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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 377}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,59  ~ \(\times\)  ~ 100
\item   87  ~ \(\times\)  ~ 100
\item   5,58  ~ \(\times\)  ~ 10
\item   5,24  ~ \(\times\)  ~ 10
\item   29,1  ~ \(\times\)  ~ 1 000
\item   597  ~ \(\times\)  ~ 100
\item   6,76  ~ \(\times\)  ~ 1 000
\item   0,02  ~ \(\times\)  ~ 1 000
\item   947  ~ \(\times\)  ~ 100
\item   0,844  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 031  ~ : ~ 1 000
\item   5 498  ~ : ~ 10
\item   71,78  ~ : ~ 100
\item   8,565  ~ : ~ 100
\item   28  ~ : ~ 10
\item   73,38  ~ : ~ 10
\item   5 933  ~ : ~ 100
\item   96,18  ~ : ~ 10
\item   23,7  ~ : ~ 10
\item   734,4  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,553  ~ \(\times\)  ~ ... ~ = ~ 553
\item   0,245  ~ \(\times\)  ~ ... ~ = ~ 2,45
\item   0,87  ~ \(\times\)  ~ ... ~ = ~ 87
\item   2,47  ~ \(\times\)  ~ ... ~ = ~ 247
\item   0,098  ~ \(\times\)  ~ ... ~ = ~ 0,98
\item   0,284  ~ \(\times\)  ~ ... ~ = ~ 28,4
\item   415  ~ \(\times\)  ~ ... ~ = ~ 4 150
\item   268  ~ \(\times\)  ~ ... ~ = ~ 268 000
\item   27,5  ~ \(\times\)  ~ ... ~ = ~ 275
\item   146  ~ \(\times\)  ~ ... ~ = ~ 146 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   348,7  ~ \(\times\)  ~ 0,01
\item   8,373  ~ \(\times\)  ~ 0,1
\item   4 320  ~ \(\times\)  ~ 0,01
\item   8 080  ~ \(\times\)  ~ 0,01
\item   4,767  ~ \(\times\)  ~ 0,001
\item   3,975  ~ \(\times\)  ~ 0,01
\item   4,468  ~ \(\times\)  ~ 0,01
\item   2 657  ~ \(\times\)  ~ 0,1
\item   96,72  ~ \(\times\)  ~ 0,01
\item   80,34  ~ \(\times\)  ~ 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   97,67  ~ \(\times\)  ~ ... ~ = ~  0,976 7
\item   5 507  ~ \(\times\)  ~ ... ~ = ~  5,507
\item   5,262  ~ \(\times\)  ~ ... ~ = ~  0,052 62
\item   84,92  ~ \(\times\)  ~ ... ~ = ~  0,084 92
\item   7 292  ~ \(\times\)  ~ ... ~ = ~  72,92
\item   71,78  ~ \(\times\)  ~ ... ~ = ~  0,071 78
\item   1 701  ~ \(\times\)  ~ ... ~ = ~  170,1
\item   8,379  ~ \(\times\)  ~ ... ~ = ~  0,083 79
\item   203,3  ~ \(\times\)  ~ ... ~ = ~  20,33
\item   593,8  ~ \(\times\)  ~ ... ~ = ~  5,938
\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 ~m~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   883,63 ~cg~ = ...~dag
\item   718,47 ~dm~ = ...~km
\item   955,27 ~kg~ = ...~dg
\item   172,04 ~hm~ = ...~m
\item   1 691,5 ~kg~ = ...~mg
\item   7 776,2 ~dg~ = ...~hg
\item   7 252,6 ~mg~ = ...~cg
\item   4 030,6 ~dag~ = ...~cg
\item   698,06 ~hL~ = ...~dL
\item   6 134,8 ~mL~ = ...~L
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{130}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{720}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,59  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 259}
\item   87  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 700}
\item   5,58  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 55,8}
\item   5,24  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 52,4}
\item   29,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 29 100}
\item   597  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 59 700}
\item   6,76  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 760}
\item   0,02  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 20}
\item   947  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 94 700}
\item   0,844  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,44}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 031 ~ : ~ 1 000 ~ = ~{\color{red} 4,031}
\item   5 498 ~ : ~ 10 ~ = ~{\color{red} 549,8}
\item   71,78 ~ : ~ 100 ~ = ~{\color{red} 0,717 8}
\item   8,565 ~ : ~ 100 ~ = ~{\color{red} 0,085 65}
\item   28 ~ : ~ 10 ~ = ~{\color{red} 2,8}
\item   73,38 ~ : ~ 10 ~ = ~{\color{red} 7,338}
\item   5 933 ~ : ~ 100 ~ = ~{\color{red} 59,33}
\item   96,18 ~ : ~ 10 ~ = ~{\color{red} 9,618}
\item   23,7 ~ : ~ 10 ~ = ~{\color{red} 2,37}
\item   734,4 ~ : ~ 10 ~ = ~{\color{red} 73,44}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,553 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~553
\item   0,245 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,45
\item   0,87 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~87
\item   2,47 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~247
\item   0,098 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,98
\item   0,284 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~28,4
\item   415 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 150
\item   268 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~268 000
\item   27,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~275
\item   146 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~146 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   348,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,487
}\item   8,373 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,837 3
}\item   4 320 ~ \(\times\)  0,01 ~ = ~{\color{red} 43,2
}\item   8 080 ~ \(\times\)  0,01 ~ = ~{\color{red} 80,8
}\item   4,767 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 767
}\item   3,975 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,039 75
}\item   4,468 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,044 68
}\item   2 657 ~ \(\times\)  0,1 ~ = ~{\color{red} 265,7
}\item   96,72 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,967 2
}\item   80,34 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,803 4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   97,67 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,976 7
\item   5 507 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,507
\item   5,262 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,052 62
\item   84,92 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,084 92
\item   7 292 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 72,92
\item   71,78 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,071 78
\item   1 701 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 170,1
\item   8,379 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,083 79
\item   203,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 20,33
\item   593,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,938
\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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   883,63 ~cg~ = {\color{red}  0,883 63 }~dag
\item   718,47 ~dm~ = {\color{red}  0,071 847 }~km
\item   955,27 ~kg~ = {\color{red}  9 552 700 }~dg
\item   172,04 ~hm~ = {\color{red}  17 204 }~m
\item   1 691,5 ~kg~ = {\color{red}  1 691 500 000 }~mg
\item   7 776,2 ~dg~ = {\color{red}  7,776 2 }~hg
\item   7 252,6 ~mg~ = {\color{red}  725,26 }~cg
\item   4 030,6 ~dag~ = {\color{red}  4 030 600 }~cg
\item   698,06 ~hL~ = {\color{red}  698 060 }~dL
\item   6 134,8 ~mL~ = {\color{red}  6,134 8 }~L
\end{itemize}
\end{multicols}
\end{document}
