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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 248}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{98}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{24}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,41  ~ \(\times\)  ~ 1 000
\item   0,715  ~ \(\times\)  ~ 100
\item   387  ~ \(\times\)  ~ 100
\item   0,635  ~ \(\times\)  ~ 10
\item   0,292  ~ \(\times\)  ~ 1 000
\item   0,629  ~ \(\times\)  ~ 1 000
\item   20  ~ \(\times\)  ~ 100
\item   0,293  ~ \(\times\)  ~ 1 000
\item   2,46  ~ \(\times\)  ~ 1 000
\item   0,065  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   760,7  ~ : ~ 100
\item   9,515  ~ : ~ 100
\item   300  ~ : ~ 10
\item   801,8  ~ : ~ 10
\item   9 236  ~ : ~ 100
\item   23,16  ~ : ~ 100
\item   5 743  ~ : ~ 10
\item   3,837  ~ : ~ 10
\item   7 015  ~ : ~ 10
\item   625  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\item   365  ~ \(\times\)  ~ ... ~ = ~ 3 650
\item   0,142  ~ \(\times\)  ~ ... ~ = ~ 142
\item   0,57  ~ \(\times\)  ~ ... ~ = ~ 570
\item   377  ~ \(\times\)  ~ ... ~ = ~ 37 700
\item   529  ~ \(\times\)  ~ ... ~ = ~ 529 000
\item   86,8  ~ \(\times\)  ~ ... ~ = ~ 868
\item   0,888  ~ \(\times\)  ~ ... ~ = ~ 88,8
\item   0,235  ~ \(\times\)  ~ ... ~ = ~ 23,5
\item   0,255  ~ \(\times\)  ~ ... ~ = ~ 2,55
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   91,45  ~ \(\times\)  ~ 0,001
\item   295  ~ \(\times\)  ~ 0,001
\item   57,47  ~ \(\times\)  ~ 0,001
\item   3,704  ~ \(\times\)  ~ 0,01
\item   6 252  ~ \(\times\)  ~ 0,001
\item   65,68  ~ \(\times\)  ~ 0,1
\item   60,8  ~ \(\times\)  ~ 0,01
\item   3,087  ~ \(\times\)  ~ 0,1
\item   32,48  ~ \(\times\)  ~ 0,001
\item   180  ~ \(\times\)  ~ 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   53,16  ~ \(\times\)  ~ ... ~ = ~  0,531 6
\item   5,684  ~ \(\times\)  ~ ... ~ = ~  0,056 84
\item   0,621  ~ \(\times\)  ~ ... ~ = ~  0,062 1
\item   0,823  ~ \(\times\)  ~ ... ~ = ~  0,082 3
\item   0,607  ~ \(\times\)  ~ ... ~ = ~  0,006 07
\item   28,84  ~ \(\times\)  ~ ... ~ = ~  0,288 4
\item   6,953  ~ \(\times\)  ~ ... ~ = ~  0,069 53
\item   88,67  ~ \(\times\)  ~ ... ~ = ~  0,886 7
\item   650,5  ~ \(\times\)  ~ ... ~ = ~  6,505
\item   2 857  ~ \(\times\)  ~ ... ~ = ~  2,857
\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 ~cm~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   336,38 ~mL~ = ...~kL
\item   312,52 ~km~ = ...~mm
\item   404,71 ~dag~ = ...~cg
\item   335,02 ~hg~ = ...~g
\item   704,96 ~m~ = ...~dam
\item   953,89 ~mL~ = ...~daL
\item   4 239,7 ~kL~ = ...~L
\item   3 270,7 ~L~ = ...~hL
\item   400,8 ~dam~ = ...~m
\item   267,67 ~hm~ = ...~cm
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{360}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{98}{10}\) = \(\dfrac{980}{100}\)
\item   \(\dfrac{24}{100}\) = \(\dfrac{240}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,41  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 410}
\item   0,715  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 71,5}
\item   387  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 38 700}
\item   0,635  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,35}
\item   0,292  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 292}
\item   0,629  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 629}
\item   20  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 000}
\item   0,293  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 293}
\item   2,46  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 460}
\item   0,065  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,65}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   760,7 ~ : ~ 100 ~ = ~{\color{red} 7,607}
\item   9,515 ~ : ~ 100 ~ = ~{\color{red} 0,095 15}
\item   300 ~ : ~ 10 ~ = ~{\color{red} 30}
\item   801,8 ~ : ~ 10 ~ = ~{\color{red} 80,18}
\item   9 236 ~ : ~ 100 ~ = ~{\color{red} 92,36}
\item   23,16 ~ : ~ 100 ~ = ~{\color{red} 0,231 6}
\item   5 743 ~ : ~ 10 ~ = ~{\color{red} 574,3}
\item   3,837 ~ : ~ 10 ~ = ~{\color{red} 0,383 7}
\item   7 015 ~ : ~ 10 ~ = ~{\color{red} 701,5}
\item   625 ~ : ~ 10 ~ = ~{\color{red} 62,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\item   365 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 650
\item   0,142 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~142
\item   0,57 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~570
\item   377 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~37 700
\item   529 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~529 000
\item   86,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~868
\item   0,888 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~88,8
\item   0,235 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~23,5
\item   0,255 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,55
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   91,45 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,091 45
}\item   295 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,295
}\item   57,47 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,057 47
}\item   3,704 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,037 04
}\item   6 252 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,252
}\item   65,68 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,568
}\item   60,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,608
}\item   3,087 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,308 7
}\item   32,48 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,032 48
}\item   180 ~ \(\times\)  0,1 ~ = ~{\color{red} 18
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   53,16 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,531 6
\item   5,684 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,056 84
\item   0,621 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,062 1
\item   0,823 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,082 3
\item   0,607 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,006 07
\item   28,84 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,288 4
\item   6,953 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,069 53
\item   88,67 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,886 7
\item   650,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,505
\item   2 857 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,857
\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 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   336,38 ~mL~ = {\color{red}  0,000 336 38 }~kL
\item   312,52 ~km~ = {\color{red}  312 520 000 }~mm
\item   404,71 ~dag~ = {\color{red}  404 710 }~cg
\item   335,02 ~hg~ = {\color{red}  33 502 }~g
\item   704,96 ~m~ = {\color{red}  70,496 }~dam
\item   953,89 ~mL~ = {\color{red}  0,095 389 }~daL
\item   4 239,7 ~kL~ = {\color{red}  4 239 700 }~L
\item   3 270,7 ~L~ = {\color{red}  32,707 }~hL
\item   400,8 ~dam~ = {\color{red}  4 008 }~m
\item   267,67 ~hm~ = {\color{red}  2 676 700 }~cm
\end{itemize}
\end{multicols}
\end{document}
