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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 221}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{82}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85  ~ \(\times\)  ~ 100
\item   0,576  ~ \(\times\)  ~ 1 000
\item   0,073  ~ \(\times\)  ~ 10
\item   0,44  ~ \(\times\)  ~ 1 000
\item   0,94  ~ \(\times\)  ~ 1 000
\item   0,192  ~ \(\times\)  ~ 100
\item   69,9  ~ \(\times\)  ~ 10
\item   7,95  ~ \(\times\)  ~ 10
\item   0,029  ~ \(\times\)  ~ 10
\item   63,8  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,729  ~ : ~ 10
\item   69,61  ~ : ~ 1 000
\item   6 513  ~ : ~ 100
\item   5,56  ~ : ~ 10
\item   356,1  ~ : ~ 10
\item   8 228  ~ : ~ 100
\item   651,9  ~ : ~ 1 000
\item   1 284  ~ : ~ 1 000
\item   6 331  ~ : ~ 10
\item   31,4  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,3  ~ \(\times\)  ~ ... ~ = ~ 7 300
\item   57,5  ~ \(\times\)  ~ ... ~ = ~ 575
\item   0,953  ~ \(\times\)  ~ ... ~ = ~ 95,3
\item   234  ~ \(\times\)  ~ ... ~ = ~ 23 400
\item   188  ~ \(\times\)  ~ ... ~ = ~ 18 800
\item   0,987  ~ \(\times\)  ~ ... ~ = ~ 9,87
\item   209  ~ \(\times\)  ~ ... ~ = ~ 209 000
\item   0,611  ~ \(\times\)  ~ ... ~ = ~ 6,11
\item   1,85  ~ \(\times\)  ~ ... ~ = ~ 185
\item   0,48  ~ \(\times\)  ~ ... ~ = ~ 4,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   161  ~ \(\times\)  ~ 0,001
\item   38,6  ~ \(\times\)  ~ 0,001
\item   8 056  ~ \(\times\)  ~ 0,001
\item   6 823  ~ \(\times\)  ~ 0,001
\item   64,31  ~ \(\times\)  ~ 0,1
\item   9,8  ~ \(\times\)  ~ 0,01
\item   2 733  ~ \(\times\)  ~ 0,01
\item   823,8  ~ \(\times\)  ~ 0,001
\item   11,13  ~ \(\times\)  ~ 0,01
\item   6,014  ~ \(\times\)  ~ 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   134,9  ~ \(\times\)  ~ ... ~ = ~  0,134 9
\item   2,201  ~ \(\times\)  ~ ... ~ = ~  0,002 201
\item   1,076  ~ \(\times\)  ~ ... ~ = ~  0,001 076
\item   980,6  ~ \(\times\)  ~ ... ~ = ~  9,806
\item   35,9  ~ \(\times\)  ~ ... ~ = ~  0,035 9
\item   50,33  ~ \(\times\)  ~ ... ~ = ~  5,033
\item   65,2  ~ \(\times\)  ~ ... ~ = ~  6,52
\item   44,15  ~ \(\times\)  ~ ... ~ = ~  0,441 5
\item   4 718  ~ \(\times\)  ~ ... ~ = ~  47,18
\item   63,17  ~ \(\times\)  ~ ... ~ = ~  0,063 17
\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 ~m~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~hm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   975,77 ~dm~ = ...~hm
\item   8 977,3 ~dg~ = ...~mg
\item   839,39 ~g~ = ...~hg
\item   3 457,9 ~cL~ = ...~kL
\item   9 153,5 ~hL~ = ...~L
\item   5 639,5 ~hL~ = ...~kL
\item   992,21 ~hm~ = ...~dam
\item   2 268,4 ~dg~ = ...~kg
\item   1 268,5 ~g~ = ...~cg
\item   1 578,9 ~hm~ = ...~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   4 = \(\dfrac{40}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{2200}{100}\) = \(\dfrac{220}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{460}{100}\)
\item   \(\dfrac{82}{100}\) = \(\dfrac{820}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   85  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 500}
\item   0,576  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 576}
\item   0,073  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,73}
\item   0,44  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 440}
\item   0,94  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 940}
\item   0,192  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 19,2}
\item   69,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 699}
\item   7,95  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 79,5}
\item   0,029  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,29}
\item   63,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 63 800}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,729 ~ : ~ 10 ~ = ~{\color{red} 0,872 9}
\item   69,61 ~ : ~ 1 000 ~ = ~{\color{red} 0,069 61}
\item   6 513 ~ : ~ 100 ~ = ~{\color{red} 65,13}
\item   5,56 ~ : ~ 10 ~ = ~{\color{red} 0,556}
\item   356,1 ~ : ~ 10 ~ = ~{\color{red} 35,61}
\item   8 228 ~ : ~ 100 ~ = ~{\color{red} 82,28}
\item   651,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,651 9}
\item   1 284 ~ : ~ 1 000 ~ = ~{\color{red} 1,284}
\item   6 331 ~ : ~ 10 ~ = ~{\color{red} 633,1}
\item   31,4 ~ : ~ 100 ~ = ~{\color{red} 0,314}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 300
\item   57,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~575
\item   0,953 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~95,3
\item   234 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~23 400
\item   188 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~18 800
\item   0,987 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,87
\item   209 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~209 000
\item   0,611 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,11
\item   1,85 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~185
\item   0,48 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,8
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   161 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,161
}\item   38,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,038 6
}\item   8 056 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,056
}\item   6 823 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,823
}\item   64,31 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,431
}\item   9,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,098
}\item   2 733 ~ \(\times\)  0,01 ~ = ~{\color{red} 27,33
}\item   823,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,823 8
}\item   11,13 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,111 3
}\item   6,014 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,060 14
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   134,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,134 9
\item   2,201 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 201
\item   1,076 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 076
\item   980,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,806
\item   35,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,035 9
\item   50,33 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,033
\item   65,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,52
\item   44,15 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,441 5
\item   4 718 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 47,18
\item   63,17 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,063 17
\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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   975,77 ~dm~ = {\color{red}  0,975 77 }~hm
\item   8 977,3 ~dg~ = {\color{red}  897 730 }~mg
\item   839,39 ~g~ = {\color{red}  8,393 9 }~hg
\item   3 457,9 ~cL~ = {\color{red}  0,034 579 }~kL
\item   9 153,5 ~hL~ = {\color{red}  915 350 }~L
\item   5 639,5 ~hL~ = {\color{red}  563,95 }~kL
\item   992,21 ~hm~ = {\color{red}  9 922,1 }~dam
\item   2 268,4 ~dg~ = {\color{red}  0,226 84 }~kg
\item   1 268,5 ~g~ = {\color{red}  126 850 }~cg
\item   1 578,9 ~hm~ = {\color{red}  157,89 }~km
\end{itemize}
\end{multicols}
\end{document}
