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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 374}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,8  ~ \(\times\)  ~ 100
\item   8,99  ~ \(\times\)  ~ 100
\item   5,43  ~ \(\times\)  ~ 100
\item   5,58  ~ \(\times\)  ~ 100
\item   53,8  ~ \(\times\)  ~ 100
\item   0,847  ~ \(\times\)  ~ 1 000
\item   0,04  ~ \(\times\)  ~ 1 000
\item   8,37  ~ \(\times\)  ~ 10
\item   58  ~ \(\times\)  ~ 100
\item   60  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 247  ~ : ~ 100
\item   487,8  ~ : ~ 1 000
\item   593,4  ~ : ~ 1 000
\item   8 728  ~ : ~ 1 000
\item   4,01  ~ : ~ 10
\item   73,89  ~ : ~ 10
\item   893,8  ~ : ~ 1 000
\item   61,91  ~ : ~ 100
\item   81,25  ~ : ~ 10
\item   71,96  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   685  ~ \(\times\)  ~ ... ~ = ~ 685 000
\item   95  ~ \(\times\)  ~ ... ~ = ~ 950
\item   42,9  ~ \(\times\)  ~ ... ~ = ~ 42 900
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 28
\item   20,1  ~ \(\times\)  ~ ... ~ = ~ 201
\item   0,684  ~ \(\times\)  ~ ... ~ = ~ 684
\item   31,8  ~ \(\times\)  ~ ... ~ = ~ 3 180
\item   2,7  ~ \(\times\)  ~ ... ~ = ~ 27
\item   861  ~ \(\times\)  ~ ... ~ = ~ 8 610
\item   0,083  ~ \(\times\)  ~ ... ~ = ~ 0,83
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,052  ~ \(\times\)  ~ 0,01
\item   9,98  ~ \(\times\)  ~ 0,001
\item   2 725  ~ \(\times\)  ~ 0,001
\item   5 475  ~ \(\times\)  ~ 0,01
\item   300,3  ~ \(\times\)  ~ 0,01
\item   693,1  ~ \(\times\)  ~ 0,1
\item   7 549  ~ \(\times\)  ~ 0,001
\item   75,64  ~ \(\times\)  ~ 0,1
\item   293,6  ~ \(\times\)  ~ 0,001
\item   4,074  ~ \(\times\)  ~ 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   8,01  ~ \(\times\)  ~ ... ~ = ~  0,008 01
\item   780,5  ~ \(\times\)  ~ ... ~ = ~  0,780 5
\item   6,974  ~ \(\times\)  ~ ... ~ = ~  0,069 74
\item   594  ~ \(\times\)  ~ ... ~ = ~  5,94
\item   87,12  ~ \(\times\)  ~ ... ~ = ~  8,712
\item   2,803  ~ \(\times\)  ~ ... ~ = ~  0,280 3
\item   876  ~ \(\times\)  ~ ... ~ = ~  0,876
\item   82,84  ~ \(\times\)  ~ ... ~ = ~  0,828 4
\item   1,97  ~ \(\times\)  ~ ... ~ = ~  0,019 7
\item   6 396  ~ \(\times\)  ~ ... ~ = ~  639,6
\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~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   216,36 ~dg~ = ...~g
\item   336,67 ~mL~ = ...~kL
\item   1 449,6 ~kL~ = ...~dL
\item   8 389,9 ~cg~ = ...~hg
\item   360,51 ~hg~ = ...~cg
\item   4 360,5 ~mg~ = ...~dg
\item   238,44 ~km~ = ...~mm
\item   1 387,2 ~mg~ = ...~dag
\item   266,8 ~mm~ = ...~hm
\item   6 574,9 ~g~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{750}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{290}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{760}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 680}
\item   8,99  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 899}
\item   5,43  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 543}
\item   5,58  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 558}
\item   53,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 380}
\item   0,847  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 847}
\item   0,04  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 40}
\item   8,37  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 83,7}
\item   58  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 800}
\item   60  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 600}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 247 ~ : ~ 100 ~ = ~{\color{red} 12,47}
\item   487,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,487 8}
\item   593,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,593 4}
\item   8 728 ~ : ~ 1 000 ~ = ~{\color{red} 8,728}
\item   4,01 ~ : ~ 10 ~ = ~{\color{red} 0,401}
\item   73,89 ~ : ~ 10 ~ = ~{\color{red} 7,389}
\item   893,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,893 8}
\item   61,91 ~ : ~ 100 ~ = ~{\color{red} 0,619 1}
\item   81,25 ~ : ~ 10 ~ = ~{\color{red} 8,125}
\item   71,96 ~ : ~ 1 000 ~ = ~{\color{red} 0,071 96}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   685 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~685 000
\item   95 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~950
\item   42,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~42 900
\item   0,028 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~28
\item   20,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~201
\item   0,684 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~684
\item   31,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 180
\item   2,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~27
\item   861 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 610
\item   0,083 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,83
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,052 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,070 52
}\item   9,98 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 98
}\item   2 725 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,725
}\item   5 475 ~ \(\times\)  0,01 ~ = ~{\color{red} 54,75
}\item   300,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,003
}\item   693,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 69,31
}\item   7 549 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,549
}\item   75,64 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,564
}\item   293,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,293 6
}\item   4,074 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,407 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   8,01 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 01
\item   780,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,780 5
\item   6,974 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,069 74
\item   594 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,94
\item   87,12 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,712
\item   2,803 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,280 3
\item   876 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,876
\item   82,84 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,828 4
\item   1,97 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,019 7
\item   6 396 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 639,6
\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~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   216,36 ~dg~ = {\color{red}  21,636 }~g
\item   336,67 ~mL~ = {\color{red}  0,000 336 67 }~kL
\item   1 449,6 ~kL~ = {\color{red}  14 496 000 }~dL
\item   8 389,9 ~cg~ = {\color{red}  0,838 99 }~hg
\item   360,51 ~hg~ = {\color{red}  3 605 100 }~cg
\item   4 360,5 ~mg~ = {\color{red}  43,605 }~dg
\item   238,44 ~km~ = {\color{red}  238 440 000 }~mm
\item   1 387,2 ~mg~ = {\color{red}  0,138 72 }~dag
\item   266,8 ~mm~ = {\color{red}  0,002 668 }~hm
\item   6 574,9 ~g~ = {\color{red}  65 749 }~dg
\end{itemize}
\end{multicols}
\end{document}
