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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 137}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,09  ~ \(\times\)  ~ 10
\item   0,849  ~ \(\times\)  ~ 1 000
\item   0,338  ~ \(\times\)  ~ 1 000
\item   49,3  ~ \(\times\)  ~ 100
\item   0,054  ~ \(\times\)  ~ 100
\item   0,001  ~ \(\times\)  ~ 10
\item   69,5  ~ \(\times\)  ~ 100
\item   9,25  ~ \(\times\)  ~ 10
\item   36,8  ~ \(\times\)  ~ 100
\item   4,04  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,26  ~ : ~ 100
\item   11,99  ~ : ~ 1 000
\item   8 464  ~ : ~ 10
\item   7,8  ~ : ~ 1 000
\item   93,48  ~ : ~ 10
\item   3 977  ~ : ~ 100
\item   8 569  ~ : ~ 1 000
\item   36,73  ~ : ~ 10
\item   3,878  ~ : ~ 10
\item   721,9  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,07  ~ \(\times\)  ~ ... ~ = ~ 807
\item   0,068  ~ \(\times\)  ~ ... ~ = ~ 6,8
\item   81  ~ \(\times\)  ~ ... ~ = ~ 81 000
\item   0,845  ~ \(\times\)  ~ ... ~ = ~ 845
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 6,1
\item   0,079  ~ \(\times\)  ~ ... ~ = ~ 0,79
\item   0,161  ~ \(\times\)  ~ ... ~ = ~ 1,61
\item   880  ~ \(\times\)  ~ ... ~ = ~ 8 800
\item   1,05  ~ \(\times\)  ~ ... ~ = ~ 1 050
\item   0,02  ~ \(\times\)  ~ ... ~ = ~ 0,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,013  ~ \(\times\)  ~ 0,01
\item   347,4  ~ \(\times\)  ~ 0,001
\item   174,7  ~ \(\times\)  ~ 0,001
\item   9,33  ~ \(\times\)  ~ 0,1
\item   6 557  ~ \(\times\)  ~ 0,1
\item   63,95  ~ \(\times\)  ~ 0,001
\item   63,17  ~ \(\times\)  ~ 0,1
\item   8,28  ~ \(\times\)  ~ 0,1
\item   78,1  ~ \(\times\)  ~ 0,01
\item   5,524  ~ \(\times\)  ~ 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   78,11  ~ \(\times\)  ~ ... ~ = ~  7,811
\item   7 367  ~ \(\times\)  ~ ... ~ = ~  7,367
\item   3,276  ~ \(\times\)  ~ ... ~ = ~  0,003 276
\item   9,037  ~ \(\times\)  ~ ... ~ = ~  0,903 7
\item   2 324  ~ \(\times\)  ~ ... ~ = ~  232,4
\item   33,24  ~ \(\times\)  ~ ... ~ = ~  0,332 4
\item   1,263  ~ \(\times\)  ~ ... ~ = ~  0,001 263
\item   2,429  ~ \(\times\)  ~ ... ~ = ~  0,024 29
\item   623,5  ~ \(\times\)  ~ ... ~ = ~  0,623 5
\item   38,51  ~ \(\times\)  ~ ... ~ = ~  0,385 1
\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 ~km~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   813,86 ~cg~ = ...~hg
\item   357,45 ~cg~ = ...~g
\item   1 592,2 ~kg~ = ...~hg
\item   9 365,6 ~hL~ = ...~dL
\item   908,33 ~hg~ = ...~dg
\item   676,56 ~mg~ = ...~dag
\item   165,89 ~dL~ = ...~daL
\item   888,03 ~L~ = ...~kL
\item   676,74 ~hm~ = ...~mm
\item   481,89 ~km~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{400}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,09  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 50,9}
\item   0,849  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 849}
\item   0,338  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 338}
\item   49,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 930}
\item   0,054  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,4}
\item   0,001  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,01}
\item   69,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 950}
\item   9,25  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 92,5}
\item   36,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 680}
\item   4,04  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 404}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,26 ~ : ~ 100 ~ = ~{\color{red} 0,002 6}
\item   11,99 ~ : ~ 1 000 ~ = ~{\color{red} 0,011 99}
\item   8 464 ~ : ~ 10 ~ = ~{\color{red} 846,4}
\item   7,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 8}
\item   93,48 ~ : ~ 10 ~ = ~{\color{red} 9,348}
\item   3 977 ~ : ~ 100 ~ = ~{\color{red} 39,77}
\item   8 569 ~ : ~ 1 000 ~ = ~{\color{red} 8,569}
\item   36,73 ~ : ~ 10 ~ = ~{\color{red} 3,673}
\item   3,878 ~ : ~ 10 ~ = ~{\color{red} 0,387 8}
\item   721,9 ~ : ~ 100 ~ = ~{\color{red} 7,219}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~807
\item   0,068 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,8
\item   81 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~81 000
\item   0,845 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~845
\item   0,061 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,1
\item   0,079 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,79
\item   0,161 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,61
\item   880 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 800
\item   1,05 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 050
\item   0,02 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,2
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,013 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,050 13
}\item   347,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,347 4
}\item   174,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,174 7
}\item   9,33 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,933
}\item   6 557 ~ \(\times\)  0,1 ~ = ~{\color{red} 655,7
}\item   63,95 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,063 95
}\item   63,17 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,317
}\item   8,28 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,828
}\item   78,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,781
}\item   5,524 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,552 4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,11 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,811
\item   7 367 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,367
\item   3,276 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 276
\item   9,037 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,903 7
\item   2 324 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 232,4
\item   33,24 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,332 4
\item   1,263 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 263
\item   2,429 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,024 29
\item   623,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,623 5
\item   38,51 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,385 1
\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 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   813,86 ~cg~ = {\color{red}  0,081 386 }~hg
\item   357,45 ~cg~ = {\color{red}  3,574 5 }~g
\item   1 592,2 ~kg~ = {\color{red}  15 922 }~hg
\item   9 365,6 ~hL~ = {\color{red}  9 365 600 }~dL
\item   908,33 ~hg~ = {\color{red}  908 330 }~dg
\item   676,56 ~mg~ = {\color{red}  0,067 656 }~dag
\item   165,89 ~dL~ = {\color{red}  1,658 9 }~daL
\item   888,03 ~L~ = {\color{red}  0,888 03 }~kL
\item   676,74 ~hm~ = {\color{red}  67 674 000 }~mm
\item   481,89 ~km~ = {\color{red}  4 818 900 }~dm
\end{itemize}
\end{multicols}
\end{document}
