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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 32}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{74}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   33  ~ \(\times\)  ~ 10
\item   0,034  ~ \(\times\)  ~ 100
\item   872  ~ \(\times\)  ~ 1 000
\item   0,716  ~ \(\times\)  ~ 100
\item   624  ~ \(\times\)  ~ 1 000
\item   78,2  ~ \(\times\)  ~ 1 000
\item   0,018  ~ \(\times\)  ~ 1 000
\item   80  ~ \(\times\)  ~ 100
\item   98,5  ~ \(\times\)  ~ 100
\item   0,92  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   677  ~ : ~ 1 000
\item   2,714  ~ : ~ 10
\item   7 168  ~ : ~ 10
\item   92,03  ~ : ~ 10
\item   2,775  ~ : ~ 100
\item   816,8  ~ : ~ 1 000
\item   5 004  ~ : ~ 10
\item   97,19  ~ : ~ 10
\item   48,26  ~ : ~ 10
\item   4,098  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   445  ~ \(\times\)  ~ ... ~ = ~ 44 500
\item   1,8  ~ \(\times\)  ~ ... ~ = ~ 180
\item   175  ~ \(\times\)  ~ ... ~ = ~ 1 750
\item   1,44  ~ \(\times\)  ~ ... ~ = ~ 14,4
\item   5,74  ~ \(\times\)  ~ ... ~ = ~ 57,4
\item   402  ~ \(\times\)  ~ ... ~ = ~ 4 020
\item   612  ~ \(\times\)  ~ ... ~ = ~ 61 200
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 2
\item   7,14  ~ \(\times\)  ~ ... ~ = ~ 714
\item   0,512  ~ \(\times\)  ~ ... ~ = ~ 5,12
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   539  ~ \(\times\)  ~ 0,1
\item   6,384  ~ \(\times\)  ~ 0,001
\item   617,5  ~ \(\times\)  ~ 0,001
\item   22,08  ~ \(\times\)  ~ 0,001
\item   617,1  ~ \(\times\)  ~ 0,001
\item   4 160  ~ \(\times\)  ~ 0,01
\item   549  ~ \(\times\)  ~ 0,1
\item   981,6  ~ \(\times\)  ~ 0,01
\item   693  ~ \(\times\)  ~ 0,01
\item   6 665  ~ \(\times\)  ~ 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   721,2  ~ \(\times\)  ~ ... ~ = ~  7,212
\item   5 063  ~ \(\times\)  ~ ... ~ = ~  5,063
\item   832,9  ~ \(\times\)  ~ ... ~ = ~  83,29
\item   96,76  ~ \(\times\)  ~ ... ~ = ~  0,967 6
\item   6,105  ~ \(\times\)  ~ ... ~ = ~  0,610 5
\item   67  ~ \(\times\)  ~ ... ~ = ~  6,7
\item   89,1  ~ \(\times\)  ~ ... ~ = ~  0,089 1
\item   87,83  ~ \(\times\)  ~ ... ~ = ~  0,878 3
\item   3 715  ~ \(\times\)  ~ ... ~ = ~  37,15
\item   531,4  ~ \(\times\)  ~ ... ~ = ~  0,531 4
\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~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~km~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 807,6 ~hg~ = ...~dg
\item   3 436,1 ~hm~ = ...~mm
\item   504,36 ~L~ = ...~daL
\item   217,22 ~cm~ = ...~hm
\item   3 526,3 ~dL~ = ...~daL
\item   9 311,9 ~km~ = ...~m
\item   150,68 ~cm~ = ...~m
\item   827,59 ~mg~ = ...~cg
\item   797,86 ~cg~ = ...~kg
\item   1 644,1 ~dm~ = ...~cm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{2900}{100}\) = \(\dfrac{290}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{410}{100}\)
\item   \(\dfrac{74}{100}\) = \(\dfrac{740}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   33  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 330}
\item   0,034  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,4}
\item   872  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 872 000}
\item   0,716  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 71,6}
\item   624  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 624 000}
\item   78,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 78 200}
\item   0,018  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 18}
\item   80  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 000}
\item   98,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 850}
\item   0,92  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   677 ~ : ~ 1 000 ~ = ~{\color{red} 0,677}
\item   2,714 ~ : ~ 10 ~ = ~{\color{red} 0,271 4}
\item   7 168 ~ : ~ 10 ~ = ~{\color{red} 716,8}
\item   92,03 ~ : ~ 10 ~ = ~{\color{red} 9,203}
\item   2,775 ~ : ~ 100 ~ = ~{\color{red} 0,027 75}
\item   816,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,816 8}
\item   5 004 ~ : ~ 10 ~ = ~{\color{red} 500,4}
\item   97,19 ~ : ~ 10 ~ = ~{\color{red} 9,719}
\item   48,26 ~ : ~ 10 ~ = ~{\color{red} 4,826}
\item   4,098 ~ : ~ 100 ~ = ~{\color{red} 0,040 98}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   445 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~44 500
\item   1,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~180
\item   175 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 750
\item   1,44 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~14,4
\item   5,74 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~57,4
\item   402 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 020
\item   612 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~61 200
\item   0,002 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2
\item   7,14 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~714
\item   0,512 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,12
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   539 ~ \(\times\)  0,1 ~ = ~{\color{red} 53,9
}\item   6,384 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 384
}\item   617,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,617 5
}\item   22,08 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,022 08
}\item   617,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,617 1
}\item   4 160 ~ \(\times\)  0,01 ~ = ~{\color{red} 41,6
}\item   549 ~ \(\times\)  0,1 ~ = ~{\color{red} 54,9
}\item   981,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,816
}\item   693 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,93
}\item   6 665 ~ \(\times\)  0,01 ~ = ~{\color{red} 66,65
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   721,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,212
\item   5 063 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,063
\item   832,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 83,29
\item   96,76 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,967 6
\item   6,105 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,610 5
\item   67 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,7
\item   89,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,089 1
\item   87,83 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,878 3
\item   3 715 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 37,15
\item   531,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,531 4
\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}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 807,6 ~hg~ = {\color{red}  1 807 600 }~dg
\item   3 436,1 ~hm~ = {\color{red}  343 610 000 }~mm
\item   504,36 ~L~ = {\color{red}  50,436 }~daL
\item   217,22 ~cm~ = {\color{red}  0,021 722 }~hm
\item   3 526,3 ~dL~ = {\color{red}  35,263 }~daL
\item   9 311,9 ~km~ = {\color{red}  9 311 900 }~m
\item   150,68 ~cm~ = {\color{red}  1,506 8 }~m
\item   827,59 ~mg~ = {\color{red}  82,759 }~cg
\item   797,86 ~cg~ = {\color{red}  0,007 978 6 }~kg
\item   1 644,1 ~dm~ = {\color{red}  16 441 }~cm
\end{itemize}
\end{multicols}
\end{document}
