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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 88}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{12}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   548  ~ \(\times\)  ~ 100
\item   0,711  ~ \(\times\)  ~ 10
\item   238  ~ \(\times\)  ~ 1 000
\item   0,015  ~ \(\times\)  ~ 10
\item   0,461  ~ \(\times\)  ~ 100
\item   0,694  ~ \(\times\)  ~ 10
\item   32,1  ~ \(\times\)  ~ 10
\item   4,84  ~ \(\times\)  ~ 10
\item   16,5  ~ \(\times\)  ~ 100
\item   90,9  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 996  ~ : ~ 10
\item   8,685  ~ : ~ 1 000
\item   0,511  ~ : ~ 1 000
\item   6,294  ~ : ~ 100
\item   8 313  ~ : ~ 100
\item   2,507  ~ : ~ 10
\item   237,2  ~ : ~ 100
\item   5 198  ~ : ~ 10
\item   1 804  ~ : ~ 100
\item   47,83  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,23  ~ \(\times\)  ~ ... ~ = ~ 23
\item   533  ~ \(\times\)  ~ ... ~ = ~ 53 300
\item   7,31  ~ \(\times\)  ~ ... ~ = ~ 7 310
\item   0,034  ~ \(\times\)  ~ ... ~ = ~ 34
\item   0,63  ~ \(\times\)  ~ ... ~ = ~ 6,3
\item   3,64  ~ \(\times\)  ~ ... ~ = ~ 3 640
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 45
\item   8,09  ~ \(\times\)  ~ ... ~ = ~ 809
\item   496  ~ \(\times\)  ~ ... ~ = ~ 496 000
\item   0,315  ~ \(\times\)  ~ ... ~ = ~ 3,15
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68,52  ~ \(\times\)  ~ 0,1
\item   9,35  ~ \(\times\)  ~ 0,1
\item   8,527  ~ \(\times\)  ~ 0,001
\item   4 729  ~ \(\times\)  ~ 0,001
\item   9,65  ~ \(\times\)  ~ 0,1
\item   6,19  ~ \(\times\)  ~ 0,001
\item   338  ~ \(\times\)  ~ 0,001
\item   0,381  ~ \(\times\)  ~ 0,01
\item   2,333  ~ \(\times\)  ~ 0,1
\item   854  ~ \(\times\)  ~ 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   80,12  ~ \(\times\)  ~ ... ~ = ~  0,080 12
\item   4 724  ~ \(\times\)  ~ ... ~ = ~  4,724
\item   4,71  ~ \(\times\)  ~ ... ~ = ~  0,471
\item   4 496  ~ \(\times\)  ~ ... ~ = ~  449,6
\item   544,2  ~ \(\times\)  ~ ... ~ = ~  54,42
\item   649,7  ~ \(\times\)  ~ ... ~ = ~  6,497
\item   8,769  ~ \(\times\)  ~ ... ~ = ~  0,008 769
\item   641,4  ~ \(\times\)  ~ ... ~ = ~  0,641 4
\item   6,77  ~ \(\times\)  ~ ... ~ = ~  0,067 7
\item   5,246  ~ \(\times\)  ~ ... ~ = ~  0,052 46
\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 ~cm~ = ...~m
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   217 ~mL~ = ...~dL
\item   9 769,4 ~hm~ = ...~km
\item   4 301 ~cm~ = ...~dm
\item   3 993 ~cL~ = ...~kL
\item   2 053,3 ~m~ = ...~dam
\item   1 859,7 ~cm~ = ...~km
\item   7 379,1 ~kg~ = ...~dg
\item   3 790,8 ~kg~ = ...~cg
\item   5 586,1 ~dL~ = ...~mL
\item   996,4 ~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   7 = \(\dfrac{70}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{530}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{91}{10}\) = \(\dfrac{910}{100}\)
\item   \(\dfrac{12}{100}\) = \(\dfrac{120}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   548  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 54 800}
\item   0,711  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,11}
\item   238  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 238 000}
\item   0,015  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,15}
\item   0,461  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 46,1}
\item   0,694  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,94}
\item   32,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 321}
\item   4,84  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 48,4}
\item   16,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 650}
\item   90,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 909}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 996 ~ : ~ 10 ~ = ~{\color{red} 299,6}
\item   8,685 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 685}
\item   0,511 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 511}
\item   6,294 ~ : ~ 100 ~ = ~{\color{red} 0,062 94}
\item   8 313 ~ : ~ 100 ~ = ~{\color{red} 83,13}
\item   2,507 ~ : ~ 10 ~ = ~{\color{red} 0,250 7}
\item   237,2 ~ : ~ 100 ~ = ~{\color{red} 2,372}
\item   5 198 ~ : ~ 10 ~ = ~{\color{red} 519,8}
\item   1 804 ~ : ~ 100 ~ = ~{\color{red} 18,04}
\item   47,83 ~ : ~ 1 000 ~ = ~{\color{red} 0,047 83}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,23 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~23
\item   533 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~53 300
\item   7,31 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 310
\item   0,034 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~34
\item   0,63 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,3
\item   3,64 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 640
\item   0,045 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~45
\item   8,09 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~809
\item   496 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~496 000
\item   0,315 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,15
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68,52 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,852
}\item   9,35 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,935
}\item   8,527 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 527
}\item   4 729 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,729
}\item   9,65 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,965
}\item   6,19 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 19
}\item   338 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,338
}\item   0,381 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,003 81
}\item   2,333 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,233 3
}\item   854 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,854
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,12 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,080 12
\item   4 724 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,724
\item   4,71 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,471
\item   4 496 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 449,6
\item   544,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 54,42
\item   649,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,497
\item   8,769 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 769
\item   641,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,641 4
\item   6,77 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,067 7
\item   5,246 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,052 46
\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 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\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   217 ~mL~ = {\color{red}  2,17 }~dL
\item   9 769,4 ~hm~ = {\color{red}  976,94 }~km
\item   4 301 ~cm~ = {\color{red}  430,1 }~dm
\item   3 993 ~cL~ = {\color{red}  0,039 93 }~kL
\item   2 053,3 ~m~ = {\color{red}  205,33 }~dam
\item   1 859,7 ~cm~ = {\color{red}  0,018 597 }~km
\item   7 379,1 ~kg~ = {\color{red}  73 791 000 }~dg
\item   3 790,8 ~kg~ = {\color{red}  379 080 000 }~cg
\item   5 586,1 ~dL~ = {\color{red}  558 610 }~mL
\item   996,4 ~g~ = {\color{red}  9 964 }~dg
\end{itemize}
\end{multicols}
\end{document}
