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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 195}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{97}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{37}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   416  ~ \(\times\)  ~ 1 000
\item   0,032  ~ \(\times\)  ~ 1 000
\item   2,12  ~ \(\times\)  ~ 100
\item   250  ~ \(\times\)  ~ 1 000
\item   0,534  ~ \(\times\)  ~ 1 000
\item   159  ~ \(\times\)  ~ 10
\item   709  ~ \(\times\)  ~ 10
\item   0,094  ~ \(\times\)  ~ 10
\item   932  ~ \(\times\)  ~ 10
\item   0,067  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   266,8  ~ : ~ 100
\item   8 706  ~ : ~ 100
\item   92,98  ~ : ~ 1 000
\item   18,91  ~ : ~ 10
\item   694,9  ~ : ~ 1 000
\item   9,636  ~ : ~ 10
\item   34,11  ~ : ~ 1 000
\item   63,7  ~ : ~ 1 000
\item   4,975  ~ : ~ 10
\item   4 209  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 95
\item   50  ~ \(\times\)  ~ ... ~ = ~ 500
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 0,96
\item   23  ~ \(\times\)  ~ ... ~ = ~ 23 000
\item   6,84  ~ \(\times\)  ~ ... ~ = ~ 684
\item   3,83  ~ \(\times\)  ~ ... ~ = ~ 3 830
\item   0,394  ~ \(\times\)  ~ ... ~ = ~ 394
\item   257  ~ \(\times\)  ~ ... ~ = ~ 257 000
\item   90,1  ~ \(\times\)  ~ ... ~ = ~ 9 010
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 0,84
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,034  ~ \(\times\)  ~ 0,1
\item   63,66  ~ \(\times\)  ~ 0,1
\item   52,73  ~ \(\times\)  ~ 0,01
\item   917,7  ~ \(\times\)  ~ 0,1
\item   98,49  ~ \(\times\)  ~ 0,01
\item   47,71  ~ \(\times\)  ~ 0,01
\item   407  ~ \(\times\)  ~ 0,01
\item   310,3  ~ \(\times\)  ~ 0,01
\item   3,695  ~ \(\times\)  ~ 0,01
\item   656,1  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 696  ~ \(\times\)  ~ ... ~ = ~  4,696
\item   35,1  ~ \(\times\)  ~ ... ~ = ~  0,035 1
\item   6,908  ~ \(\times\)  ~ ... ~ = ~  0,006 908
\item   48,02  ~ \(\times\)  ~ ... ~ = ~  0,480 2
\item   18,3  ~ \(\times\)  ~ ... ~ = ~  0,183
\item   260,3  ~ \(\times\)  ~ ... ~ = ~  0,260 3
\item   81,68  ~ \(\times\)  ~ ... ~ = ~  8,168
\item   257,1  ~ \(\times\)  ~ ... ~ = ~  2,571
\item   7 765  ~ \(\times\)  ~ ... ~ = ~  77,65
\item   10,65  ~ \(\times\)  ~ ... ~ = ~  0,106 5
\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 ~m~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 916,5 ~mL~ = ...~hL
\item   401,5 ~dam~ = ...~m
\item   945,66 ~kg~ = ...~cg
\item   890,73 ~cm~ = ...~mm
\item   602 ~dg~ = ...~cg
\item   3 522,3 ~daL~ = ...~hL
\item   2 558,4 ~mL~ = ...~L
\item   912,82 ~dag~ = ...~cg
\item   993,68 ~hL~ = ...~daL
\item   7 031,3 ~hg~ = ...~dag
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{9300}{100}\) = \(\dfrac{930}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{97}{10}\) = \(\dfrac{970}{100}\)
\item   \(\dfrac{37}{100}\) = \(\dfrac{370}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   416  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 416 000}
\item   0,032  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32}
\item   2,12  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 212}
\item   250  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 250 000}
\item   0,534  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 534}
\item   159  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 590}
\item   709  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 090}
\item   0,094  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,94}
\item   932  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9 320}
\item   0,067  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 67}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   266,8 ~ : ~ 100 ~ = ~{\color{red} 2,668}
\item   8 706 ~ : ~ 100 ~ = ~{\color{red} 87,06}
\item   92,98 ~ : ~ 1 000 ~ = ~{\color{red} 0,092 98}
\item   18,91 ~ : ~ 10 ~ = ~{\color{red} 1,891}
\item   694,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,694 9}
\item   9,636 ~ : ~ 10 ~ = ~{\color{red} 0,963 6}
\item   34,11 ~ : ~ 1 000 ~ = ~{\color{red} 0,034 11}
\item   63,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,063 7}
\item   4,975 ~ : ~ 10 ~ = ~{\color{red} 0,497 5}
\item   4 209 ~ : ~ 100 ~ = ~{\color{red} 42,09}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~95
\item   50 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~500
\item   0,096 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,96
\item   23 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~23 000
\item   6,84 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~684
\item   3,83 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 830
\item   0,394 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~394
\item   257 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~257 000
\item   90,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 010
\item   0,084 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,84
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,034 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,203 4
}\item   63,66 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,366
}\item   52,73 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,527 3
}\item   917,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 91,77
}\item   98,49 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,984 9
}\item   47,71 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,477 1
}\item   407 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,07
}\item   310,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,103
}\item   3,695 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,036 95
}\item   656,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,561
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 696 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,696
\item   35,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,035 1
\item   6,908 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 908
\item   48,02 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,480 2
\item   18,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,183
\item   260,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,260 3
\item   81,68 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,168
\item   257,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,571
\item   7 765 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 77,65
\item   10,65 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,106 5
\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 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 916,5 ~mL~ = {\color{red}  0,049 165 }~hL
\item   401,5 ~dam~ = {\color{red}  4 015 }~m
\item   945,66 ~kg~ = {\color{red}  94 566 000 }~cg
\item   890,73 ~cm~ = {\color{red}  8 907,3 }~mm
\item   602 ~dg~ = {\color{red}  6 020 }~cg
\item   3 522,3 ~daL~ = {\color{red}  352,23 }~hL
\item   2 558,4 ~mL~ = {\color{red}  2,558 4 }~L
\item   912,82 ~dag~ = {\color{red}  912 820 }~cg
\item   993,68 ~hL~ = {\color{red}  9 936,8 }~daL
\item   7 031,3 ~hg~ = {\color{red}  70 313 }~dag
\end{itemize}
\end{multicols}
\end{document}
