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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 63}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{72}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{95}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,098  ~ \(\times\)  ~ 1 000
\item   89  ~ \(\times\)  ~ 1 000
\item   2,16  ~ \(\times\)  ~ 10
\item   8,55  ~ \(\times\)  ~ 1 000
\item   634  ~ \(\times\)  ~ 10
\item   68,6  ~ \(\times\)  ~ 100
\item   2,49  ~ \(\times\)  ~ 1 000
\item   698  ~ \(\times\)  ~ 10
\item   0,094  ~ \(\times\)  ~ 1 000
\item   17,5  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,204  ~ : ~ 100
\item   6,015  ~ : ~ 1 000
\item   3 477  ~ : ~ 10
\item   6,88  ~ : ~ 1 000
\item   5 502  ~ : ~ 10
\item   956,8  ~ : ~ 1 000
\item   0,275  ~ : ~ 100
\item   9,35  ~ : ~ 10
\item   6 144  ~ : ~ 100
\item   7 024  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,098  ~ \(\times\)  ~ ... ~ = ~ 98
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\item   0,021  ~ \(\times\)  ~ ... ~ = ~ 0,21
\item   0,596  ~ \(\times\)  ~ ... ~ = ~ 596
\item   47,5  ~ \(\times\)  ~ ... ~ = ~ 47 500
\item   864  ~ \(\times\)  ~ ... ~ = ~ 86 400
\item   0,228  ~ \(\times\)  ~ ... ~ = ~ 22,8
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 0,7
\item   0,31  ~ \(\times\)  ~ ... ~ = ~ 3,1
\item   0,954  ~ \(\times\)  ~ ... ~ = ~ 9,54
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   601,8  ~ \(\times\)  ~ 0,1
\item   5 137  ~ \(\times\)  ~ 0,01
\item   4 052  ~ \(\times\)  ~ 0,1
\item   688,6  ~ \(\times\)  ~ 0,01
\item   49,03  ~ \(\times\)  ~ 0,1
\item   9,756  ~ \(\times\)  ~ 0,1
\item   37,44  ~ \(\times\)  ~ 0,001
\item   0,308  ~ \(\times\)  ~ 0,01
\item   1 517  ~ \(\times\)  ~ 0,001
\item   79,07  ~ \(\times\)  ~ 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   267,2  ~ \(\times\)  ~ ... ~ = ~  0,267 2
\item   80,16  ~ \(\times\)  ~ ... ~ = ~  8,016
\item   58,66  ~ \(\times\)  ~ ... ~ = ~  0,058 66
\item   8 909  ~ \(\times\)  ~ ... ~ = ~  8,909
\item   69,54  ~ \(\times\)  ~ ... ~ = ~  6,954
\item   6,831  ~ \(\times\)  ~ ... ~ = ~  0,683 1
\item   91,48  ~ \(\times\)  ~ ... ~ = ~  0,914 8
\item   1,008  ~ \(\times\)  ~ ... ~ = ~  0,010 08
\item   6,125  ~ \(\times\)  ~ ... ~ = ~  0,061 25
\item   7,999  ~ \(\times\)  ~ ... ~ = ~  0,079 99
\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 ~km~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   503,42 ~mm~ = ...~km
\item   470,27 ~hg~ = ...~dg
\item   6 949,9 ~dam~ = ...~hm
\item   7 210,2 ~hL~ = ...~daL
\item   5 585 ~mg~ = ...~hg
\item   5 717,6 ~mm~ = ...~m
\item   451,61 ~cm~ = ...~km
\item   2 644,7 ~L~ = ...~hL
\item   892,05 ~mL~ = ...~L
\item   4 103,1 ~daL~ = ...~mL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{4800}{100}\) = \(\dfrac{480}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{72}{10}\) = \(\dfrac{720}{100}\)
\item   \(\dfrac{95}{100}\) = \(\dfrac{950}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,098  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 98}
\item   89  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 89 000}
\item   2,16  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 21,6}
\item   8,55  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 550}
\item   634  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 340}
\item   68,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 860}
\item   2,49  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 490}
\item   698  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 980}
\item   0,094  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 94}
\item   17,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 17 500}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,204 ~ : ~ 100 ~ = ~{\color{red} 0,092 04}
\item   6,015 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 015}
\item   3 477 ~ : ~ 10 ~ = ~{\color{red} 347,7}
\item   6,88 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 88}
\item   5 502 ~ : ~ 10 ~ = ~{\color{red} 550,2}
\item   956,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,956 8}
\item   0,275 ~ : ~ 100 ~ = ~{\color{red} 0,002 75}
\item   9,35 ~ : ~ 10 ~ = ~{\color{red} 0,935}
\item   6 144 ~ : ~ 100 ~ = ~{\color{red} 61,44}
\item   7 024 ~ : ~ 100 ~ = ~{\color{red} 70,24}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,098 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~98
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\item   0,021 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,21
\item   0,596 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~596
\item   47,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~47 500
\item   864 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~86 400
\item   0,228 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22,8
\item   0,07 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,7
\item   0,31 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,1
\item   0,954 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,54
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   601,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 60,18
}\item   5 137 ~ \(\times\)  0,01 ~ = ~{\color{red} 51,37
}\item   4 052 ~ \(\times\)  0,1 ~ = ~{\color{red} 405,2
}\item   688,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,886
}\item   49,03 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,903
}\item   9,756 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,975 6
}\item   37,44 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,037 44
}\item   0,308 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,003 08
}\item   1 517 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,517
}\item   79,07 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,790 7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   267,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,267 2
\item   80,16 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,016
\item   58,66 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,058 66
\item   8 909 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,909
\item   69,54 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,954
\item   6,831 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,683 1
\item   91,48 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,914 8
\item   1,008 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,010 08
\item   6,125 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,061 25
\item   7,999 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,079 99
\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 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   503,42 ~mm~ = {\color{red}  0,000 503 42 }~km
\item   470,27 ~hg~ = {\color{red}  470 270 }~dg
\item   6 949,9 ~dam~ = {\color{red}  694,99 }~hm
\item   7 210,2 ~hL~ = {\color{red}  72 102 }~daL
\item   5 585 ~mg~ = {\color{red}  0,055 85 }~hg
\item   5 717,6 ~mm~ = {\color{red}  5,717 6 }~m
\item   451,61 ~cm~ = {\color{red}  0,004 516 1 }~km
\item   2 644,7 ~L~ = {\color{red}  26,447 }~hL
\item   892,05 ~mL~ = {\color{red}  0,892 05 }~L
\item   4 103,1 ~daL~ = {\color{red}  41 031 000 }~mL
\end{itemize}
\end{multicols}
\end{document}
