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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 244}

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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   \(\dfrac{8500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{19}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{56}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,2  ~ \(\times\)  ~ 100
\item   2,9  ~ \(\times\)  ~ 1 000
\item   78,1  ~ \(\times\)  ~ 10
\item   0,244  ~ \(\times\)  ~ 10
\item   1,28  ~ \(\times\)  ~ 10
\item   4,16  ~ \(\times\)  ~ 100
\item   941  ~ \(\times\)  ~ 10
\item   0,127  ~ \(\times\)  ~ 10
\item   853  ~ \(\times\)  ~ 100
\item   0,066  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 414  ~ : ~ 10
\item   83,64  ~ : ~ 10
\item   1,926  ~ : ~ 10
\item   981,2  ~ : ~ 1 000
\item   5,527  ~ : ~ 10
\item   4 624  ~ : ~ 1 000
\item   30,68  ~ : ~ 1 000
\item   436,8  ~ : ~ 10
\item   9 283  ~ : ~ 10
\item   31,66  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   97  ~ \(\times\)  ~ ... ~ = ~ 9 700
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 27
\item   0,452  ~ \(\times\)  ~ ... ~ = ~ 452
\item   985  ~ \(\times\)  ~ ... ~ = ~ 985 000
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 0,2
\item   0,031  ~ \(\times\)  ~ ... ~ = ~ 31
\item   23,1  ~ \(\times\)  ~ ... ~ = ~ 231
\item   3,66  ~ \(\times\)  ~ ... ~ = ~ 3 660
\item   0,306  ~ \(\times\)  ~ ... ~ = ~ 30,6
\item   0,85  ~ \(\times\)  ~ ... ~ = ~ 8,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,68  ~ \(\times\)  ~ 0,01
\item   8,252  ~ \(\times\)  ~ 0,001
\item   0,641  ~ \(\times\)  ~ 0,01
\item   207,8  ~ \(\times\)  ~ 0,01
\item   3,147  ~ \(\times\)  ~ 0,1
\item   9,519  ~ \(\times\)  ~ 0,001
\item   970  ~ \(\times\)  ~ 0,001
\item   890,1  ~ \(\times\)  ~ 0,01
\item   270  ~ \(\times\)  ~ 0,01
\item   373,2  ~ \(\times\)  ~ 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   8 389  ~ \(\times\)  ~ ... ~ = ~  8,389
\item   968,7  ~ \(\times\)  ~ ... ~ = ~  9,687
\item   849  ~ \(\times\)  ~ ... ~ = ~  84,9
\item   76,31  ~ \(\times\)  ~ ... ~ = ~  7,631
\item   6,124  ~ \(\times\)  ~ ... ~ = ~  0,612 4
\item   6 684  ~ \(\times\)  ~ ... ~ = ~  668,4
\item   874,3  ~ \(\times\)  ~ ... ~ = ~  87,43
\item   7,622  ~ \(\times\)  ~ ... ~ = ~  0,076 22
\item   43,33  ~ \(\times\)  ~ ... ~ = ~  0,043 33
\item   4,239  ~ \(\times\)  ~ ... ~ = ~  0,004 239
\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~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   154,59 ~mg~ = ...~g
\item   3 473 ~daL~ = ...~kL
\item   948,9 ~mg~ = ...~cg
\item   603,54 ~dag~ = ...~kg
\item   9 247 ~mg~ = ...~kg
\item   856,88 ~hg~ = ...~mg
\item   4 831,7 ~kL~ = ...~cL
\item   6 612,1 ~mg~ = ...~dag
\item   560,64 ~cg~ = ...~mg
\item   213,11 ~dm~ = ...~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   \(\dfrac{8500}{100}\) = \(\dfrac{850}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{19}{10}\) = \(\dfrac{190}{100}\)
\item   \(\dfrac{56}{100}\) = \(\dfrac{560}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 120}
\item   2,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 900}
\item   78,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 781}
\item   0,244  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,44}
\item   1,28  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 12,8}
\item   4,16  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 416}
\item   941  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9 410}
\item   0,127  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,27}
\item   853  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 85 300}
\item   0,066  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 66}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 414 ~ : ~ 10 ~ = ~{\color{red} 841,4}
\item   83,64 ~ : ~ 10 ~ = ~{\color{red} 8,364}
\item   1,926 ~ : ~ 10 ~ = ~{\color{red} 0,192 6}
\item   981,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,981 2}
\item   5,527 ~ : ~ 10 ~ = ~{\color{red} 0,552 7}
\item   4 624 ~ : ~ 1 000 ~ = ~{\color{red} 4,624}
\item   30,68 ~ : ~ 1 000 ~ = ~{\color{red} 0,030 68}
\item   436,8 ~ : ~ 10 ~ = ~{\color{red} 43,68}
\item   9 283 ~ : ~ 10 ~ = ~{\color{red} 928,3}
\item   31,66 ~ : ~ 1 000 ~ = ~{\color{red} 0,031 66}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   97 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 700
\item   0,027 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27
\item   0,452 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~452
\item   985 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~985 000
\item   0,002 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,2
\item   0,031 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~31
\item   23,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~231
\item   3,66 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 660
\item   0,306 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30,6
\item   0,85 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,68 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,896 8
}\item   8,252 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 252
}\item   0,641 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,006 41
}\item   207,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,078
}\item   3,147 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,314 7
}\item   9,519 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 519
}\item   970 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,97
}\item   890,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,901
}\item   270 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,7
}\item   373,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,732
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 389 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,389
\item   968,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,687
\item   849 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 84,9
\item   76,31 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,631
\item   6,124 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,612 4
\item   6 684 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 668,4
\item   874,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 87,43
\item   7,622 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,076 22
\item   43,33 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,043 33
\item   4,239 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 239
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   154,59 ~mg~ = {\color{red}  0,154 59 }~g
\item   3 473 ~daL~ = {\color{red}  34,73 }~kL
\item   948,9 ~mg~ = {\color{red}  94,89 }~cg
\item   603,54 ~dag~ = {\color{red}  6,035 4 }~kg
\item   9 247 ~mg~ = {\color{red}  0,009 247 }~kg
\item   856,88 ~hg~ = {\color{red}  85 688 000 }~mg
\item   4 831,7 ~kL~ = {\color{red}  483 170 000 }~cL
\item   6 612,1 ~mg~ = {\color{red}  0,661 21 }~dag
\item   560,64 ~cg~ = {\color{red}  5 606,4 }~mg
\item   213,11 ~dm~ = {\color{red}  21 311 }~mm
\end{itemize}
\end{multicols}
\end{document}
