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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 142}

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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   \(\dfrac{7300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{55}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{56}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,62  ~ \(\times\)  ~ 10
\item   1,09  ~ \(\times\)  ~ 10
\item   0,06  ~ \(\times\)  ~ 10
\item   0,09  ~ \(\times\)  ~ 1 000
\item   904  ~ \(\times\)  ~ 100
\item   264  ~ \(\times\)  ~ 1 000
\item   0,033  ~ \(\times\)  ~ 100
\item   97  ~ \(\times\)  ~ 100
\item   807  ~ \(\times\)  ~ 100
\item   146  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   630,1  ~ : ~ 1 000
\item   5,424  ~ : ~ 10
\item   49,32  ~ : ~ 1 000
\item   5 819  ~ : ~ 10
\item   396,7  ~ : ~ 100
\item   19,62  ~ : ~ 10
\item   30,39  ~ : ~ 100
\item   215,1  ~ : ~ 10
\item   349,7  ~ : ~ 100
\item   3 252  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24,9  ~ \(\times\)  ~ ... ~ = ~ 24 900
\item   30,1  ~ \(\times\)  ~ ... ~ = ~ 301
\item   0,086  ~ \(\times\)  ~ ... ~ = ~ 8,6
\item   96,4  ~ \(\times\)  ~ ... ~ = ~ 9 640
\item   53,1  ~ \(\times\)  ~ ... ~ = ~ 531
\item   94  ~ \(\times\)  ~ ... ~ = ~ 94 000
\item   0,09  ~ \(\times\)  ~ ... ~ = ~ 9
\item   0,651  ~ \(\times\)  ~ ... ~ = ~ 651
\item   0,921  ~ \(\times\)  ~ ... ~ = ~ 92,1
\item   0,856  ~ \(\times\)  ~ ... ~ = ~ 8,56
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 813  ~ \(\times\)  ~ 0,001
\item   79,7  ~ \(\times\)  ~ 0,001
\item   1 872  ~ \(\times\)  ~ 0,001
\item   1,3  ~ \(\times\)  ~ 0,001
\item   834,1  ~ \(\times\)  ~ 0,1
\item   538,9  ~ \(\times\)  ~ 0,001
\item   8,089  ~ \(\times\)  ~ 0,001
\item   6 601  ~ \(\times\)  ~ 0,001
\item   544  ~ \(\times\)  ~ 0,01
\item   34,36  ~ \(\times\)  ~ 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   42,13  ~ \(\times\)  ~ ... ~ = ~  4,213
\item   14,45  ~ \(\times\)  ~ ... ~ = ~  0,144 5
\item   4,07  ~ \(\times\)  ~ ... ~ = ~  0,040 7
\item   8 285  ~ \(\times\)  ~ ... ~ = ~  828,5
\item   3,98  ~ \(\times\)  ~ ... ~ = ~  0,003 98
\item   7 342  ~ \(\times\)  ~ ... ~ = ~  73,42
\item   497,8  ~ \(\times\)  ~ ... ~ = ~  49,78
\item   4 217  ~ \(\times\)  ~ ... ~ = ~  42,17
\item   70,94  ~ \(\times\)  ~ ... ~ = ~  0,709 4
\item   9,341  ~ \(\times\)  ~ ... ~ = ~  0,093 41
\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 ~hm~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 322,9 ~hm~ = ...~km
\item   679,35 ~kg~ = ...~dg
\item   280 ~dm~ = ...~hm
\item   6 602,3 ~dam~ = ...~hm
\item   710,29 ~mm~ = ...~cm
\item   664,28 ~mm~ = ...~m
\item   475,5 ~kg~ = ...~g
\item   3 541,5 ~dg~ = ...~dag
\item   3 951 ~kL~ = ...~daL
\item   1 865,1 ~kL~ = ...~hL
\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   \(\dfrac{7300}{100}\) = \(\dfrac{730}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{55}{10}\) = \(\dfrac{550}{100}\)
\item   \(\dfrac{56}{100}\) = \(\dfrac{560}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,62  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 86,2}
\item   1,09  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 10,9}
\item   0,06  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,6}
\item   0,09  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 90}
\item   904  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 90 400}
\item   264  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 264 000}
\item   0,033  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,3}
\item   97  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 700}
\item   807  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80 700}
\item   146  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14 600}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   630,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,630 1}
\item   5,424 ~ : ~ 10 ~ = ~{\color{red} 0,542 4}
\item   49,32 ~ : ~ 1 000 ~ = ~{\color{red} 0,049 32}
\item   5 819 ~ : ~ 10 ~ = ~{\color{red} 581,9}
\item   396,7 ~ : ~ 100 ~ = ~{\color{red} 3,967}
\item   19,62 ~ : ~ 10 ~ = ~{\color{red} 1,962}
\item   30,39 ~ : ~ 100 ~ = ~{\color{red} 0,303 9}
\item   215,1 ~ : ~ 10 ~ = ~{\color{red} 21,51}
\item   349,7 ~ : ~ 100 ~ = ~{\color{red} 3,497}
\item   3 252 ~ : ~ 1 000 ~ = ~{\color{red} 3,252}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~24 900
\item   30,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~301
\item   0,086 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,6
\item   96,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 640
\item   53,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~531
\item   94 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~94 000
\item   0,09 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9
\item   0,651 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~651
\item   0,921 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~92,1
\item   0,856 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,56
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 813 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,813
}\item   79,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,079 7
}\item   1 872 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,872
}\item   1,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 3
}\item   834,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 83,41
}\item   538,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,538 9
}\item   8,089 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 089
}\item   6 601 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,601
}\item   544 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,44
}\item   34,36 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,034 36
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42,13 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,213
\item   14,45 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,144 5
\item   4,07 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,040 7
\item   8 285 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 828,5
\item   3,98 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 98
\item   7 342 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 73,42
\item   497,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 49,78
\item   4 217 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 42,17
\item   70,94 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,709 4
\item   9,341 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,093 41
\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 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 322,9 ~hm~ = {\color{red}  132,29 }~km
\item   679,35 ~kg~ = {\color{red}  6 793 500 }~dg
\item   280 ~dm~ = {\color{red}  0,28 }~hm
\item   6 602,3 ~dam~ = {\color{red}  660,23 }~hm
\item   710,29 ~mm~ = {\color{red}  71,029 }~cm
\item   664,28 ~mm~ = {\color{red}  0,664 28 }~m
\item   475,5 ~kg~ = {\color{red}  475 500 }~g
\item   3 541,5 ~dg~ = {\color{red}  35,415 }~dag
\item   3 951 ~kL~ = {\color{red}  395 100 }~daL
\item   1 865,1 ~kL~ = {\color{red}  18 651 }~hL
\end{itemize}
\end{multicols}
\end{document}
