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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 322}

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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   \(\dfrac{1900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{47}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{51}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,2  ~ \(\times\)  ~ 100
\item   0,02  ~ \(\times\)  ~ 1 000
\item   0,084  ~ \(\times\)  ~ 10
\item   87,2  ~ \(\times\)  ~ 1 000
\item   0,022  ~ \(\times\)  ~ 100
\item   0,238  ~ \(\times\)  ~ 1 000
\item   3,75  ~ \(\times\)  ~ 10
\item   472  ~ \(\times\)  ~ 100
\item   0,031  ~ \(\times\)  ~ 1 000
\item   824  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,6  ~ : ~ 10
\item   5,02  ~ : ~ 100
\item   6,229  ~ : ~ 1 000
\item   6,427  ~ : ~ 100
\item   229,8  ~ : ~ 10
\item   906,8  ~ : ~ 10
\item   6 152  ~ : ~ 100
\item   26,37  ~ : ~ 100
\item   29,99  ~ : ~ 10
\item   2 066  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,24  ~ \(\times\)  ~ ... ~ = ~ 9 240
\item   974  ~ \(\times\)  ~ ... ~ = ~ 9 740
\item   0,921  ~ \(\times\)  ~ ... ~ = ~ 9,21
\item   0,729  ~ \(\times\)  ~ ... ~ = ~ 729
\item   4,18  ~ \(\times\)  ~ ... ~ = ~ 4 180
\item   6,14  ~ \(\times\)  ~ ... ~ = ~ 6 140
\item   43,6  ~ \(\times\)  ~ ... ~ = ~ 436
\item   950  ~ \(\times\)  ~ ... ~ = ~ 950 000
\item   32,6  ~ \(\times\)  ~ ... ~ = ~ 3 260
\item   80,6  ~ \(\times\)  ~ ... ~ = ~ 80 600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   780,4  ~ \(\times\)  ~ 0,001
\item   20,62  ~ \(\times\)  ~ 0,001
\item   14,97  ~ \(\times\)  ~ 0,1
\item   883,5  ~ \(\times\)  ~ 0,1
\item   2 679  ~ \(\times\)  ~ 0,1
\item   1 951  ~ \(\times\)  ~ 0,01
\item   6 883  ~ \(\times\)  ~ 0,01
\item   4,502  ~ \(\times\)  ~ 0,001
\item   678  ~ \(\times\)  ~ 0,1
\item   26,82  ~ \(\times\)  ~ 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   67,35  ~ \(\times\)  ~ ... ~ = ~  6,735
\item   27,92  ~ \(\times\)  ~ ... ~ = ~  0,027 92
\item   54,98  ~ \(\times\)  ~ ... ~ = ~  0,549 8
\item   2,048  ~ \(\times\)  ~ ... ~ = ~  0,002 048
\item   1 750  ~ \(\times\)  ~ ... ~ = ~  175
\item   9 025  ~ \(\times\)  ~ ... ~ = ~  90,25
\item   5 597  ~ \(\times\)  ~ ... ~ = ~  55,97
\item   900  ~ \(\times\)  ~ ... ~ = ~  90
\item   28,56  ~ \(\times\)  ~ ... ~ = ~  0,285 6
\item   152,2  ~ \(\times\)  ~ ... ~ = ~  0,152 2
\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 ~hm~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   600,7 ~g~ = ...~mg
\item   514,76 ~mL~ = ...~daL
\item   741,93 ~kg~ = ...~mg
\item   677,26 ~dL~ = ...~mL
\item   2 808,2 ~daL~ = ...~L
\item   6 659,4 ~g~ = ...~hg
\item   386,41 ~daL~ = ...~hL
\item   936,41 ~dam~ = ...~m
\item   1 617,1 ~daL~ = ...~cL
\item   7 516,4 ~dL~ = ...~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   \(\dfrac{1900}{100}\) = \(\dfrac{190}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{47}{10}\) = \(\dfrac{470}{100}\)
\item   \(\dfrac{51}{100}\) = \(\dfrac{510}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 920}
\item   0,02  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 20}
\item   0,084  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,84}
\item   87,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 87 200}
\item   0,022  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,2}
\item   0,238  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 238}
\item   3,75  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 37,5}
\item   472  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 47 200}
\item   0,031  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 31}
\item   824  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 824 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   74,6 ~ : ~ 10 ~ = ~{\color{red} 7,46}
\item   5,02 ~ : ~ 100 ~ = ~{\color{red} 0,050 2}
\item   6,229 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 229}
\item   6,427 ~ : ~ 100 ~ = ~{\color{red} 0,064 27}
\item   229,8 ~ : ~ 10 ~ = ~{\color{red} 22,98}
\item   906,8 ~ : ~ 10 ~ = ~{\color{red} 90,68}
\item   6 152 ~ : ~ 100 ~ = ~{\color{red} 61,52}
\item   26,37 ~ : ~ 100 ~ = ~{\color{red} 0,263 7}
\item   29,99 ~ : ~ 10 ~ = ~{\color{red} 2,999}
\item   2 066 ~ : ~ 100 ~ = ~{\color{red} 20,66}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,24 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 240
\item   974 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 740
\item   0,921 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,21
\item   0,729 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~729
\item   4,18 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 180
\item   6,14 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 140
\item   43,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~436
\item   950 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~950 000
\item   32,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 260
\item   80,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~80 600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   780,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,780 4
}\item   20,62 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,020 62
}\item   14,97 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,497
}\item   883,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 88,35
}\item   2 679 ~ \(\times\)  0,1 ~ = ~{\color{red} 267,9
}\item   1 951 ~ \(\times\)  0,01 ~ = ~{\color{red} 19,51
}\item   6 883 ~ \(\times\)  0,01 ~ = ~{\color{red} 68,83
}\item   4,502 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 502
}\item   678 ~ \(\times\)  0,1 ~ = ~{\color{red} 67,8
}\item   26,82 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,026 82
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   67,35 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,735
\item   27,92 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,027 92
\item   54,98 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,549 8
\item   2,048 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 048
\item   1 750 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 175
\item   9 025 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 90,25
\item   5 597 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 55,97
\item   900 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 90
\item   28,56 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,285 6
\item   152,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,152 2
\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 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   600,7 ~g~ = {\color{red}  600 700 }~mg
\item   514,76 ~mL~ = {\color{red}  0,051 476 }~daL
\item   741,93 ~kg~ = {\color{red}  741 930 000 }~mg
\item   677,26 ~dL~ = {\color{red}  67 726 }~mL
\item   2 808,2 ~daL~ = {\color{red}  28 082 }~L
\item   6 659,4 ~g~ = {\color{red}  66,594 }~hg
\item   386,41 ~daL~ = {\color{red}  38,641 }~hL
\item   936,41 ~dam~ = {\color{red}  9 364,1 }~m
\item   1 617,1 ~daL~ = {\color{red}  1 617 100 }~cL
\item   7 516,4 ~dL~ = {\color{red}  75,164 }~daL
\end{itemize}
\end{multicols}
\end{document}
