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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 349}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,48  ~ \(\times\)  ~ 100
\item   0,054  ~ \(\times\)  ~ 10
\item   4,6  ~ \(\times\)  ~ 10
\item   77,1  ~ \(\times\)  ~ 100
\item   0,029  ~ \(\times\)  ~ 100
\item   2,61  ~ \(\times\)  ~ 1 000
\item   1,34  ~ \(\times\)  ~ 1 000
\item   0,037  ~ \(\times\)  ~ 100
\item   0,043  ~ \(\times\)  ~ 1 000
\item   0,729  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,691  ~ : ~ 1 000
\item   1 316  ~ : ~ 1 000
\item   8,508  ~ : ~ 10
\item   95,67  ~ : ~ 10
\item   4,68  ~ : ~ 10
\item   775,2  ~ : ~ 100
\item   284,2  ~ : ~ 1 000
\item   49,14  ~ : ~ 1 000
\item   27,7  ~ : ~ 10
\item   1,618  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 0,88
\item   0,05  ~ \(\times\)  ~ ... ~ = ~ 5
\item   146  ~ \(\times\)  ~ ... ~ = ~ 146 000
\item   41,4  ~ \(\times\)  ~ ... ~ = ~ 41 400
\item   53,6  ~ \(\times\)  ~ ... ~ = ~ 536
\item   0,098  ~ \(\times\)  ~ ... ~ = ~ 0,98
\item   0,601  ~ \(\times\)  ~ ... ~ = ~ 60,1
\item   0,446  ~ \(\times\)  ~ ... ~ = ~ 4,46
\item   465  ~ \(\times\)  ~ ... ~ = ~ 465 000
\item   274  ~ \(\times\)  ~ ... ~ = ~ 2 740
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   32,68  ~ \(\times\)  ~ 0,001
\item   589,9  ~ \(\times\)  ~ 0,001
\item   52,99  ~ \(\times\)  ~ 0,01
\item   0,849  ~ \(\times\)  ~ 0,1
\item   8 712  ~ \(\times\)  ~ 0,001
\item   0,127  ~ \(\times\)  ~ 0,001
\item   0,142  ~ \(\times\)  ~ 0,01
\item   5,47  ~ \(\times\)  ~ 0,01
\item   2,259  ~ \(\times\)  ~ 0,1
\item   9,782  ~ \(\times\)  ~ 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   7,421  ~ \(\times\)  ~ ... ~ = ~  0,074 21
\item   1 868  ~ \(\times\)  ~ ... ~ = ~  18,68
\item   3 687  ~ \(\times\)  ~ ... ~ = ~  368,7
\item   85,89  ~ \(\times\)  ~ ... ~ = ~  8,589
\item   47,54  ~ \(\times\)  ~ ... ~ = ~  0,047 54
\item   205,6  ~ \(\times\)  ~ ... ~ = ~  2,056
\item   327,8  ~ \(\times\)  ~ ... ~ = ~  0,327 8
\item   708,2  ~ \(\times\)  ~ ... ~ = ~  7,082
\item   916,8  ~ \(\times\)  ~ ... ~ = ~  91,68
\item   582,3  ~ \(\times\)  ~ ... ~ = ~  58,23
\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 ~km~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   146,38 ~hg~ = ...~dg
\item   5 375,7 ~dag~ = ...~hg
\item   3 879 ~mm~ = ...~hm
\item   731,58 ~hL~ = ...~kL
\item   3 370,1 ~hL~ = ...~daL
\item   4 465,3 ~daL~ = ...~hL
\item   553,79 ~kg~ = ...~dag
\item   5 629,7 ~km~ = ...~hm
\item   351,77 ~dm~ = ...~km
\item   8 953,3 ~cm~ = ...~mm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{4800}{100}\) = \(\dfrac{480}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{45}{100}\) = \(\dfrac{450}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,48  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 648}
\item   0,054  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,54}
\item   4,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 46}
\item   77,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 710}
\item   0,029  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,9}
\item   2,61  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 610}
\item   1,34  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 340}
\item   0,037  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,7}
\item   0,043  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 43}
\item   0,729  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,29}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,691 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 691}
\item   1 316 ~ : ~ 1 000 ~ = ~{\color{red} 1,316}
\item   8,508 ~ : ~ 10 ~ = ~{\color{red} 0,850 8}
\item   95,67 ~ : ~ 10 ~ = ~{\color{red} 9,567}
\item   4,68 ~ : ~ 10 ~ = ~{\color{red} 0,468}
\item   775,2 ~ : ~ 100 ~ = ~{\color{red} 7,752}
\item   284,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,284 2}
\item   49,14 ~ : ~ 1 000 ~ = ~{\color{red} 0,049 14}
\item   27,7 ~ : ~ 10 ~ = ~{\color{red} 2,77}
\item   1,618 ~ : ~ 100 ~ = ~{\color{red} 0,016 18}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,088 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,88
\item   0,05 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5
\item   146 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~146 000
\item   41,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~41 400
\item   53,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~536
\item   0,098 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,98
\item   0,601 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~60,1
\item   0,446 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,46
\item   465 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~465 000
\item   274 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 740
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   32,68 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,032 68
}\item   589,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,589 9
}\item   52,99 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,529 9
}\item   0,849 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,084 9
}\item   8 712 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,712
}\item   0,127 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 127
}\item   0,142 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,001 42
}\item   5,47 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,054 7
}\item   2,259 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,225 9
}\item   9,782 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,097 82
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,421 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,074 21
\item   1 868 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 18,68
\item   3 687 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 368,7
\item   85,89 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,589
\item   47,54 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,047 54
\item   205,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,056
\item   327,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,327 8
\item   708,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,082
\item   916,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 91,68
\item   582,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 58,23
\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 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   146,38 ~hg~ = {\color{red}  146 380 }~dg
\item   5 375,7 ~dag~ = {\color{red}  537,57 }~hg
\item   3 879 ~mm~ = {\color{red}  0,038 79 }~hm
\item   731,58 ~hL~ = {\color{red}  73,158 }~kL
\item   3 370,1 ~hL~ = {\color{red}  33 701 }~daL
\item   4 465,3 ~daL~ = {\color{red}  446,53 }~hL
\item   553,79 ~kg~ = {\color{red}  55 379 }~dag
\item   5 629,7 ~km~ = {\color{red}  56 297 }~hm
\item   351,77 ~dm~ = {\color{red}  0,035 177 }~km
\item   8 953,3 ~cm~ = {\color{red}  89 533 }~mm
\end{itemize}
\end{multicols}
\end{document}
