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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 268}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{26}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,082  ~ \(\times\)  ~ 100
\item   237  ~ \(\times\)  ~ 1 000
\item   72,9  ~ \(\times\)  ~ 100
\item   16,7  ~ \(\times\)  ~ 10
\item   0,393  ~ \(\times\)  ~ 10
\item   9,81  ~ \(\times\)  ~ 1 000
\item   972  ~ \(\times\)  ~ 100
\item   15,6  ~ \(\times\)  ~ 10
\item   5,59  ~ \(\times\)  ~ 100
\item   0,037  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,875  ~ : ~ 1 000
\item   6 703  ~ : ~ 10
\item   981,4  ~ : ~ 10
\item   2,784  ~ : ~ 100
\item   218,1  ~ : ~ 1 000
\item   95,91  ~ : ~ 100
\item   6 187  ~ : ~ 1 000
\item   2,456  ~ : ~ 100
\item   729,3  ~ : ~ 1 000
\item   85,6  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   23,5  ~ \(\times\)  ~ ... ~ = ~ 2 350
\item   2,16  ~ \(\times\)  ~ ... ~ = ~ 2 160
\item   0,212  ~ \(\times\)  ~ ... ~ = ~ 2,12
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 0,45
\item   0,19  ~ \(\times\)  ~ ... ~ = ~ 190
\item   0,073  ~ \(\times\)  ~ ... ~ = ~ 7,3
\item   0,042  ~ \(\times\)  ~ ... ~ = ~ 42
\item   43,6  ~ \(\times\)  ~ ... ~ = ~ 43 600
\item   32,9  ~ \(\times\)  ~ ... ~ = ~ 3 290
\item   8,68  ~ \(\times\)  ~ ... ~ = ~ 8 680
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,478  ~ \(\times\)  ~ 0,001
\item   73,79  ~ \(\times\)  ~ 0,01
\item   495,3  ~ \(\times\)  ~ 0,1
\item   19,51  ~ \(\times\)  ~ 0,001
\item   327  ~ \(\times\)  ~ 0,1
\item   0,184  ~ \(\times\)  ~ 0,1
\item   3,394  ~ \(\times\)  ~ 0,001
\item   551  ~ \(\times\)  ~ 0,1
\item   282,9  ~ \(\times\)  ~ 0,1
\item   3 961  ~ \(\times\)  ~ 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   90,29  ~ \(\times\)  ~ ... ~ = ~  0,902 9
\item   7,422  ~ \(\times\)  ~ ... ~ = ~  0,074 22
\item   725,8  ~ \(\times\)  ~ ... ~ = ~  72,58
\item   0,489  ~ \(\times\)  ~ ... ~ = ~  0,048 9
\item   9 235  ~ \(\times\)  ~ ... ~ = ~  9,235
\item   17,7  ~ \(\times\)  ~ ... ~ = ~  0,177
\item   6 796  ~ \(\times\)  ~ ... ~ = ~  679,6
\item   434,7  ~ \(\times\)  ~ ... ~ = ~  4,347
\item   7 888  ~ \(\times\)  ~ ... ~ = ~  788,8
\item   313,7  ~ \(\times\)  ~ ... ~ = ~  31,37
\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 ~cm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 488,1 ~cL~ = ...~hL
\item   6 207,3 ~dag~ = ...~kg
\item   8 261,6 ~daL~ = ...~cL
\item   8 379,1 ~mm~ = ...~m
\item   747,9 ~hm~ = ...~km
\item   482,6 ~kg~ = ...~g
\item   488,59 ~g~ = ...~mg
\item   346,27 ~m~ = ...~dm
\item   6 505,7 ~hg~ = ...~dg
\item   473,33 ~hm~ = ...~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   9 = \(\dfrac{90}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{1600}{100}\) = \(\dfrac{160}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{26}{10}\) = \(\dfrac{260}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{330}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,082  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,2}
\item   237  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 237 000}
\item   72,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 290}
\item   16,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 167}
\item   0,393  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,93}
\item   9,81  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 810}
\item   972  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 97 200}
\item   15,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 156}
\item   5,59  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 559}
\item   0,037  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,37}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,875 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 875}
\item   6 703 ~ : ~ 10 ~ = ~{\color{red} 670,3}
\item   981,4 ~ : ~ 10 ~ = ~{\color{red} 98,14}
\item   2,784 ~ : ~ 100 ~ = ~{\color{red} 0,027 84}
\item   218,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,218 1}
\item   95,91 ~ : ~ 100 ~ = ~{\color{red} 0,959 1}
\item   6 187 ~ : ~ 1 000 ~ = ~{\color{red} 6,187}
\item   2,456 ~ : ~ 100 ~ = ~{\color{red} 0,024 56}
\item   729,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,729 3}
\item   85,6 ~ : ~ 10 ~ = ~{\color{red} 8,56}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   23,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 350
\item   2,16 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 160
\item   0,212 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,12
\item   0,045 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,45
\item   0,19 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~190
\item   0,073 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,3
\item   0,042 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~42
\item   43,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43 600
\item   32,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 290
\item   8,68 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 680
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,478 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 478
}\item   73,79 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,737 9
}\item   495,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 49,53
}\item   19,51 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,019 51
}\item   327 ~ \(\times\)  0,1 ~ = ~{\color{red} 32,7
}\item   0,184 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,018 4
}\item   3,394 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 394
}\item   551 ~ \(\times\)  0,1 ~ = ~{\color{red} 55,1
}\item   282,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 28,29
}\item   3 961 ~ \(\times\)  0,01 ~ = ~{\color{red} 39,61
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,29 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,902 9
\item   7,422 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,074 22
\item   725,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 72,58
\item   0,489 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,048 9
\item   9 235 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,235
\item   17,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,177
\item   6 796 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 679,6
\item   434,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,347
\item   7 888 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 788,8
\item   313,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 31,37
\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 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 488,1 ~cL~ = {\color{red}  0,848 81 }~hL
\item   6 207,3 ~dag~ = {\color{red}  62,073 }~kg
\item   8 261,6 ~daL~ = {\color{red}  8 261 600 }~cL
\item   8 379,1 ~mm~ = {\color{red}  8,379 1 }~m
\item   747,9 ~hm~ = {\color{red}  74,79 }~km
\item   482,6 ~kg~ = {\color{red}  482 600 }~g
\item   488,59 ~g~ = {\color{red}  488 590 }~mg
\item   346,27 ~m~ = {\color{red}  3 462,7 }~dm
\item   6 505,7 ~hg~ = {\color{red}  6 505 700 }~dg
\item   473,33 ~hm~ = {\color{red}  47 333 }~m
\end{itemize}
\end{multicols}
\end{document}
