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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 31}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{98}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,3  ~ \(\times\)  ~ 10
\item   55,7  ~ \(\times\)  ~ 1 000
\item   78,4  ~ \(\times\)  ~ 10
\item   767  ~ \(\times\)  ~ 1 000
\item   7,1  ~ \(\times\)  ~ 10
\item   0,557  ~ \(\times\)  ~ 1 000
\item   43,1  ~ \(\times\)  ~ 1 000
\item   104  ~ \(\times\)  ~ 10
\item   0,797  ~ \(\times\)  ~ 100
\item   21,2  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   65,22  ~ : ~ 1 000
\item   414  ~ : ~ 1 000
\item   3,655  ~ : ~ 1 000
\item   9 069  ~ : ~ 10
\item   30,48  ~ : ~ 10
\item   344,1  ~ : ~ 100
\item   598  ~ : ~ 1 000
\item   8,804  ~ : ~ 1 000
\item   367,8  ~ : ~ 100
\item   612,1  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,5  ~ \(\times\)  ~ ... ~ = ~ 6 650
\item   0,51  ~ \(\times\)  ~ ... ~ = ~ 51
\item   3,09  ~ \(\times\)  ~ ... ~ = ~ 3 090
\item   0,414  ~ \(\times\)  ~ ... ~ = ~ 414
\item   6,75  ~ \(\times\)  ~ ... ~ = ~ 67,5
\item   776  ~ \(\times\)  ~ ... ~ = ~ 77 600
\item   92,6  ~ \(\times\)  ~ ... ~ = ~ 92 600
\item   0,065  ~ \(\times\)  ~ ... ~ = ~ 65
\item   311  ~ \(\times\)  ~ ... ~ = ~ 3 110
\item   206  ~ \(\times\)  ~ ... ~ = ~ 206 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 240  ~ \(\times\)  ~ 0,001
\item   66,41  ~ \(\times\)  ~ 0,01
\item   3 326  ~ \(\times\)  ~ 0,01
\item   34,2  ~ \(\times\)  ~ 0,01
\item   6 702  ~ \(\times\)  ~ 0,001
\item   20,34  ~ \(\times\)  ~ 0,1
\item   205,5  ~ \(\times\)  ~ 0,1
\item   559,3  ~ \(\times\)  ~ 0,001
\item   2,589  ~ \(\times\)  ~ 0,1
\item   82,62  ~ \(\times\)  ~ 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   8 133  ~ \(\times\)  ~ ... ~ = ~  813,3
\item   805,4  ~ \(\times\)  ~ ... ~ = ~  0,805 4
\item   8 254  ~ \(\times\)  ~ ... ~ = ~  82,54
\item   8,125  ~ \(\times\)  ~ ... ~ = ~  0,081 25
\item   3 991  ~ \(\times\)  ~ ... ~ = ~  399,1
\item   62,48  ~ \(\times\)  ~ ... ~ = ~  0,624 8
\item   2 986  ~ \(\times\)  ~ ... ~ = ~  298,6
\item   2 146  ~ \(\times\)  ~ ... ~ = ~  2,146
\item   348,4  ~ \(\times\)  ~ ... ~ = ~  3,484
\item   3,112  ~ \(\times\)  ~ ... ~ = ~  0,003 112
\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 ~dam~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   204,28 ~L~ = ...~cL
\item   178,64 ~dL~ = ...~hL
\item   5 407,3 ~mg~ = ...~dg
\item   878,47 ~m~ = ...~dm
\item   3 475,9 ~hL~ = ...~mL
\item   483,68 ~g~ = ...~mg
\item   387,1 ~hg~ = ...~dag
\item   655,28 ~dL~ = ...~cL
\item   7 249,4 ~dm~ = ...~km
\item   608,76 ~g~ = ...~cg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{250}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{290}{100}\)
\item   \(\dfrac{98}{100}\) = \(\dfrac{980}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 53}
\item   55,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 55 700}
\item   78,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 784}
\item   767  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 767 000}
\item   7,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 71}
\item   0,557  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 557}
\item   43,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 43 100}
\item   104  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 040}
\item   0,797  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 79,7}
\item   21,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 120}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   65,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,065 22}
\item   414 ~ : ~ 1 000 ~ = ~{\color{red} 0,414}
\item   3,655 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 655}
\item   9 069 ~ : ~ 10 ~ = ~{\color{red} 906,9}
\item   30,48 ~ : ~ 10 ~ = ~{\color{red} 3,048}
\item   344,1 ~ : ~ 100 ~ = ~{\color{red} 3,441}
\item   598 ~ : ~ 1 000 ~ = ~{\color{red} 0,598}
\item   8,804 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 804}
\item   367,8 ~ : ~ 100 ~ = ~{\color{red} 3,678}
\item   612,1 ~ : ~ 100 ~ = ~{\color{red} 6,121}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 650
\item   0,51 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~51
\item   3,09 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 090
\item   0,414 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~414
\item   6,75 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~67,5
\item   776 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~77 600
\item   92,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~92 600
\item   0,065 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~65
\item   311 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 110
\item   206 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~206 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 240 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,24
}\item   66,41 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,664 1
}\item   3 326 ~ \(\times\)  0,01 ~ = ~{\color{red} 33,26
}\item   34,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,342
}\item   6 702 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,702
}\item   20,34 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,034
}\item   205,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 20,55
}\item   559,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,559 3
}\item   2,589 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,258 9
}\item   82,62 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,826 2
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 133 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 813,3
\item   805,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,805 4
\item   8 254 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 82,54
\item   8,125 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,081 25
\item   3 991 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 399,1
\item   62,48 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,624 8
\item   2 986 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 298,6
\item   2 146 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,146
\item   348,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,484
\item   3,112 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 112
\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 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   204,28 ~L~ = {\color{red}  20 428 }~cL
\item   178,64 ~dL~ = {\color{red}  0,178 64 }~hL
\item   5 407,3 ~mg~ = {\color{red}  54,073 }~dg
\item   878,47 ~m~ = {\color{red}  8 784,7 }~dm
\item   3 475,9 ~hL~ = {\color{red}  347 590 000 }~mL
\item   483,68 ~g~ = {\color{red}  483 680 }~mg
\item   387,1 ~hg~ = {\color{red}  3 871 }~dag
\item   655,28 ~dL~ = {\color{red}  6 552,8 }~cL
\item   7 249,4 ~dm~ = {\color{red}  0,724 94 }~km
\item   608,76 ~g~ = {\color{red}  60 876 }~cg
\end{itemize}
\end{multicols}
\end{document}
