,436  ~ \(\times\)  ~ 0,01
\item   6,69  ~ \(\times\)  ~ 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   540  ~ \(\times\)  ~ ... ~ = ~  5,4
\item   2 848  ~ \(\times\)  ~ ... ~ = ~  284,8
\item   8 016  ~ \(\times\)  ~ ... ~ = ~  8,016
\item   3 043  ~ \(\times\)  ~ ... ~ = ~  3,043
\item   0,736  ~ \(\times\)  ~ ... ~ = ~  0,007 36
\item   57,54  ~ \(\times\)  ~ ... ~ = ~  0,575 4
\item   1,704  ~ \(\times\)  ~ ... ~ = ~  0,017 04
\item   784,5  ~ \(\times\)  ~ ... ~ = ~  78,45
\item   498  ~ \(\times\)  ~ ... ~ = ~  4,98
\item   16,1  ~ \(\times\)  ~ ... ~ = ~  0,161
\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~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 702,1 ~dam~ = ...~hm
\item   1 126,4 ~mm~ = ...~km
\item   789,35 ~cL~ = ...~kL
\item   4 607 ~kg~ = ...~dag
\item   616,52 ~kg~ = ...~g
\item   4 922,3 ~cm~ = ...~m
\item   646,88 ~dam~ = ...~dm
\item   6 937,7 ~hL~ = ...~dL
\item   2 423,4 ~mm~ = ...~dam
\item   168,33 ~mm~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{560}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{410}{100}\)
\item   \(\dfrac{87}{100}\) = \(\dfrac{870}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,067  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,67}
\item   6,53  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 653}
\item   7,65  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 650}
\item   150  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 500}
\item   0,072  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,72}
\item   0,053  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 53}
\item   0,024  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,4}
\item   174  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 174 000}
\item   679  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 790}
\item   77,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 774}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   591,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,591 7}
\item   570,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,570 2}
\item   643 ~ : ~ 100 ~ = ~{\color{red} 6,43}
\item   893 ~ : ~ 10 ~ = ~{\color{red} 89,3}
\item   83,51 ~ : ~ 1 000 ~ = ~{\color{red} 0,083 51}
\item   92,48 ~ : ~ 1 000 ~ = ~{\color{red} 0,092 48}
\item   3,033 ~ : ~ 10 ~ = ~{\color{red} 0,303 3}
\item   9,485 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 485}
\item   1,3 ~ : ~ 10 ~ = ~{\color{red} 0,13}
\item   5,877 ~ : ~ 100 ~ = ~{\color{red} 0,058 77}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,306 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,06
\item   0,65 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~650
\item   0,349 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~34,9
\item   8,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 800
\item   0,577 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~57,7
\item   133 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 330
\item   331 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~33 100
\item   0,968 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~968
\item   0,077 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,7
\item   0,736 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~736
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 155 ~ \(\times\)  0,1 ~ = ~{\color{red} 215,5
}\item   1,176 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,117 6
}\item   37,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,75
}\item   6,027 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,602 7
}\item   6 226 ~ \(\times\)  0,01 ~ = ~{\color{red} 62,26
}\item   7,093 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,070 93
}\item   746,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,746 1
}\item   3 859 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,59
}\item   6,436 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,064 36
}\item   6,69 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,669
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   540 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,4
\item   2 848 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 284,8
\item   8 016 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,016
\item   3 043 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,043
\item   0,736 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,007 36
\item   57,54 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,575 4
\item   1,704 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,017 04
\item   784,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 78,45
\item   498 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,98
\item   16,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,161
\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~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 702,1 ~dam~ = {\color{red}  470,21 }~hm
\item   1 126,4 ~mm~ = {\color{red}  0,001 126 4 }~km
\item   789,35 ~cL~ = {\color{red}  0,007 893 5 }~kL
\item   4 607 ~kg~ = {\color{red}  460 700 }~dag
\item   616,52 ~kg~ = {\color{red}  616 520 }~g
\item   4 922,3 ~cm~ = {\color{red}  49,223 }~m
\item   646,88 ~dam~ = {\color{red}  64 688 }~dm
\item   6 937,7 ~hL~ = {\color{red}  6 937 700 }~dL
\item   2 423,4 ~mm~ = {\color{red}  0,242 34 }~dam
\item   168,33 ~mm~ = {\color{red}  1,683 3 }~dm
\end{itemize}
\end{multicols}
\end{document}
