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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 233}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{21}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   862  ~ \(\times\)  ~ 100
\item   248  ~ \(\times\)  ~ 10
\item   96,4  ~ \(\times\)  ~ 1 000
\item   73  ~ \(\times\)  ~ 1 000
\item   300  ~ \(\times\)  ~ 100
\item   33,8  ~ \(\times\)  ~ 10
\item   8,49  ~ \(\times\)  ~ 100
\item   54,7  ~ \(\times\)  ~ 1 000
\item   7,31  ~ \(\times\)  ~ 100
\item   0,011  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,546  ~ : ~ 10
\item   667,1  ~ : ~ 10
\item   1 148  ~ : ~ 10
\item   27,3  ~ : ~ 100
\item   8,564  ~ : ~ 10
\item   0,531  ~ : ~ 10
\item   5 783  ~ : ~ 1 000
\item   14,29  ~ : ~ 10
\item   65,18  ~ : ~ 1 000
\item   0,749  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   747  ~ \(\times\)  ~ ... ~ = ~ 7 470
\item   5,01  ~ \(\times\)  ~ ... ~ = ~ 501
\item   0,14  ~ \(\times\)  ~ ... ~ = ~ 14
\item   0,031  ~ \(\times\)  ~ ... ~ = ~ 31
\item   74,6  ~ \(\times\)  ~ ... ~ = ~ 746
\item   0,876  ~ \(\times\)  ~ ... ~ = ~ 876
\item   69,7  ~ \(\times\)  ~ ... ~ = ~ 6 970
\item   72,2  ~ \(\times\)  ~ ... ~ = ~ 722
\item   0,071  ~ \(\times\)  ~ ... ~ = ~ 71
\item   117  ~ \(\times\)  ~ ... ~ = ~ 11 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,064  ~ \(\times\)  ~ 0,1
\item   53,26  ~ \(\times\)  ~ 0,1
\item   507,2  ~ \(\times\)  ~ 0,1
\item   8 758  ~ \(\times\)  ~ 0,001
\item   70,8  ~ \(\times\)  ~ 0,001
\item   9,508  ~ \(\times\)  ~ 0,001
\item   98,64  ~ \(\times\)  ~ 0,1
\item   17,68  ~ \(\times\)  ~ 0,1
\item   89,01  ~ \(\times\)  ~ 0,01
\item   703,7  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,69  ~ \(\times\)  ~ ... ~ = ~  0,006 9
\item   34,33  ~ \(\times\)  ~ ... ~ = ~  0,343 3
\item   1,936  ~ \(\times\)  ~ ... ~ = ~  0,001 936
\item   5,033  ~ \(\times\)  ~ ... ~ = ~  0,050 33
\item   703  ~ \(\times\)  ~ ... ~ = ~  70,3
\item   195,5  ~ \(\times\)  ~ ... ~ = ~  0,195 5
\item   1,613  ~ \(\times\)  ~ ... ~ = ~  0,001 613
\item   8,36  ~ \(\times\)  ~ ... ~ = ~  0,836
\item   6,67  ~ \(\times\)  ~ ... ~ = ~  0,006 67
\item   739,4  ~ \(\times\)  ~ ... ~ = ~  73,94
\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~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 361,5 ~dg~ = ...~dag
\item   681,27 ~dam~ = ...~mm
\item   614,94 ~g~ = ...~dag
\item   226,04 ~hm~ = ...~dam
\item   3 814,3 ~km~ = ...~dm
\item   851,15 ~L~ = ...~mL
\item   192,25 ~L~ = ...~hL
\item   134,74 ~daL~ = ...~dL
\item   5 100,6 ~daL~ = ...~kL
\item   139,23 ~g~ = ...~mg
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{720}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{370}{100}\)
\item   \(\dfrac{21}{100}\) = \(\dfrac{210}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   862  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 86 200}
\item   248  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 480}
\item   96,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 96 400}
\item   73  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 73 000}
\item   300  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 30 000}
\item   33,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 338}
\item   8,49  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 849}
\item   54,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 54 700}
\item   7,31  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 731}
\item   0,011  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,546 ~ : ~ 10 ~ = ~{\color{red} 0,454 6}
\item   667,1 ~ : ~ 10 ~ = ~{\color{red} 66,71}
\item   1 148 ~ : ~ 10 ~ = ~{\color{red} 114,8}
\item   27,3 ~ : ~ 100 ~ = ~{\color{red} 0,273}
\item   8,564 ~ : ~ 10 ~ = ~{\color{red} 0,856 4}
\item   0,531 ~ : ~ 10 ~ = ~{\color{red} 0,053 1}
\item   5 783 ~ : ~ 1 000 ~ = ~{\color{red} 5,783}
\item   14,29 ~ : ~ 10 ~ = ~{\color{red} 1,429}
\item   65,18 ~ : ~ 1 000 ~ = ~{\color{red} 0,065 18}
\item   0,749 ~ : ~ 100 ~ = ~{\color{red} 0,007 49}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   747 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 470
\item   5,01 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~501
\item   0,14 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~14
\item   0,031 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~31
\item   74,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~746
\item   0,876 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~876
\item   69,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 970
\item   72,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~722
\item   0,071 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~71
\item   117 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~11 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,064 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,706 4
}\item   53,26 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,326
}\item   507,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 50,72
}\item   8 758 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,758
}\item   70,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,070 8
}\item   9,508 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 508
}\item   98,64 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,864
}\item   17,68 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,768
}\item   89,01 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,890 1
}\item   703,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,037
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,69 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,006 9
\item   34,33 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,343 3
\item   1,936 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 936
\item   5,033 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,050 33
\item   703 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 70,3
\item   195,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,195 5
\item   1,613 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 613
\item   8,36 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,836
\item   6,67 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 67
\item   739,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 73,94
\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}  100 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 361,5 ~dg~ = {\color{red}  93,615 }~dag
\item   681,27 ~dam~ = {\color{red}  6 812 700 }~mm
\item   614,94 ~g~ = {\color{red}  61,494 }~dag
\item   226,04 ~hm~ = {\color{red}  2 260,4 }~dam
\item   3 814,3 ~km~ = {\color{red}  38 143 000 }~dm
\item   851,15 ~L~ = {\color{red}  851 150 }~mL
\item   192,25 ~L~ = {\color{red}  1,922 5 }~hL
\item   134,74 ~daL~ = {\color{red}  13 474 }~dL
\item   5 100,6 ~daL~ = {\color{red}  51,006 }~kL
\item   139,23 ~g~ = {\color{red}  139 230 }~mg
\end{itemize}
\end{multicols}
\end{document}
