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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 165}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   97,1  ~ \(\times\)  ~ 100
\item   9,23  ~ \(\times\)  ~ 1 000
\item   504  ~ \(\times\)  ~ 10
\item   0,077  ~ \(\times\)  ~ 1 000
\item   0,014  ~ \(\times\)  ~ 100
\item   0,061  ~ \(\times\)  ~ 1 000
\item   39,5  ~ \(\times\)  ~ 10
\item   0,498  ~ \(\times\)  ~ 1 000
\item   4,47  ~ \(\times\)  ~ 1 000
\item   0,016  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   320,2  ~ : ~ 100
\item   923,2  ~ : ~ 10
\item   625,2  ~ : ~ 10
\item   65,59  ~ : ~ 10
\item   91,42  ~ : ~ 10
\item   30  ~ : ~ 10
\item   878,9  ~ : ~ 100
\item   763,5  ~ : ~ 1 000
\item   9 172  ~ : ~ 10
\item   35,07  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   865  ~ \(\times\)  ~ ... ~ = ~ 86 500
\item   0,018  ~ \(\times\)  ~ ... ~ = ~ 0,18
\item   52,1  ~ \(\times\)  ~ ... ~ = ~ 5 210
\item   1,58  ~ \(\times\)  ~ ... ~ = ~ 15,8
\item   319  ~ \(\times\)  ~ ... ~ = ~ 3 190
\item   0,408  ~ \(\times\)  ~ ... ~ = ~ 408
\item   63  ~ \(\times\)  ~ ... ~ = ~ 630
\item   0,85  ~ \(\times\)  ~ ... ~ = ~ 8,5
\item   301  ~ \(\times\)  ~ ... ~ = ~ 30 100
\item   0,055  ~ \(\times\)  ~ ... ~ = ~ 55
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 126  ~ \(\times\)  ~ 0,01
\item   7,44  ~ \(\times\)  ~ 0,001
\item   482,7  ~ \(\times\)  ~ 0,01
\item   506  ~ \(\times\)  ~ 0,1
\item   3 021  ~ \(\times\)  ~ 0,1
\item   85,67  ~ \(\times\)  ~ 0,1
\item   3,711  ~ \(\times\)  ~ 0,001
\item   76,01  ~ \(\times\)  ~ 0,1
\item   836,8  ~ \(\times\)  ~ 0,1
\item   2,214  ~ \(\times\)  ~ 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   89,73  ~ \(\times\)  ~ ... ~ = ~  0,897 3
\item   1,306  ~ \(\times\)  ~ ... ~ = ~  0,001 306
\item   3 800  ~ \(\times\)  ~ ... ~ = ~  3,8
\item   1 419  ~ \(\times\)  ~ ... ~ = ~  14,19
\item   356,2  ~ \(\times\)  ~ ... ~ = ~  0,356 2
\item   103,2  ~ \(\times\)  ~ ... ~ = ~  0,103 2
\item   7 241  ~ \(\times\)  ~ ... ~ = ~  7,241
\item   2,53  ~ \(\times\)  ~ ... ~ = ~  0,025 3
\item   2 681  ~ \(\times\)  ~ ... ~ = ~  2,681
\item   741,6  ~ \(\times\)  ~ ... ~ = ~  0,741 6
\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 ~hm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   763,2 ~cg~ = ...~mg
\item   344,61 ~dam~ = ...~mm
\item   434,43 ~dg~ = ...~dag
\item   134,46 ~km~ = ...~dm
\item   2 762,8 ~kL~ = ...~daL
\item   361,28 ~hg~ = ...~kg
\item   5 983,5 ~daL~ = ...~hL
\item   684,39 ~hL~ = ...~daL
\item   4 018,9 ~cL~ = ...~kL
\item   118,85 ~daL~ = ...~kL
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{74}{10}\) = \(\dfrac{740}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{400}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   97,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 710}
\item   9,23  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 230}
\item   504  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 040}
\item   0,077  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 77}
\item   0,014  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,4}
\item   0,061  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 61}
\item   39,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 395}
\item   0,498  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 498}
\item   4,47  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 470}
\item   0,016  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   320,2 ~ : ~ 100 ~ = ~{\color{red} 3,202}
\item   923,2 ~ : ~ 10 ~ = ~{\color{red} 92,32}
\item   625,2 ~ : ~ 10 ~ = ~{\color{red} 62,52}
\item   65,59 ~ : ~ 10 ~ = ~{\color{red} 6,559}
\item   91,42 ~ : ~ 10 ~ = ~{\color{red} 9,142}
\item   30 ~ : ~ 10 ~ = ~{\color{red} 3}
\item   878,9 ~ : ~ 100 ~ = ~{\color{red} 8,789}
\item   763,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,763 5}
\item   9 172 ~ : ~ 10 ~ = ~{\color{red} 917,2}
\item   35,07 ~ : ~ 10 ~ = ~{\color{red} 3,507}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   865 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~86 500
\item   0,018 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,18
\item   52,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 210
\item   1,58 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~15,8
\item   319 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 190
\item   0,408 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~408
\item   63 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~630
\item   0,85 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,5
\item   301 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30 100
\item   0,055 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~55
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 126 ~ \(\times\)  0,01 ~ = ~{\color{red} 41,26
}\item   7,44 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 44
}\item   482,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,827
}\item   506 ~ \(\times\)  0,1 ~ = ~{\color{red} 50,6
}\item   3 021 ~ \(\times\)  0,1 ~ = ~{\color{red} 302,1
}\item   85,67 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,567
}\item   3,711 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 711
}\item   76,01 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,601
}\item   836,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 83,68
}\item   2,214 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,221 4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,73 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,897 3
\item   1,306 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 306
\item   3 800 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,8
\item   1 419 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 14,19
\item   356,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,356 2
\item   103,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,103 2
\item   7 241 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,241
\item   2,53 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,025 3
\item   2 681 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,681
\item   741,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,741 6
\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 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   763,2 ~cg~ = {\color{red}  7 632 }~mg
\item   344,61 ~dam~ = {\color{red}  3 446 100 }~mm
\item   434,43 ~dg~ = {\color{red}  4,344 3 }~dag
\item   134,46 ~km~ = {\color{red}  1 344 600 }~dm
\item   2 762,8 ~kL~ = {\color{red}  276 280 }~daL
\item   361,28 ~hg~ = {\color{red}  36,128 }~kg
\item   5 983,5 ~daL~ = {\color{red}  598,35 }~hL
\item   684,39 ~hL~ = {\color{red}  6 843,9 }~daL
\item   4 018,9 ~cL~ = {\color{red}  0,040 189 }~kL
\item   118,85 ~daL~ = {\color{red}  1,188 5 }~kL
\end{itemize}
\end{multicols}
\end{document}
