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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 259}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{94}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   806  ~ \(\times\)  ~ 10
\item   5,37  ~ \(\times\)  ~ 10
\item   92,5  ~ \(\times\)  ~ 1 000
\item   29  ~ \(\times\)  ~ 10
\item   185  ~ \(\times\)  ~ 100
\item   0,095  ~ \(\times\)  ~ 1 000
\item   0,169  ~ \(\times\)  ~ 10
\item   31,9  ~ \(\times\)  ~ 100
\item   711  ~ \(\times\)  ~ 100
\item   0,234  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 810  ~ : ~ 10
\item   2,704  ~ : ~ 1 000
\item   1,108  ~ : ~ 1 000
\item   18,33  ~ : ~ 100
\item   517,9  ~ : ~ 1 000
\item   7 822  ~ : ~ 1 000
\item   9 063  ~ : ~ 100
\item   960,2  ~ : ~ 1 000
\item   1,955  ~ : ~ 10
\item   8,585  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   696  ~ \(\times\)  ~ ... ~ = ~ 69 600
\item   452  ~ \(\times\)  ~ ... ~ = ~ 452 000
\item   3,18  ~ \(\times\)  ~ ... ~ = ~ 318
\item   954  ~ \(\times\)  ~ ... ~ = ~ 9 540
\item   0,007  ~ \(\times\)  ~ ... ~ = ~ 0,07
\item   0,895  ~ \(\times\)  ~ ... ~ = ~ 895
\item   0,044  ~ \(\times\)  ~ ... ~ = ~ 44
\item   2,38  ~ \(\times\)  ~ ... ~ = ~ 2 380
\item   0,327  ~ \(\times\)  ~ ... ~ = ~ 32,7
\item   0,349  ~ \(\times\)  ~ ... ~ = ~ 34,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,69  ~ \(\times\)  ~ 0,001
\item   6,651  ~ \(\times\)  ~ 0,01
\item   1,386  ~ \(\times\)  ~ 0,1
\item   5,647  ~ \(\times\)  ~ 0,001
\item   701,1  ~ \(\times\)  ~ 0,001
\item   42,93  ~ \(\times\)  ~ 0,001
\item   634,6  ~ \(\times\)  ~ 0,001
\item   137  ~ \(\times\)  ~ 0,01
\item   371,9  ~ \(\times\)  ~ 0,001
\item   333,4  ~ \(\times\)  ~ 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   9 351  ~ \(\times\)  ~ ... ~ = ~  935,1
\item   4 361  ~ \(\times\)  ~ ... ~ = ~  43,61
\item   3 411  ~ \(\times\)  ~ ... ~ = ~  34,11
\item   757,9  ~ \(\times\)  ~ ... ~ = ~  7,579
\item   85,3  ~ \(\times\)  ~ ... ~ = ~  0,853
\item   60,99  ~ \(\times\)  ~ ... ~ = ~  0,609 9
\item   5 370  ~ \(\times\)  ~ ... ~ = ~  537
\item   649,4  ~ \(\times\)  ~ ... ~ = ~  0,649 4
\item   858,5  ~ \(\times\)  ~ ... ~ = ~  0,858 5
\item   69,1  ~ \(\times\)  ~ ... ~ = ~  0,691
\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 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 033,4 ~cL~ = ...~hL
\item   555 ~mg~ = ...~hg
\item   7 576,2 ~kg~ = ...~dg
\item   842,27 ~dg~ = ...~cg
\item   9 736,6 ~kL~ = ...~dL
\item   462,83 ~dag~ = ...~hg
\item   713,89 ~L~ = ...~daL
\item   795,15 ~kg~ = ...~hg
\item   300,36 ~km~ = ...~m
\item   4 578,7 ~cg~ = ...~g
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{94}{10}\) = \(\dfrac{940}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{410}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   806  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 060}
\item   5,37  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 53,7}
\item   92,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 92 500}
\item   29  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 290}
\item   185  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 18 500}
\item   0,095  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 95}
\item   0,169  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,69}
\item   31,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 190}
\item   711  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 71 100}
\item   0,234  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 234}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 810 ~ : ~ 10 ~ = ~{\color{red} 181}
\item   2,704 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 704}
\item   1,108 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 108}
\item   18,33 ~ : ~ 100 ~ = ~{\color{red} 0,183 3}
\item   517,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,517 9}
\item   7 822 ~ : ~ 1 000 ~ = ~{\color{red} 7,822}
\item   9 063 ~ : ~ 100 ~ = ~{\color{red} 90,63}
\item   960,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,960 2}
\item   1,955 ~ : ~ 10 ~ = ~{\color{red} 0,195 5}
\item   8,585 ~ : ~ 100 ~ = ~{\color{red} 0,085 85}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   696 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~69 600
\item   452 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~452 000
\item   3,18 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~318
\item   954 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 540
\item   0,007 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,07
\item   0,895 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~895
\item   0,044 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~44
\item   2,38 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 380
\item   0,327 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~32,7
\item   0,349 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~34,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,69 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 69
}\item   6,651 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,066 51
}\item   1,386 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,138 6
}\item   5,647 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 647
}\item   701,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,701 1
}\item   42,93 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,042 93
}\item   634,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,634 6
}\item   137 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,37
}\item   371,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,371 9
}\item   333,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 33,34
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 351 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 935,1
\item   4 361 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 43,61
\item   3 411 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 34,11
\item   757,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,579
\item   85,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,853
\item   60,99 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,609 9
\item   5 370 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 537
\item   649,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,649 4
\item   858,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,858 5
\item   69,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,691
\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 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\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   7 033,4 ~cL~ = {\color{red}  0,703 34 }~hL
\item   555 ~mg~ = {\color{red}  0,005 55 }~hg
\item   7 576,2 ~kg~ = {\color{red}  75 762 000 }~dg
\item   842,27 ~dg~ = {\color{red}  8 422,7 }~cg
\item   9 736,6 ~kL~ = {\color{red}  97 366 000 }~dL
\item   462,83 ~dag~ = {\color{red}  46,283 }~hg
\item   713,89 ~L~ = {\color{red}  71,389 }~daL
\item   795,15 ~kg~ = {\color{red}  7 951,5 }~hg
\item   300,36 ~km~ = {\color{red}  300 360 }~m
\item   4 578,7 ~cg~ = {\color{red}  45,787 }~g
\end{itemize}
\end{multicols}
\end{document}
