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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 84}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{95}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   33,5  ~ \(\times\)  ~ 100
\item   0,052  ~ \(\times\)  ~ 1 000
\item   0,038  ~ \(\times\)  ~ 10
\item   5,66  ~ \(\times\)  ~ 1 000
\item   0,487  ~ \(\times\)  ~ 1 000
\item   0,035  ~ \(\times\)  ~ 10
\item   0,137  ~ \(\times\)  ~ 10
\item   534  ~ \(\times\)  ~ 10
\item   0,056  ~ \(\times\)  ~ 1 000
\item   7,12  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 865  ~ : ~ 10
\item   3,417  ~ : ~ 10
\item   4 894  ~ : ~ 100
\item   2 083  ~ : ~ 1 000
\item   1,301  ~ : ~ 1 000
\item   58,2  ~ : ~ 1 000
\item   7 981  ~ : ~ 1 000
\item   232,3  ~ : ~ 10
\item   442,9  ~ : ~ 100
\item   61,32  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,836  ~ \(\times\)  ~ ... ~ = ~ 83,6
\item   0,019  ~ \(\times\)  ~ ... ~ = ~ 19
\item   877  ~ \(\times\)  ~ ... ~ = ~ 8 770
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 0,22
\item   6,17  ~ \(\times\)  ~ ... ~ = ~ 61,7
\item   66  ~ \(\times\)  ~ ... ~ = ~ 6 600
\item   0,548  ~ \(\times\)  ~ ... ~ = ~ 54,8
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 6,7
\item   3,71  ~ \(\times\)  ~ ... ~ = ~ 371
\item   114  ~ \(\times\)  ~ ... ~ = ~ 11 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,66  ~ \(\times\)  ~ 0,001
\item   125,5  ~ \(\times\)  ~ 0,001
\item   62,69  ~ \(\times\)  ~ 0,01
\item   44,18  ~ \(\times\)  ~ 0,01
\item   0,139  ~ \(\times\)  ~ 0,1
\item   4 607  ~ \(\times\)  ~ 0,1
\item   37,22  ~ \(\times\)  ~ 0,001
\item   754,3  ~ \(\times\)  ~ 0,01
\item   4,032  ~ \(\times\)  ~ 0,001
\item   4 411  ~ \(\times\)  ~ 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   135  ~ \(\times\)  ~ ... ~ = ~  13,5
\item   40,3  ~ \(\times\)  ~ ... ~ = ~  0,403
\item   29,24  ~ \(\times\)  ~ ... ~ = ~  0,029 24
\item   763  ~ \(\times\)  ~ ... ~ = ~  0,763
\item   8 186  ~ \(\times\)  ~ ... ~ = ~  81,86
\item   606,4  ~ \(\times\)  ~ ... ~ = ~  0,606 4
\item   31,74  ~ \(\times\)  ~ ... ~ = ~  0,317 4
\item   0,417  ~ \(\times\)  ~ ... ~ = ~  0,000 417
\item   1,36  ~ \(\times\)  ~ ... ~ = ~  0,001 36
\item   21,07  ~ \(\times\)  ~ ... ~ = ~  2,107
\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 ~hm~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   938,82 ~dm~ = ...~hm
\item   4 856,5 ~mg~ = ...~dg
\item   6 559,2 ~cm~ = ...~dam
\item   370,47 ~kL~ = ...~dL
\item   914,97 ~L~ = ...~mL
\item   775,76 ~hg~ = ...~g
\item   819,8 ~kg~ = ...~dag
\item   8 966,9 ~km~ = ...~dm
\item   442,64 ~mg~ = ...~kg
\item   587,34 ~kL~ = ...~cL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{7300}{100}\) = \(\dfrac{730}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{770}{100}\)
\item   \(\dfrac{95}{100}\) = \(\dfrac{950}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   33,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 350}
\item   0,052  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 52}
\item   0,038  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,38}
\item   5,66  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 660}
\item   0,487  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 487}
\item   0,035  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,35}
\item   0,137  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,37}
\item   534  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 340}
\item   0,056  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 56}
\item   7,12  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 120}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 865 ~ : ~ 10 ~ = ~{\color{red} 186,5}
\item   3,417 ~ : ~ 10 ~ = ~{\color{red} 0,341 7}
\item   4 894 ~ : ~ 100 ~ = ~{\color{red} 48,94}
\item   2 083 ~ : ~ 1 000 ~ = ~{\color{red} 2,083}
\item   1,301 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 301}
\item   58,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,058 2}
\item   7 981 ~ : ~ 1 000 ~ = ~{\color{red} 7,981}
\item   232,3 ~ : ~ 10 ~ = ~{\color{red} 23,23}
\item   442,9 ~ : ~ 100 ~ = ~{\color{red} 4,429}
\item   61,32 ~ : ~ 10 ~ = ~{\color{red} 6,132}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,836 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~83,6
\item   0,019 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~19
\item   877 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 770
\item   0,022 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,22
\item   6,17 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~61,7
\item   66 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 600
\item   0,548 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~54,8
\item   0,067 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,7
\item   3,71 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~371
\item   114 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~11 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,66 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,058 66
}\item   125,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,125 5
}\item   62,69 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,626 9
}\item   44,18 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,441 8
}\item   0,139 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,013 9
}\item   4 607 ~ \(\times\)  0,1 ~ = ~{\color{red} 460,7
}\item   37,22 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,037 22
}\item   754,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,543
}\item   4,032 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 032
}\item   4 411 ~ \(\times\)  0,1 ~ = ~{\color{red} 441,1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   135 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 13,5
\item   40,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,403
\item   29,24 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,029 24
\item   763 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,763
\item   8 186 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 81,86
\item   606,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,606 4
\item   31,74 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,317 4
\item   0,417 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 417
\item   1,36 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 36
\item   21,07 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,107
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   938,82 ~dm~ = {\color{red}  0,938 82 }~hm
\item   4 856,5 ~mg~ = {\color{red}  48,565 }~dg
\item   6 559,2 ~cm~ = {\color{red}  6,559 2 }~dam
\item   370,47 ~kL~ = {\color{red}  3 704 700 }~dL
\item   914,97 ~L~ = {\color{red}  914 970 }~mL
\item   775,76 ~hg~ = {\color{red}  77 576 }~g
\item   819,8 ~kg~ = {\color{red}  81 980 }~dag
\item   8 966,9 ~km~ = {\color{red}  89 669 000 }~dm
\item   442,64 ~mg~ = {\color{red}  0,000 442 64 }~kg
\item   587,34 ~kL~ = {\color{red}  58 734 000 }~cL
\end{itemize}
\end{multicols}
\end{document}
