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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 335}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{63}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{18}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   784  ~ \(\times\)  ~ 10
\item   0,513  ~ \(\times\)  ~ 1 000
\item   5,13  ~ \(\times\)  ~ 100
\item   0,036  ~ \(\times\)  ~ 10
\item   60,7  ~ \(\times\)  ~ 100
\item   0,164  ~ \(\times\)  ~ 100
\item   0,184  ~ \(\times\)  ~ 1 000
\item   28,9  ~ \(\times\)  ~ 10
\item   894  ~ \(\times\)  ~ 100
\item   1,01  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   550,1  ~ : ~ 10
\item   52,77  ~ : ~ 100
\item   4,601  ~ : ~ 1 000
\item   4,116  ~ : ~ 10
\item   587,1  ~ : ~ 1 000
\item   23,52  ~ : ~ 1 000
\item   7 743  ~ : ~ 1 000
\item   8,828  ~ : ~ 1 000
\item   671,7  ~ : ~ 100
\item   6,3  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 6
\item   1,3  ~ \(\times\)  ~ ... ~ = ~ 130
\item   0,184  ~ \(\times\)  ~ ... ~ = ~ 184
\item   149  ~ \(\times\)  ~ ... ~ = ~ 149 000
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 2
\item   0,29  ~ \(\times\)  ~ ... ~ = ~ 290
\item   1  ~ \(\times\)  ~ ... ~ = ~ 100
\item   6,68  ~ \(\times\)  ~ ... ~ = ~ 6 680
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 7
\item   0,227  ~ \(\times\)  ~ ... ~ = ~ 22,7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,293  ~ \(\times\)  ~ 0,001
\item   6,043  ~ \(\times\)  ~ 0,1
\item   698  ~ \(\times\)  ~ 0,1
\item   748,8  ~ \(\times\)  ~ 0,001
\item   7 632  ~ \(\times\)  ~ 0,1
\item   70,84  ~ \(\times\)  ~ 0,01
\item   2,475  ~ \(\times\)  ~ 0,001
\item   6,317  ~ \(\times\)  ~ 0,1
\item   3 410  ~ \(\times\)  ~ 0,001
\item   9,862  ~ \(\times\)  ~ 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   67,57  ~ \(\times\)  ~ ... ~ = ~  6,757
\item   393,1  ~ \(\times\)  ~ ... ~ = ~  3,931
\item   7 213  ~ \(\times\)  ~ ... ~ = ~  72,13
\item   62,5  ~ \(\times\)  ~ ... ~ = ~  0,625
\item   31,21  ~ \(\times\)  ~ ... ~ = ~  0,031 21
\item   85,12  ~ \(\times\)  ~ ... ~ = ~  0,085 12
\item   4 581  ~ \(\times\)  ~ ... ~ = ~  45,81
\item   5,405  ~ \(\times\)  ~ ... ~ = ~  0,540 5
\item   3 730  ~ \(\times\)  ~ ... ~ = ~  3,73
\item   2 577  ~ \(\times\)  ~ ... ~ = ~  2,577
\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~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   920,16 ~hm~ = ...~dam
\item   897,28 ~dL~ = ...~kL
\item   2 451,4 ~cg~ = ...~dag
\item   785,82 ~g~ = ...~dg
\item   695,27 ~hg~ = ...~dag
\item   6 158,6 ~dL~ = ...~L
\item   976,29 ~dL~ = ...~daL
\item   130,52 ~mm~ = ...~dam
\item   243,42 ~kL~ = ...~dL
\item   423,35 ~mg~ = ...~hg
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{6800}{100}\) = \(\dfrac{680}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{63}{10}\) = \(\dfrac{630}{100}\)
\item   \(\dfrac{18}{100}\) = \(\dfrac{180}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   784  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 840}
\item   0,513  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 513}
\item   5,13  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 513}
\item   0,036  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,36}
\item   60,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 070}
\item   0,164  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 16,4}
\item   0,184  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 184}
\item   28,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 289}
\item   894  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 89 400}
\item   1,01  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 101}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   550,1 ~ : ~ 10 ~ = ~{\color{red} 55,01}
\item   52,77 ~ : ~ 100 ~ = ~{\color{red} 0,527 7}
\item   4,601 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 601}
\item   4,116 ~ : ~ 10 ~ = ~{\color{red} 0,411 6}
\item   587,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,587 1}
\item   23,52 ~ : ~ 1 000 ~ = ~{\color{red} 0,023 52}
\item   7 743 ~ : ~ 1 000 ~ = ~{\color{red} 7,743}
\item   8,828 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 828}
\item   671,7 ~ : ~ 100 ~ = ~{\color{red} 6,717}
\item   6,3 ~ : ~ 10 ~ = ~{\color{red} 0,63}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,06 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6
\item   1,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~130
\item   0,184 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~184
\item   149 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~149 000
\item   0,002 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2
\item   0,29 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~290
\item   1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~100
\item   6,68 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 680
\item   0,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7
\item   0,227 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22,7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,293 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 293
}\item   6,043 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,604 3
}\item   698 ~ \(\times\)  0,1 ~ = ~{\color{red} 69,8
}\item   748,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,748 8
}\item   7 632 ~ \(\times\)  0,1 ~ = ~{\color{red} 763,2
}\item   70,84 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,708 4
}\item   2,475 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 475
}\item   6,317 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,631 7
}\item   3 410 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,41
}\item   9,862 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,098 62
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   67,57 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,757
\item   393,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,931
\item   7 213 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 72,13
\item   62,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,625
\item   31,21 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,031 21
\item   85,12 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,085 12
\item   4 581 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 45,81
\item   5,405 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,540 5
\item   3 730 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,73
\item   2 577 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,577
\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}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   920,16 ~hm~ = {\color{red}  9 201,6 }~dam
\item   897,28 ~dL~ = {\color{red}  0,089 728 }~kL
\item   2 451,4 ~cg~ = {\color{red}  2,451 4 }~dag
\item   785,82 ~g~ = {\color{red}  7 858,2 }~dg
\item   695,27 ~hg~ = {\color{red}  6 952,7 }~dag
\item   6 158,6 ~dL~ = {\color{red}  615,86 }~L
\item   976,29 ~dL~ = {\color{red}  9,762 9 }~daL
\item   130,52 ~mm~ = {\color{red}  0,013 052 }~dam
\item   243,42 ~kL~ = {\color{red}  2 434 200 }~dL
\item   423,35 ~mg~ = {\color{red}  0,004 233 5 }~hg
\end{itemize}
\end{multicols}
\end{document}
