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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 232}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,49  ~ \(\times\)  ~ 10
\item   43,7  ~ \(\times\)  ~ 1 000
\item   973  ~ \(\times\)  ~ 100
\item   2,85  ~ \(\times\)  ~ 100
\item   653  ~ \(\times\)  ~ 10
\item   0,285  ~ \(\times\)  ~ 100
\item   83,4  ~ \(\times\)  ~ 1 000
\item   0,64  ~ \(\times\)  ~ 1 000
\item   0,041  ~ \(\times\)  ~ 10
\item   295  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 935  ~ : ~ 100
\item   97,17  ~ : ~ 100
\item   2,704  ~ : ~ 100
\item   29,7  ~ : ~ 10
\item   2,36  ~ : ~ 10
\item   4,12  ~ : ~ 100
\item   3 482  ~ : ~ 10
\item   6,32  ~ : ~ 100
\item   16,65  ~ : ~ 10
\item   79,8  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,68  ~ \(\times\)  ~ ... ~ = ~ 668
\item   0,837  ~ \(\times\)  ~ ... ~ = ~ 8,37
\item   82,8  ~ \(\times\)  ~ ... ~ = ~ 8 280
\item   55,2  ~ \(\times\)  ~ ... ~ = ~ 552
\item   8,4  ~ \(\times\)  ~ ... ~ = ~ 8 400
\item   0,303  ~ \(\times\)  ~ ... ~ = ~ 30,3
\item   91  ~ \(\times\)  ~ ... ~ = ~ 9 100
\item   60,6  ~ \(\times\)  ~ ... ~ = ~ 6 060
\item   2,27  ~ \(\times\)  ~ ... ~ = ~ 22,7
\item   434  ~ \(\times\)  ~ ... ~ = ~ 43 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   88,82  ~ \(\times\)  ~ 0,01
\item   4 479  ~ \(\times\)  ~ 0,1
\item   2,156  ~ \(\times\)  ~ 0,01
\item   69,45  ~ \(\times\)  ~ 0,001
\item   15,85  ~ \(\times\)  ~ 0,01
\item   4,608  ~ \(\times\)  ~ 0,001
\item   640,4  ~ \(\times\)  ~ 0,001
\item   0,846  ~ \(\times\)  ~ 0,001
\item   805  ~ \(\times\)  ~ 0,001
\item   2 787  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   47,45  ~ \(\times\)  ~ ... ~ = ~  0,047 45
\item   95,4  ~ \(\times\)  ~ ... ~ = ~  0,954
\item   37,52  ~ \(\times\)  ~ ... ~ = ~  0,037 52
\item   5 520  ~ \(\times\)  ~ ... ~ = ~  5,52
\item   4 071  ~ \(\times\)  ~ ... ~ = ~  40,71
\item   487,9  ~ \(\times\)  ~ ... ~ = ~  48,79
\item   60,94  ~ \(\times\)  ~ ... ~ = ~  0,060 94
\item   1,369  ~ \(\times\)  ~ ... ~ = ~  0,001 369
\item   36,06  ~ \(\times\)  ~ ... ~ = ~  0,036 06
\item   8 337  ~ \(\times\)  ~ ... ~ = ~  833,7
\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~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   442,53 ~cm~ = ...~m
\item   820,32 ~mL~ = ...~daL
\item   8 335,8 ~L~ = ...~hL
\item   237,29 ~kL~ = ...~hL
\item   2 506 ~L~ = ...~kL
\item   7 698,8 ~kg~ = ...~dg
\item   6 294,8 ~cL~ = ...~kL
\item   1 707,8 ~dL~ = ...~daL
\item   3 948,1 ~g~ = ...~cg
\item   249,48 ~km~ = ...~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   5 = \(\dfrac{50}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{4000}{100}\) = \(\dfrac{400}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{200}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{450}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,49  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 84,9}
\item   43,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 43 700}
\item   973  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 97 300}
\item   2,85  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 285}
\item   653  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 530}
\item   0,285  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 28,5}
\item   83,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 83 400}
\item   0,64  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 640}
\item   0,041  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,41}
\item   295  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 29 500}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 935 ~ : ~ 100 ~ = ~{\color{red} 29,35}
\item   97,17 ~ : ~ 100 ~ = ~{\color{red} 0,971 7}
\item   2,704 ~ : ~ 100 ~ = ~{\color{red} 0,027 04}
\item   29,7 ~ : ~ 10 ~ = ~{\color{red} 2,97}
\item   2,36 ~ : ~ 10 ~ = ~{\color{red} 0,236}
\item   4,12 ~ : ~ 100 ~ = ~{\color{red} 0,041 2}
\item   3 482 ~ : ~ 10 ~ = ~{\color{red} 348,2}
\item   6,32 ~ : ~ 100 ~ = ~{\color{red} 0,063 2}
\item   16,65 ~ : ~ 10 ~ = ~{\color{red} 1,665}
\item   79,8 ~ : ~ 100 ~ = ~{\color{red} 0,798}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,68 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~668
\item   0,837 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,37
\item   82,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 280
\item   55,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~552
\item   8,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 400
\item   0,303 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30,3
\item   91 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 100
\item   60,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 060
\item   2,27 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~22,7
\item   434 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~43 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   88,82 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,888 2
}\item   4 479 ~ \(\times\)  0,1 ~ = ~{\color{red} 447,9
}\item   2,156 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,021 56
}\item   69,45 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,069 45
}\item   15,85 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,158 5
}\item   4,608 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 608
}\item   640,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,640 4
}\item   0,846 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 846
}\item   805 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,805
}\item   2 787 ~ \(\times\)  0,1 ~ = ~{\color{red} 278,7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   47,45 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,047 45
\item   95,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,954
\item   37,52 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,037 52
\item   5 520 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,52
\item   4 071 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 40,71
\item   487,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 48,79
\item   60,94 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,060 94
\item   1,369 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 369
\item   36,06 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,036 06
\item   8 337 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 833,7
\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~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   442,53 ~cm~ = {\color{red}  4,425 3 }~m
\item   820,32 ~mL~ = {\color{red}  0,082 032 }~daL
\item   8 335,8 ~L~ = {\color{red}  83,358 }~hL
\item   237,29 ~kL~ = {\color{red}  2 372,9 }~hL
\item   2 506 ~L~ = {\color{red}  2,506 }~kL
\item   7 698,8 ~kg~ = {\color{red}  76 988 000 }~dg
\item   6 294,8 ~cL~ = {\color{red}  0,062 948 }~kL
\item   1 707,8 ~dL~ = {\color{red}  17,078 }~daL
\item   3 948,1 ~g~ = {\color{red}  394 810 }~cg
\item   249,48 ~km~ = {\color{red}  24 948 000 }~cm
\end{itemize}
\end{multicols}
\end{document}
