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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 122}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,8  ~ \(\times\)  ~ 100
\item   0,086  ~ \(\times\)  ~ 10
\item   1,17  ~ \(\times\)  ~ 100
\item   74,2  ~ \(\times\)  ~ 1 000
\item   0,416  ~ \(\times\)  ~ 1 000
\item   65,2  ~ \(\times\)  ~ 100
\item   0,296  ~ \(\times\)  ~ 10
\item   405  ~ \(\times\)  ~ 1 000
\item   0,663  ~ \(\times\)  ~ 1 000
\item   0,009  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   81,92  ~ : ~ 100
\item   7,44  ~ : ~ 100
\item   725,9  ~ : ~ 1 000
\item   6,128  ~ : ~ 10
\item   7 566  ~ : ~ 1 000
\item   462  ~ : ~ 10
\item   7,883  ~ : ~ 100
\item   6,092  ~ : ~ 1 000
\item   3 451  ~ : ~ 1 000
\item   37,94  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,114  ~ \(\times\)  ~ ... ~ = ~ 11,4
\item   626  ~ \(\times\)  ~ ... ~ = ~ 6 260
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 61
\item   834  ~ \(\times\)  ~ ... ~ = ~ 83 400
\item   984  ~ \(\times\)  ~ ... ~ = ~ 984 000
\item   3,07  ~ \(\times\)  ~ ... ~ = ~ 3 070
\item   0,093  ~ \(\times\)  ~ ... ~ = ~ 93
\item   87,9  ~ \(\times\)  ~ ... ~ = ~ 8 790
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 84
\item   25,7  ~ \(\times\)  ~ ... ~ = ~ 257
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,119  ~ \(\times\)  ~ 0,01
\item   5,673  ~ \(\times\)  ~ 0,001
\item   2,956  ~ \(\times\)  ~ 0,01
\item   0,981  ~ \(\times\)  ~ 0,1
\item   8,318  ~ \(\times\)  ~ 0,001
\item   2 903  ~ \(\times\)  ~ 0,01
\item   3,045  ~ \(\times\)  ~ 0,1
\item   858,8  ~ \(\times\)  ~ 0,1
\item   8 378  ~ \(\times\)  ~ 0,01
\item   175  ~ \(\times\)  ~ 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   7,431  ~ \(\times\)  ~ ... ~ = ~  0,074 31
\item   12,64  ~ \(\times\)  ~ ... ~ = ~  0,012 64
\item   1 546  ~ \(\times\)  ~ ... ~ = ~  15,46
\item   483,4  ~ \(\times\)  ~ ... ~ = ~  48,34
\item   9 359  ~ \(\times\)  ~ ... ~ = ~  935,9
\item   84,26  ~ \(\times\)  ~ ... ~ = ~  8,426
\item   25,2  ~ \(\times\)  ~ ... ~ = ~  0,025 2
\item   47,1  ~ \(\times\)  ~ ... ~ = ~  0,047 1
\item   2,06  ~ \(\times\)  ~ ... ~ = ~  0,020 6
\item   92,38  ~ \(\times\)  ~ ... ~ = ~  9,238
\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 ~dam~ = ...~hm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   304,36 ~dam~ = ...~m
\item   2 352,8 ~dag~ = ...~hg
\item   6 911,5 ~dag~ = ...~kg
\item   5 132,6 ~cg~ = ...~dag
\item   9 730,7 ~m~ = ...~cm
\item   3 407,8 ~dg~ = ...~hg
\item   5 104,5 ~cL~ = ...~daL
\item   215,37 ~L~ = ...~cL
\item   272,42 ~dag~ = ...~dg
\item   3 966,9 ~hg~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{8700}{100}\) = \(\dfrac{870}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{20}{10}\) = \(\dfrac{200}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{570}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 880}
\item   0,086  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,86}
\item   1,17  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 117}
\item   74,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 74 200}
\item   0,416  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 416}
\item   65,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 520}
\item   0,296  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,96}
\item   405  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 405 000}
\item   0,663  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 663}
\item   0,009  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   81,92 ~ : ~ 100 ~ = ~{\color{red} 0,819 2}
\item   7,44 ~ : ~ 100 ~ = ~{\color{red} 0,074 4}
\item   725,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,725 9}
\item   6,128 ~ : ~ 10 ~ = ~{\color{red} 0,612 8}
\item   7 566 ~ : ~ 1 000 ~ = ~{\color{red} 7,566}
\item   462 ~ : ~ 10 ~ = ~{\color{red} 46,2}
\item   7,883 ~ : ~ 100 ~ = ~{\color{red} 0,078 83}
\item   6,092 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 092}
\item   3 451 ~ : ~ 1 000 ~ = ~{\color{red} 3,451}
\item   37,94 ~ : ~ 100 ~ = ~{\color{red} 0,379 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,114 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~11,4
\item   626 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 260
\item   0,061 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~61
\item   834 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~83 400
\item   984 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~984 000
\item   3,07 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 070
\item   0,093 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~93
\item   87,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 790
\item   0,084 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~84
\item   25,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~257
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,119 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,031 19
}\item   5,673 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 673
}\item   2,956 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,029 56
}\item   0,981 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,098 1
}\item   8,318 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 318
}\item   2 903 ~ \(\times\)  0,01 ~ = ~{\color{red} 29,03
}\item   3,045 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,304 5
}\item   858,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 85,88
}\item   8 378 ~ \(\times\)  0,01 ~ = ~{\color{red} 83,78
}\item   175 ~ \(\times\)  0,1 ~ = ~{\color{red} 17,5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,431 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,074 31
\item   12,64 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,012 64
\item   1 546 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 15,46
\item   483,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 48,34
\item   9 359 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 935,9
\item   84,26 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,426
\item   25,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,025 2
\item   47,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,047 1
\item   2,06 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,020 6
\item   92,38 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,238
\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 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   304,36 ~dam~ = {\color{red}  3 043,6 }~m
\item   2 352,8 ~dag~ = {\color{red}  235,28 }~hg
\item   6 911,5 ~dag~ = {\color{red}  69,115 }~kg
\item   5 132,6 ~cg~ = {\color{red}  5,132 6 }~dag
\item   9 730,7 ~m~ = {\color{red}  973 070 }~cm
\item   3 407,8 ~dg~ = {\color{red}  3,407 8 }~hg
\item   5 104,5 ~cL~ = {\color{red}  5,104 5 }~daL
\item   215,37 ~L~ = {\color{red}  21 537 }~cL
\item   272,42 ~dag~ = {\color{red}  27 242 }~dg
\item   3 966,9 ~hg~ = {\color{red}  3 966 900 }~dg
\end{itemize}
\end{multicols}
\end{document}
