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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 21}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   49,9  ~ \(\times\)  ~ 100
\item   0,084  ~ \(\times\)  ~ 10
\item   0,053  ~ \(\times\)  ~ 10
\item   816  ~ \(\times\)  ~ 10
\item   0,039  ~ \(\times\)  ~ 100
\item   7,9  ~ \(\times\)  ~ 10
\item   95,2  ~ \(\times\)  ~ 1 000
\item   0,052  ~ \(\times\)  ~ 1 000
\item   0,798  ~ \(\times\)  ~ 1 000
\item   461  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,95  ~ : ~ 1 000
\item   19,98  ~ : ~ 10
\item   2 637  ~ : ~ 10
\item   0,421  ~ : ~ 10
\item   91,45  ~ : ~ 100
\item   804,2  ~ : ~ 10
\item   0,709  ~ : ~ 10
\item   132,3  ~ : ~ 10
\item   9 616  ~ : ~ 10
\item   9,278  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,855  ~ \(\times\)  ~ ... ~ = ~ 8,55
\item   35,8  ~ \(\times\)  ~ ... ~ = ~ 35 800
\item   4,28  ~ \(\times\)  ~ ... ~ = ~ 428
\item   0,986  ~ \(\times\)  ~ ... ~ = ~ 986
\item   4,04  ~ \(\times\)  ~ ... ~ = ~ 404
\item   4,04  ~ \(\times\)  ~ ... ~ = ~ 40,4
\item   863  ~ \(\times\)  ~ ... ~ = ~ 8 630
\item   0,744  ~ \(\times\)  ~ ... ~ = ~ 7,44
\item   512  ~ \(\times\)  ~ ... ~ = ~ 512 000
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 0,62
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   94,64  ~ \(\times\)  ~ 0,001
\item   194,7  ~ \(\times\)  ~ 0,001
\item   28,87  ~ \(\times\)  ~ 0,01
\item   57,79  ~ \(\times\)  ~ 0,1
\item   179,3  ~ \(\times\)  ~ 0,1
\item   2,952  ~ \(\times\)  ~ 0,01
\item   2 720  ~ \(\times\)  ~ 0,001
\item   861,5  ~ \(\times\)  ~ 0,01
\item   2 773  ~ \(\times\)  ~ 0,01
\item   8,144  ~ \(\times\)  ~ 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   415,1  ~ \(\times\)  ~ ... ~ = ~  41,51
\item   9 305  ~ \(\times\)  ~ ... ~ = ~  93,05
\item   6,776  ~ \(\times\)  ~ ... ~ = ~  0,677 6
\item   4 819  ~ \(\times\)  ~ ... ~ = ~  48,19
\item   4 850  ~ \(\times\)  ~ ... ~ = ~  48,5
\item   417,3  ~ \(\times\)  ~ ... ~ = ~  4,173
\item   12,38  ~ \(\times\)  ~ ... ~ = ~  0,012 38
\item   249,4  ~ \(\times\)  ~ ... ~ = ~  0,249 4
\item   7 948  ~ \(\times\)  ~ ... ~ = ~  79,48
\item   2,388  ~ \(\times\)  ~ ... ~ = ~  0,238 8
\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~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   323,46 ~dL~ = ...~kL
\item   3 557,9 ~kg~ = ...~g
\item   138,69 ~L~ = ...~cL
\item   5 921 ~dL~ = ...~mL
\item   337,66 ~km~ = ...~hm
\item   4 530,3 ~dam~ = ...~dm
\item   312,26 ~kL~ = ...~mL
\item   175,09 ~cg~ = ...~mg
\item   1 359,9 ~dm~ = ...~cm
\item   3 931,6 ~dm~ = ...~m
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{990}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{920}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{470}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   49,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 990}
\item   0,084  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,84}
\item   0,053  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,53}
\item   816  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 160}
\item   0,039  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,9}
\item   7,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 79}
\item   95,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 95 200}
\item   0,052  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 52}
\item   0,798  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 798}
\item   461  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 46 100}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,95 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 95}
\item   19,98 ~ : ~ 10 ~ = ~{\color{red} 1,998}
\item   2 637 ~ : ~ 10 ~ = ~{\color{red} 263,7}
\item   0,421 ~ : ~ 10 ~ = ~{\color{red} 0,042 1}
\item   91,45 ~ : ~ 100 ~ = ~{\color{red} 0,914 5}
\item   804,2 ~ : ~ 10 ~ = ~{\color{red} 80,42}
\item   0,709 ~ : ~ 10 ~ = ~{\color{red} 0,070 9}
\item   132,3 ~ : ~ 10 ~ = ~{\color{red} 13,23}
\item   9 616 ~ : ~ 10 ~ = ~{\color{red} 961,6}
\item   9,278 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 278}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,855 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,55
\item   35,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~35 800
\item   4,28 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~428
\item   0,986 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~986
\item   4,04 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~404
\item   4,04 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~40,4
\item   863 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 630
\item   0,744 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,44
\item   512 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~512 000
\item   0,062 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,62
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   94,64 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,094 64
}\item   194,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,194 7
}\item   28,87 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,288 7
}\item   57,79 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,779
}\item   179,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 17,93
}\item   2,952 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,029 52
}\item   2 720 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,72
}\item   861,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,615
}\item   2 773 ~ \(\times\)  0,01 ~ = ~{\color{red} 27,73
}\item   8,144 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 144
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   415,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 41,51
\item   9 305 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 93,05
\item   6,776 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,677 6
\item   4 819 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 48,19
\item   4 850 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 48,5
\item   417,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,173
\item   12,38 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,012 38
\item   249,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,249 4
\item   7 948 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 79,48
\item   2,388 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,238 8
\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~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   323,46 ~dL~ = {\color{red}  0,032 346 }~kL
\item   3 557,9 ~kg~ = {\color{red}  3 557 900 }~g
\item   138,69 ~L~ = {\color{red}  13 869 }~cL
\item   5 921 ~dL~ = {\color{red}  592 100 }~mL
\item   337,66 ~km~ = {\color{red}  3 376,6 }~hm
\item   4 530,3 ~dam~ = {\color{red}  453 030 }~dm
\item   312,26 ~kL~ = {\color{red}  312 260 000 }~mL
\item   175,09 ~cg~ = {\color{red}  1 750,9 }~mg
\item   1 359,9 ~dm~ = {\color{red}  13 599 }~cm
\item   3 931,6 ~dm~ = {\color{red}  393,16 }~m
\end{itemize}
\end{multicols}
\end{document}
