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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 24}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{32}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   695  ~ \(\times\)  ~ 1 000
\item   78,4  ~ \(\times\)  ~ 1 000
\item   299  ~ \(\times\)  ~ 100
\item   487  ~ \(\times\)  ~ 10
\item   53,8  ~ \(\times\)  ~ 100
\item   0,765  ~ \(\times\)  ~ 1 000
\item   0,32  ~ \(\times\)  ~ 10
\item   7,12  ~ \(\times\)  ~ 1 000
\item   1,7  ~ \(\times\)  ~ 100
\item   0,009  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 113  ~ : ~ 10
\item   52,81  ~ : ~ 1 000
\item   12,41  ~ : ~ 10
\item   413,1  ~ : ~ 100
\item   47,56  ~ : ~ 1 000
\item   458,8  ~ : ~ 10
\item   9,544  ~ : ~ 10
\item   24,45  ~ : ~ 100
\item   334,3  ~ : ~ 100
\item   83,82  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,2  ~ \(\times\)  ~ ... ~ = ~ 79 200
\item   82,4  ~ \(\times\)  ~ ... ~ = ~ 824
\item   65,5  ~ \(\times\)  ~ ... ~ = ~ 6 550
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 33
\item   0,244  ~ \(\times\)  ~ ... ~ = ~ 2,44
\item   8,22  ~ \(\times\)  ~ ... ~ = ~ 822
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 7,7
\item   8,6  ~ \(\times\)  ~ ... ~ = ~ 860
\item   80,2  ~ \(\times\)  ~ ... ~ = ~ 80 200
\item   0,597  ~ \(\times\)  ~ ... ~ = ~ 59,7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,79  ~ \(\times\)  ~ 0,1
\item   1,047  ~ \(\times\)  ~ 0,001
\item   5,222  ~ \(\times\)  ~ 0,01
\item   1 569  ~ \(\times\)  ~ 0,1
\item   5,474  ~ \(\times\)  ~ 0,01
\item   8,929  ~ \(\times\)  ~ 0,001
\item   8,691  ~ \(\times\)  ~ 0,01
\item   37,18  ~ \(\times\)  ~ 0,01
\item   61,94  ~ \(\times\)  ~ 0,1
\item   5 608  ~ \(\times\)  ~ 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   3,82  ~ \(\times\)  ~ ... ~ = ~  0,003 82
\item   0,352  ~ \(\times\)  ~ ... ~ = ~  0,003 52
\item   65,39  ~ \(\times\)  ~ ... ~ = ~  0,653 9
\item   7,484  ~ \(\times\)  ~ ... ~ = ~  0,007 484
\item   61,85  ~ \(\times\)  ~ ... ~ = ~  0,061 85
\item   0,24  ~ \(\times\)  ~ ... ~ = ~  0,024
\item   7,987  ~ \(\times\)  ~ ... ~ = ~  0,798 7
\item   286,1  ~ \(\times\)  ~ ... ~ = ~  28,61
\item   877,7  ~ \(\times\)  ~ ... ~ = ~  8,777
\item   229,2  ~ \(\times\)  ~ ... ~ = ~  22,92
\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 ~dm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   462,63 ~cm~ = ...~hm
\item   8 671,5 ~dL~ = ...~L
\item   2 379,8 ~mL~ = ...~daL
\item   2 963,1 ~daL~ = ...~kL
\item   881,12 ~cL~ = ...~mL
\item   443,45 ~L~ = ...~dL
\item   688,99 ~kg~ = ...~cg
\item   9 598,8 ~dam~ = ...~dm
\item   9 948,9 ~mL~ = ...~L
\item   2 822,2 ~cL~ = ...~daL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{3800}{100}\) = \(\dfrac{380}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{32}{100}\) = \(\dfrac{320}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   695  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 695 000}
\item   78,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 78 400}
\item   299  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 29 900}
\item   487  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 870}
\item   53,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 380}
\item   0,765  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 765}
\item   0,32  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,2}
\item   7,12  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 120}
\item   1,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 170}
\item   0,009  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 113 ~ : ~ 10 ~ = ~{\color{red} 611,3}
\item   52,81 ~ : ~ 1 000 ~ = ~{\color{red} 0,052 81}
\item   12,41 ~ : ~ 10 ~ = ~{\color{red} 1,241}
\item   413,1 ~ : ~ 100 ~ = ~{\color{red} 4,131}
\item   47,56 ~ : ~ 1 000 ~ = ~{\color{red} 0,047 56}
\item   458,8 ~ : ~ 10 ~ = ~{\color{red} 45,88}
\item   9,544 ~ : ~ 10 ~ = ~{\color{red} 0,954 4}
\item   24,45 ~ : ~ 100 ~ = ~{\color{red} 0,244 5}
\item   334,3 ~ : ~ 100 ~ = ~{\color{red} 3,343}
\item   83,82 ~ : ~ 1 000 ~ = ~{\color{red} 0,083 82}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~79 200
\item   82,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~824
\item   65,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 550
\item   0,033 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33
\item   0,244 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,44
\item   8,22 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~822
\item   0,077 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,7
\item   8,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~860
\item   80,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~80 200
\item   0,597 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~59,7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,79 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,179
}\item   1,047 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 047
}\item   5,222 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,052 22
}\item   1 569 ~ \(\times\)  0,1 ~ = ~{\color{red} 156,9
}\item   5,474 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,054 74
}\item   8,929 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 929
}\item   8,691 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,086 91
}\item   37,18 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,371 8
}\item   61,94 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,194
}\item   5 608 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,608
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,82 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 82
\item   0,352 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,003 52
\item   65,39 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,653 9
\item   7,484 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 484
\item   61,85 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,061 85
\item   0,24 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,024
\item   7,987 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,798 7
\item   286,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 28,61
\item   877,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,777
\item   229,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 22,92
\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 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   462,63 ~cm~ = {\color{red}  0,046 263 }~hm
\item   8 671,5 ~dL~ = {\color{red}  867,15 }~L
\item   2 379,8 ~mL~ = {\color{red}  0,237 98 }~daL
\item   2 963,1 ~daL~ = {\color{red}  29,631 }~kL
\item   881,12 ~cL~ = {\color{red}  8 811,2 }~mL
\item   443,45 ~L~ = {\color{red}  4 434,5 }~dL
\item   688,99 ~kg~ = {\color{red}  68 899 000 }~cg
\item   9 598,8 ~dam~ = {\color{red}  959 880 }~dm
\item   9 948,9 ~mL~ = {\color{red}  9,948 9 }~L
\item   2 822,2 ~cL~ = {\color{red}  2,822 2 }~daL
\end{itemize}
\end{multicols}
\end{document}
