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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 131}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{61}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,026  ~ \(\times\)  ~ 10
\item   0,037  ~ \(\times\)  ~ 1 000
\item   11,1  ~ \(\times\)  ~ 10
\item   0,072  ~ \(\times\)  ~ 1 000
\item   0,746  ~ \(\times\)  ~ 100
\item   77,5  ~ \(\times\)  ~ 10
\item   566  ~ \(\times\)  ~ 1 000
\item   0,18  ~ \(\times\)  ~ 1 000
\item   61,4  ~ \(\times\)  ~ 1 000
\item   453  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   82,41  ~ : ~ 100
\item   153,6  ~ : ~ 10
\item   2 814  ~ : ~ 1 000
\item   6 217  ~ : ~ 1 000
\item   630,8  ~ : ~ 10
\item   81,68  ~ : ~ 10
\item   2,878  ~ : ~ 100
\item   266  ~ : ~ 100
\item   25,42  ~ : ~ 10
\item   754,4  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   651  ~ \(\times\)  ~ ... ~ = ~ 651 000
\item   0,845  ~ \(\times\)  ~ ... ~ = ~ 8,45
\item   78,1  ~ \(\times\)  ~ ... ~ = ~ 7 810
\item   0,534  ~ \(\times\)  ~ ... ~ = ~ 53,4
\item   0,846  ~ \(\times\)  ~ ... ~ = ~ 8,46
\item   2,96  ~ \(\times\)  ~ ... ~ = ~ 2 960
\item   1,4  ~ \(\times\)  ~ ... ~ = ~ 14
\item   732  ~ \(\times\)  ~ ... ~ = ~ 73 200
\item   48  ~ \(\times\)  ~ ... ~ = ~ 480
\item   0,39  ~ \(\times\)  ~ ... ~ = ~ 3,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   75,58  ~ \(\times\)  ~ 0,1
\item   695  ~ \(\times\)  ~ 0,001
\item   1 113  ~ \(\times\)  ~ 0,001
\item   59,95  ~ \(\times\)  ~ 0,01
\item   358,1  ~ \(\times\)  ~ 0,1
\item   0,823  ~ \(\times\)  ~ 0,001
\item   960,8  ~ \(\times\)  ~ 0,1
\item   73,65  ~ \(\times\)  ~ 0,001
\item   20,77  ~ \(\times\)  ~ 0,001
\item   79,51  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   871,2  ~ \(\times\)  ~ ... ~ = ~  8,712
\item   9,81  ~ \(\times\)  ~ ... ~ = ~  0,098 1
\item   3 849  ~ \(\times\)  ~ ... ~ = ~  3,849
\item   270,7  ~ \(\times\)  ~ ... ~ = ~  0,270 7
\item   587,8  ~ \(\times\)  ~ ... ~ = ~  58,78
\item   2,515  ~ \(\times\)  ~ ... ~ = ~  0,002 515
\item   873,2  ~ \(\times\)  ~ ... ~ = ~  8,732
\item   41,09  ~ \(\times\)  ~ ... ~ = ~  4,109
\item   9 777  ~ \(\times\)  ~ ... ~ = ~  97,77
\item   875,2  ~ \(\times\)  ~ ... ~ = ~  87,52
\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 ~dm~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 413 ~hm~ = ...~km
\item   6 534,7 ~kg~ = ...~dag
\item   514,13 ~kg~ = ...~mg
\item   588,11 ~hm~ = ...~mm
\item   4 955,1 ~hg~ = ...~cg
\item   8 299,8 ~cm~ = ...~mm
\item   1 256,7 ~L~ = ...~dL
\item   2 916,7 ~kL~ = ...~hL
\item   3 188,2 ~mg~ = ...~hg
\item   5 861,6 ~dg~ = ...~cg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{7600}{100}\) = \(\dfrac{760}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{61}{10}\) = \(\dfrac{610}{100}\)
\item   \(\dfrac{47}{100}\) = \(\dfrac{470}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,026  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,26}
\item   0,037  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 37}
\item   11,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 111}
\item   0,072  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 72}
\item   0,746  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 74,6}
\item   77,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 775}
\item   566  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 566 000}
\item   0,18  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 180}
\item   61,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 61 400}
\item   453  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 530}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   82,41 ~ : ~ 100 ~ = ~{\color{red} 0,824 1}
\item   153,6 ~ : ~ 10 ~ = ~{\color{red} 15,36}
\item   2 814 ~ : ~ 1 000 ~ = ~{\color{red} 2,814}
\item   6 217 ~ : ~ 1 000 ~ = ~{\color{red} 6,217}
\item   630,8 ~ : ~ 10 ~ = ~{\color{red} 63,08}
\item   81,68 ~ : ~ 10 ~ = ~{\color{red} 8,168}
\item   2,878 ~ : ~ 100 ~ = ~{\color{red} 0,028 78}
\item   266 ~ : ~ 100 ~ = ~{\color{red} 2,66}
\item   25,42 ~ : ~ 10 ~ = ~{\color{red} 2,542}
\item   754,4 ~ : ~ 100 ~ = ~{\color{red} 7,544}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   651 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~651 000
\item   0,845 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,45
\item   78,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 810
\item   0,534 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~53,4
\item   0,846 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,46
\item   2,96 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 960
\item   1,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~14
\item   732 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~73 200
\item   48 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~480
\item   0,39 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,9
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   75,58 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,558
}\item   695 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,695
}\item   1 113 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,113
}\item   59,95 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,599 5
}\item   358,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 35,81
}\item   0,823 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 823
}\item   960,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 96,08
}\item   73,65 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,073 65
}\item   20,77 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,020 77
}\item   79,51 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,079 51
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   871,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,712
\item   9,81 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,098 1
\item   3 849 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,849
\item   270,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,270 7
\item   587,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 58,78
\item   2,515 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 515
\item   873,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,732
\item   41,09 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,109
\item   9 777 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 97,77
\item   875,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 87,52
\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 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 413 ~hm~ = {\color{red}  641,3 }~km
\item   6 534,7 ~kg~ = {\color{red}  653 470 }~dag
\item   514,13 ~kg~ = {\color{red}  514 130 000 }~mg
\item   588,11 ~hm~ = {\color{red}  58 811 000 }~mm
\item   4 955,1 ~hg~ = {\color{red}  49 551 000 }~cg
\item   8 299,8 ~cm~ = {\color{red}  82 998 }~mm
\item   1 256,7 ~L~ = {\color{red}  12 567 }~dL
\item   2 916,7 ~kL~ = {\color{red}  29 167 }~hL
\item   3 188,2 ~mg~ = {\color{red}  0,031 882 }~hg
\item   5 861,6 ~dg~ = {\color{red}  58 616 }~cg
\end{itemize}
\end{multicols}
\end{document}
