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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 379}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{53}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{98}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,1  ~ \(\times\)  ~ 100
\item   5,93  ~ \(\times\)  ~ 1 000
\item   0,888  ~ \(\times\)  ~ 1 000
\item   793  ~ \(\times\)  ~ 100
\item   0,017  ~ \(\times\)  ~ 10
\item   5,89  ~ \(\times\)  ~ 100
\item   5,83  ~ \(\times\)  ~ 100
\item   0,085  ~ \(\times\)  ~ 10
\item   4,4  ~ \(\times\)  ~ 100
\item   74,6  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   96,99  ~ : ~ 100
\item   769,6  ~ : ~ 100
\item   26,68  ~ : ~ 1 000
\item   59,67  ~ : ~ 1 000
\item   12,43  ~ : ~ 100
\item   70,2  ~ : ~ 1 000
\item   6,209  ~ : ~ 1 000
\item   557  ~ : ~ 100
\item   4,105  ~ : ~ 10
\item   483,5  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,9  ~ \(\times\)  ~ ... ~ = ~ 99
\item   970  ~ \(\times\)  ~ ... ~ = ~ 97 000
\item   2,19  ~ \(\times\)  ~ ... ~ = ~ 21,9
\item   79,8  ~ \(\times\)  ~ ... ~ = ~ 7 980
\item   15,3  ~ \(\times\)  ~ ... ~ = ~ 153
\item   21  ~ \(\times\)  ~ ... ~ = ~ 2 100
\item   7,48  ~ \(\times\)  ~ ... ~ = ~ 748
\item   71,3  ~ \(\times\)  ~ ... ~ = ~ 7 130
\item   9,74  ~ \(\times\)  ~ ... ~ = ~ 9 740
\item   4,23  ~ \(\times\)  ~ ... ~ = ~ 423
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,966  ~ \(\times\)  ~ 0,001
\item   6,584  ~ \(\times\)  ~ 0,1
\item   4 105  ~ \(\times\)  ~ 0,001
\item   563,2  ~ \(\times\)  ~ 0,1
\item   211  ~ \(\times\)  ~ 0,01
\item   72,78  ~ \(\times\)  ~ 0,01
\item   32,62  ~ \(\times\)  ~ 0,001
\item   4,807  ~ \(\times\)  ~ 0,1
\item   6,621  ~ \(\times\)  ~ 0,1
\item   89,4  ~ \(\times\)  ~ 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   13,7  ~ \(\times\)  ~ ... ~ = ~  1,37
\item   1 368  ~ \(\times\)  ~ ... ~ = ~  13,68
\item   2,166  ~ \(\times\)  ~ ... ~ = ~  0,021 66
\item   4 212  ~ \(\times\)  ~ ... ~ = ~  4,212
\item   6,877  ~ \(\times\)  ~ ... ~ = ~  0,006 877
\item   451,2  ~ \(\times\)  ~ ... ~ = ~  45,12
\item   328,7  ~ \(\times\)  ~ ... ~ = ~  0,328 7
\item   30,7  ~ \(\times\)  ~ ... ~ = ~  0,307
\item   4 700  ~ \(\times\)  ~ ... ~ = ~  470
\item   8 078  ~ \(\times\)  ~ ... ~ = ~  8,078
\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~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 277,4 ~daL~ = ...~L
\item   375,09 ~daL~ = ...~dL
\item   4 633,8 ~mg~ = ...~cg
\item   9 744,2 ~m~ = ...~km
\item   8 730 ~hm~ = ...~mm
\item   654,59 ~dag~ = ...~mg
\item   424,77 ~km~ = ...~dam
\item   677,89 ~dm~ = ...~m
\item   3 162,2 ~hL~ = ...~kL
\item   3 840 ~mm~ = ...~km
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{790}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{53}{10}\) = \(\dfrac{530}{100}\)
\item   \(\dfrac{98}{100}\) = \(\dfrac{980}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 610}
\item   5,93  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 930}
\item   0,888  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 888}
\item   793  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 79 300}
\item   0,017  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,17}
\item   5,89  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 589}
\item   5,83  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 583}
\item   0,085  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,85}
\item   4,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 440}
\item   74,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 746}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   96,99 ~ : ~ 100 ~ = ~{\color{red} 0,969 9}
\item   769,6 ~ : ~ 100 ~ = ~{\color{red} 7,696}
\item   26,68 ~ : ~ 1 000 ~ = ~{\color{red} 0,026 68}
\item   59,67 ~ : ~ 1 000 ~ = ~{\color{red} 0,059 67}
\item   12,43 ~ : ~ 100 ~ = ~{\color{red} 0,124 3}
\item   70,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,070 2}
\item   6,209 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 209}
\item   557 ~ : ~ 100 ~ = ~{\color{red} 5,57}
\item   4,105 ~ : ~ 10 ~ = ~{\color{red} 0,410 5}
\item   483,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,483 5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~99
\item   970 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~97 000
\item   2,19 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~21,9
\item   79,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 980
\item   15,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~153
\item   21 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 100
\item   7,48 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~748
\item   71,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 130
\item   9,74 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 740
\item   4,23 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~423
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,966 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 966
}\item   6,584 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,658 4
}\item   4 105 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,105
}\item   563,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 56,32
}\item   211 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,11
}\item   72,78 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,727 8
}\item   32,62 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,032 62
}\item   4,807 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,480 7
}\item   6,621 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,662 1
}\item   89,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,94
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   13,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,37
\item   1 368 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 13,68
\item   2,166 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,021 66
\item   4 212 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,212
\item   6,877 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 877
\item   451,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 45,12
\item   328,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,328 7
\item   30,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,307
\item   4 700 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 470
\item   8 078 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,078
\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}  100 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 277,4 ~daL~ = {\color{red}  62 774 }~L
\item   375,09 ~daL~ = {\color{red}  37 509 }~dL
\item   4 633,8 ~mg~ = {\color{red}  463,38 }~cg
\item   9 744,2 ~m~ = {\color{red}  9,744 2 }~km
\item   8 730 ~hm~ = {\color{red}  873 000 000 }~mm
\item   654,59 ~dag~ = {\color{red}  6 545 900 }~mg
\item   424,77 ~km~ = {\color{red}  42 477 }~dam
\item   677,89 ~dm~ = {\color{red}  67,789 }~m
\item   3 162,2 ~hL~ = {\color{red}  316,22 }~kL
\item   3 840 ~mm~ = {\color{red}  0,003 84 }~km
\end{itemize}
\end{multicols}
\end{document}
