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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 56}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{80}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,962  ~ \(\times\)  ~ 1 000
\item   245  ~ \(\times\)  ~ 100
\item   642  ~ \(\times\)  ~ 100
\item   6,67  ~ \(\times\)  ~ 1 000
\item   221  ~ \(\times\)  ~ 1 000
\item   224  ~ \(\times\)  ~ 1 000
\item   57,9  ~ \(\times\)  ~ 100
\item   705  ~ \(\times\)  ~ 10
\item   40,3  ~ \(\times\)  ~ 10
\item   0,011  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   925,4  ~ : ~ 100
\item   3,127  ~ : ~ 10
\item   113,9  ~ : ~ 1 000
\item   305,7  ~ : ~ 10
\item   2,313  ~ : ~ 1 000
\item   6 018  ~ : ~ 1 000
\item   6,71  ~ : ~ 10
\item   9 405  ~ : ~ 1 000
\item   9 185  ~ : ~ 1 000
\item   8,263  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,377  ~ \(\times\)  ~ ... ~ = ~ 37,7
\item   0,021  ~ \(\times\)  ~ ... ~ = ~ 2,1
\item   0,572  ~ \(\times\)  ~ ... ~ = ~ 572
\item   5,4  ~ \(\times\)  ~ ... ~ = ~ 54
\item   0,36  ~ \(\times\)  ~ ... ~ = ~ 3,6
\item   1,8  ~ \(\times\)  ~ ... ~ = ~ 180
\item   0,015  ~ \(\times\)  ~ ... ~ = ~ 1,5
\item   481  ~ \(\times\)  ~ ... ~ = ~ 4 810
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 0,89
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 437  ~ \(\times\)  ~ 0,1
\item   95,9  ~ \(\times\)  ~ 0,001
\item   661,1  ~ \(\times\)  ~ 0,001
\item   1,034  ~ \(\times\)  ~ 0,001
\item   89,21  ~ \(\times\)  ~ 0,001
\item   3 653  ~ \(\times\)  ~ 0,001
\item   683,9  ~ \(\times\)  ~ 0,1
\item   901,1  ~ \(\times\)  ~ 0,001
\item   445  ~ \(\times\)  ~ 0,1
\item   80,67  ~ \(\times\)  ~ 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   845,1  ~ \(\times\)  ~ ... ~ = ~  84,51
\item   430,1  ~ \(\times\)  ~ ... ~ = ~  0,430 1
\item   9 383  ~ \(\times\)  ~ ... ~ = ~  93,83
\item   390,8  ~ \(\times\)  ~ ... ~ = ~  0,390 8
\item   19,01  ~ \(\times\)  ~ ... ~ = ~  1,901
\item   891,4  ~ \(\times\)  ~ ... ~ = ~  0,891 4
\item   9 277  ~ \(\times\)  ~ ... ~ = ~  927,7
\item   6,987  ~ \(\times\)  ~ ... ~ = ~  0,006 987
\item   187,5  ~ \(\times\)  ~ ... ~ = ~  18,75
\item   4 816  ~ \(\times\)  ~ ... ~ = ~  4,816
\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~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 070,8 ~kL~ = ...~dL
\item   921,23 ~kg~ = ...~hg
\item   778,88 ~mm~ = ...~hm
\item   5 866,7 ~cL~ = ...~dL
\item   4 103,3 ~dam~ = ...~km
\item   2 098,9 ~daL~ = ...~hL
\item   1 236,6 ~hL~ = ...~kL
\item   862,73 ~dg~ = ...~cg
\item   6 812,2 ~kg~ = ...~cg
\item   6 780 ~kg~ = ...~dg
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{7100}{100}\) = \(\dfrac{710}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{49}{10}\) = \(\dfrac{490}{100}\)
\item   \(\dfrac{80}{100}\) = \(\dfrac{800}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,962  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 962}
\item   245  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 24 500}
\item   642  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 64 200}
\item   6,67  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 670}
\item   221  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 221 000}
\item   224  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 224 000}
\item   57,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 790}
\item   705  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 050}
\item   40,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 403}
\item   0,011  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,11}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   925,4 ~ : ~ 100 ~ = ~{\color{red} 9,254}
\item   3,127 ~ : ~ 10 ~ = ~{\color{red} 0,312 7}
\item   113,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,113 9}
\item   305,7 ~ : ~ 10 ~ = ~{\color{red} 30,57}
\item   2,313 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 313}
\item   6 018 ~ : ~ 1 000 ~ = ~{\color{red} 6,018}
\item   6,71 ~ : ~ 10 ~ = ~{\color{red} 0,671}
\item   9 405 ~ : ~ 1 000 ~ = ~{\color{red} 9,405}
\item   9 185 ~ : ~ 1 000 ~ = ~{\color{red} 9,185}
\item   8,263 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 263}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,377 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~37,7
\item   0,021 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,1
\item   0,572 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~572
\item   5,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~54
\item   0,36 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,6
\item   1,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~180
\item   0,015 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,5
\item   481 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 810
\item   0,004 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,4
\item   0,089 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,89
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 437 ~ \(\times\)  0,1 ~ = ~{\color{red} 843,7
}\item   95,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,095 9
}\item   661,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,661 1
}\item   1,034 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 034
}\item   89,21 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,089 21
}\item   3 653 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,653
}\item   683,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 68,39
}\item   901,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,901 1
}\item   445 ~ \(\times\)  0,1 ~ = ~{\color{red} 44,5
}\item   80,67 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,067
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   845,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 84,51
\item   430,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,430 1
\item   9 383 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 93,83
\item   390,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,390 8
\item   19,01 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,901
\item   891,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,891 4
\item   9 277 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 927,7
\item   6,987 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 987
\item   187,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 18,75
\item   4 816 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,816
\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~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 070,8 ~kL~ = {\color{red}  90 708 000 }~dL
\item   921,23 ~kg~ = {\color{red}  9 212,3 }~hg
\item   778,88 ~mm~ = {\color{red}  0,007 788 8 }~hm
\item   5 866,7 ~cL~ = {\color{red}  586,67 }~dL
\item   4 103,3 ~dam~ = {\color{red}  41,033 }~km
\item   2 098,9 ~daL~ = {\color{red}  209,89 }~hL
\item   1 236,6 ~hL~ = {\color{red}  123,66 }~kL
\item   862,73 ~dg~ = {\color{red}  8 627,3 }~cg
\item   6 812,2 ~kg~ = {\color{red}  681 220 000 }~cg
\item   6 780 ~kg~ = {\color{red}  67 800 000 }~dg
\end{itemize}
\end{multicols}
\end{document}
