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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 344}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{97}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095  ~ \(\times\)  ~ 100
\item   0,3  ~ \(\times\)  ~ 100
\item   6,92  ~ \(\times\)  ~ 100
\item   0,591  ~ \(\times\)  ~ 100
\item   83,9  ~ \(\times\)  ~ 10
\item   38,4  ~ \(\times\)  ~ 100
\item   0,667  ~ \(\times\)  ~ 10
\item   271  ~ \(\times\)  ~ 1 000
\item   3,71  ~ \(\times\)  ~ 1 000
\item   0,083  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,7  ~ : ~ 10
\item   8 580  ~ : ~ 100
\item   1,752  ~ : ~ 100
\item   1 484  ~ : ~ 1 000
\item   66,37  ~ : ~ 10
\item   3 062  ~ : ~ 1 000
\item   7 211  ~ : ~ 10
\item   8,39  ~ : ~ 10
\item   426,2  ~ : ~ 100
\item   897,7  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,38  ~ \(\times\)  ~ ... ~ = ~ 53,8
\item   867  ~ \(\times\)  ~ ... ~ = ~ 867 000
\item   6,4  ~ \(\times\)  ~ ... ~ = ~ 640
\item   0,676  ~ \(\times\)  ~ ... ~ = ~ 676
\item   0,093  ~ \(\times\)  ~ ... ~ = ~ 9,3
\item   91,2  ~ \(\times\)  ~ ... ~ = ~ 9 120
\item   0,79  ~ \(\times\)  ~ ... ~ = ~ 790
\item   3,6  ~ \(\times\)  ~ ... ~ = ~ 3 600
\item   55,5  ~ \(\times\)  ~ ... ~ = ~ 5 550
\item   0,034  ~ \(\times\)  ~ ... ~ = ~ 34
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43,3  ~ \(\times\)  ~ 0,001
\item   2 713  ~ \(\times\)  ~ 0,01
\item   2 835  ~ \(\times\)  ~ 0,01
\item   7 812  ~ \(\times\)  ~ 0,01
\item   8 180  ~ \(\times\)  ~ 0,1
\item   7 420  ~ \(\times\)  ~ 0,001
\item   1 509  ~ \(\times\)  ~ 0,001
\item   95,85  ~ \(\times\)  ~ 0,1
\item   7 958  ~ \(\times\)  ~ 0,001
\item   2 610  ~ \(\times\)  ~ 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   212,9  ~ \(\times\)  ~ ... ~ = ~  0,212 9
\item   3 610  ~ \(\times\)  ~ ... ~ = ~  3,61
\item   7 645  ~ \(\times\)  ~ ... ~ = ~  76,45
\item   261,7  ~ \(\times\)  ~ ... ~ = ~  0,261 7
\item   87,69  ~ \(\times\)  ~ ... ~ = ~  0,876 9
\item   552,5  ~ \(\times\)  ~ ... ~ = ~  5,525
\item   5 777  ~ \(\times\)  ~ ... ~ = ~  577,7
\item   2 185  ~ \(\times\)  ~ ... ~ = ~  218,5
\item   799,2  ~ \(\times\)  ~ ... ~ = ~  7,992
\item   1 649  ~ \(\times\)  ~ ... ~ = ~  164,9
\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 ~cm~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 201,4 ~cm~ = ...~mm
\item   409,73 ~hg~ = ...~dag
\item   5 642,5 ~dg~ = ...~g
\item   1 897,6 ~dag~ = ...~g
\item   4 327,7 ~daL~ = ...~kL
\item   7 322,9 ~hm~ = ...~dam
\item   476,87 ~dam~ = ...~m
\item   772,47 ~dg~ = ...~kg
\item   5 315,8 ~dm~ = ...~mm
\item   138,45 ~daL~ = ...~dL
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{2400}{100}\) = \(\dfrac{240}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{97}{10}\) = \(\dfrac{970}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{780}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,5}
\item   0,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 30}
\item   6,92  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 692}
\item   0,591  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 59,1}
\item   83,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 839}
\item   38,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 840}
\item   0,667  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,67}
\item   271  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 271 000}
\item   3,71  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 710}
\item   0,083  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 83}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,7 ~ : ~ 10 ~ = ~{\color{red} 1,77}
\item   8 580 ~ : ~ 100 ~ = ~{\color{red} 85,8}
\item   1,752 ~ : ~ 100 ~ = ~{\color{red} 0,017 52}
\item   1 484 ~ : ~ 1 000 ~ = ~{\color{red} 1,484}
\item   66,37 ~ : ~ 10 ~ = ~{\color{red} 6,637}
\item   3 062 ~ : ~ 1 000 ~ = ~{\color{red} 3,062}
\item   7 211 ~ : ~ 10 ~ = ~{\color{red} 721,1}
\item   8,39 ~ : ~ 10 ~ = ~{\color{red} 0,839}
\item   426,2 ~ : ~ 100 ~ = ~{\color{red} 4,262}
\item   897,7 ~ : ~ 10 ~ = ~{\color{red} 89,77}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,38 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~53,8
\item   867 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~867 000
\item   6,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~640
\item   0,676 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~676
\item   0,093 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,3
\item   91,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 120
\item   0,79 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~790
\item   3,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 600
\item   55,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 550
\item   0,034 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~34
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,043 3
}\item   2 713 ~ \(\times\)  0,01 ~ = ~{\color{red} 27,13
}\item   2 835 ~ \(\times\)  0,01 ~ = ~{\color{red} 28,35
}\item   7 812 ~ \(\times\)  0,01 ~ = ~{\color{red} 78,12
}\item   8 180 ~ \(\times\)  0,1 ~ = ~{\color{red} 818
}\item   7 420 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,42
}\item   1 509 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,509
}\item   95,85 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,585
}\item   7 958 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,958
}\item   2 610 ~ \(\times\)  0,1 ~ = ~{\color{red} 261
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   212,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,212 9
\item   3 610 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,61
\item   7 645 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 76,45
\item   261,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,261 7
\item   87,69 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,876 9
\item   552,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,525
\item   5 777 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 577,7
\item   2 185 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 218,5
\item   799,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,992
\item   1 649 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 164,9
\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 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 201,4 ~cm~ = {\color{red}  82 014 }~mm
\item   409,73 ~hg~ = {\color{red}  4 097,3 }~dag
\item   5 642,5 ~dg~ = {\color{red}  564,25 }~g
\item   1 897,6 ~dag~ = {\color{red}  18 976 }~g
\item   4 327,7 ~daL~ = {\color{red}  43,277 }~kL
\item   7 322,9 ~hm~ = {\color{red}  73 229 }~dam
\item   476,87 ~dam~ = {\color{red}  4 768,7 }~m
\item   772,47 ~dg~ = {\color{red}  0,077 247 }~kg
\item   5 315,8 ~dm~ = {\color{red}  531 580 }~mm
\item   138,45 ~daL~ = {\color{red}  13 845 }~dL
\end{itemize}
\end{multicols}
\end{document}
