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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 133}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{89}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,091  ~ \(\times\)  ~ 1 000
\item   644  ~ \(\times\)  ~ 1 000
\item   0,91  ~ \(\times\)  ~ 1 000
\item   9,5  ~ \(\times\)  ~ 100
\item   232  ~ \(\times\)  ~ 100
\item   0,524  ~ \(\times\)  ~ 10
\item   1,01  ~ \(\times\)  ~ 10
\item   0,016  ~ \(\times\)  ~ 100
\item   0,096  ~ \(\times\)  ~ 10
\item   306  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 205  ~ : ~ 1 000
\item   5 400  ~ : ~ 100
\item   4,259  ~ : ~ 10
\item   1,274  ~ : ~ 100
\item   390,2  ~ : ~ 100
\item   1,786  ~ : ~ 100
\item   78,67  ~ : ~ 100
\item   8 993  ~ : ~ 1 000
\item   6,584  ~ : ~ 100
\item   911,4  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   29,4  ~ \(\times\)  ~ ... ~ = ~ 29 400
\item   0,41  ~ \(\times\)  ~ ... ~ = ~ 41
\item   0,956  ~ \(\times\)  ~ ... ~ = ~ 95,6
\item   9,31  ~ \(\times\)  ~ ... ~ = ~ 9 310
\item   867  ~ \(\times\)  ~ ... ~ = ~ 8 670
\item   59,5  ~ \(\times\)  ~ ... ~ = ~ 5 950
\item   156  ~ \(\times\)  ~ ... ~ = ~ 1 560
\item   189  ~ \(\times\)  ~ ... ~ = ~ 1 890
\item   693  ~ \(\times\)  ~ ... ~ = ~ 6 930
\item   2,1  ~ \(\times\)  ~ ... ~ = ~ 21
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   819,3  ~ \(\times\)  ~ 0,001
\item   47,02  ~ \(\times\)  ~ 0,01
\item   1,649  ~ \(\times\)  ~ 0,001
\item   8,381  ~ \(\times\)  ~ 0,1
\item   2 488  ~ \(\times\)  ~ 0,001
\item   1 388  ~ \(\times\)  ~ 0,01
\item   5 090  ~ \(\times\)  ~ 0,001
\item   148,4  ~ \(\times\)  ~ 0,001
\item   7,622  ~ \(\times\)  ~ 0,01
\item   95,35  ~ \(\times\)  ~ 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   372,4  ~ \(\times\)  ~ ... ~ = ~  0,372 4
\item   9 683  ~ \(\times\)  ~ ... ~ = ~  9,683
\item   7 421  ~ \(\times\)  ~ ... ~ = ~  742,1
\item   665,2  ~ \(\times\)  ~ ... ~ = ~  0,665 2
\item   94,44  ~ \(\times\)  ~ ... ~ = ~  9,444
\item   58,76  ~ \(\times\)  ~ ... ~ = ~  0,587 6
\item   220,5  ~ \(\times\)  ~ ... ~ = ~  2,205
\item   4,664  ~ \(\times\)  ~ ... ~ = ~  0,466 4
\item   178,3  ~ \(\times\)  ~ ... ~ = ~  1,783
\item   77,8  ~ \(\times\)  ~ ... ~ = ~  0,778
\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~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 324,2 ~L~ = ...~kL
\item   205,2 ~cg~ = ...~mg
\item   263,38 ~mm~ = ...~km
\item   7 052,9 ~hm~ = ...~dm
\item   7 251,7 ~hg~ = ...~dag
\item   730,98 ~dg~ = ...~dag
\item   4 876,2 ~dg~ = ...~g
\item   2 735,3 ~kL~ = ...~cL
\item   392,76 ~hL~ = ...~mL
\item   8 661,3 ~cL~ = ...~daL
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{720}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{89}{10}\) = \(\dfrac{890}{100}\)
\item   \(\dfrac{54}{100}\) = \(\dfrac{540}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,091  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 91}
\item   644  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 644 000}
\item   0,91  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 910}
\item   9,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 950}
\item   232  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 23 200}
\item   0,524  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,24}
\item   1,01  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 10,1}
\item   0,016  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,6}
\item   0,096  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,96}
\item   306  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 306 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 205 ~ : ~ 1 000 ~ = ~{\color{red} 2,205}
\item   5 400 ~ : ~ 100 ~ = ~{\color{red} 54}
\item   4,259 ~ : ~ 10 ~ = ~{\color{red} 0,425 9}
\item   1,274 ~ : ~ 100 ~ = ~{\color{red} 0,012 74}
\item   390,2 ~ : ~ 100 ~ = ~{\color{red} 3,902}
\item   1,786 ~ : ~ 100 ~ = ~{\color{red} 0,017 86}
\item   78,67 ~ : ~ 100 ~ = ~{\color{red} 0,786 7}
\item   8 993 ~ : ~ 1 000 ~ = ~{\color{red} 8,993}
\item   6,584 ~ : ~ 100 ~ = ~{\color{red} 0,065 84}
\item   911,4 ~ : ~ 100 ~ = ~{\color{red} 9,114}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   29,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~29 400
\item   0,41 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~41
\item   0,956 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~95,6
\item   9,31 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 310
\item   867 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 670
\item   59,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 950
\item   156 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 560
\item   189 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 890
\item   693 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 930
\item   2,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~21
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   819,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,819 3
}\item   47,02 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,470 2
}\item   1,649 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 649
}\item   8,381 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,838 1
}\item   2 488 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,488
}\item   1 388 ~ \(\times\)  0,01 ~ = ~{\color{red} 13,88
}\item   5 090 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,09
}\item   148,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,148 4
}\item   7,622 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,076 22
}\item   95,35 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,095 35
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   372,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,372 4
\item   9 683 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,683
\item   7 421 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 742,1
\item   665,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,665 2
\item   94,44 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,444
\item   58,76 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,587 6
\item   220,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,205
\item   4,664 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,466 4
\item   178,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,783
\item   77,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,778
\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~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 324,2 ~L~ = {\color{red}  5,324 2 }~kL
\item   205,2 ~cg~ = {\color{red}  2 052 }~mg
\item   263,38 ~mm~ = {\color{red}  0,000 263 38 }~km
\item   7 052,9 ~hm~ = {\color{red}  7 052 900 }~dm
\item   7 251,7 ~hg~ = {\color{red}  72 517 }~dag
\item   730,98 ~dg~ = {\color{red}  7,309 8 }~dag
\item   4 876,2 ~dg~ = {\color{red}  487,62 }~g
\item   2 735,3 ~kL~ = {\color{red}  273 530 000 }~cL
\item   392,76 ~hL~ = {\color{red}  39 276 000 }~mL
\item   8 661,3 ~cL~ = {\color{red}  8,661 3 }~daL
\end{itemize}
\end{multicols}
\end{document}
