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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 44}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{48}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,8  ~ \(\times\)  ~ 10
\item   591  ~ \(\times\)  ~ 10
\item   0,017  ~ \(\times\)  ~ 1 000
\item   0,319  ~ \(\times\)  ~ 1 000
\item   4,23  ~ \(\times\)  ~ 100
\item   0,84  ~ \(\times\)  ~ 100
\item   64,1  ~ \(\times\)  ~ 10
\item   532  ~ \(\times\)  ~ 1 000
\item   1,05  ~ \(\times\)  ~ 100
\item   1,19  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,746  ~ : ~ 10
\item   7,92  ~ : ~ 10
\item   319  ~ : ~ 100
\item   4 163  ~ : ~ 10
\item   7 250  ~ : ~ 1 000
\item   54,85  ~ : ~ 100
\item   753,3  ~ : ~ 10
\item   8,021  ~ : ~ 1 000
\item   5 768  ~ : ~ 100
\item   2 677  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   913  ~ \(\times\)  ~ ... ~ = ~ 913 000
\item   0,078  ~ \(\times\)  ~ ... ~ = ~ 78
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 5,8
\item   9,76  ~ \(\times\)  ~ ... ~ = ~ 9 760
\item   0,212  ~ \(\times\)  ~ ... ~ = ~ 2,12
\item   3,78  ~ \(\times\)  ~ ... ~ = ~ 37,8
\item   86,7  ~ \(\times\)  ~ ... ~ = ~ 86 700
\item   742  ~ \(\times\)  ~ ... ~ = ~ 74 200
\item   787  ~ \(\times\)  ~ ... ~ = ~ 787 000
\item   0,647  ~ \(\times\)  ~ ... ~ = ~ 6,47
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   243,8  ~ \(\times\)  ~ 0,001
\item   1,89  ~ \(\times\)  ~ 0,001
\item   11,34  ~ \(\times\)  ~ 0,1
\item   0,211  ~ \(\times\)  ~ 0,01
\item   302,3  ~ \(\times\)  ~ 0,1
\item   4,678  ~ \(\times\)  ~ 0,01
\item   11,63  ~ \(\times\)  ~ 0,001
\item   8 090  ~ \(\times\)  ~ 0,01
\item   81,47  ~ \(\times\)  ~ 0,01
\item   67,05  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 470  ~ \(\times\)  ~ ... ~ = ~  74,7
\item   423,2  ~ \(\times\)  ~ ... ~ = ~  42,32
\item   2 270  ~ \(\times\)  ~ ... ~ = ~  22,7
\item   65,88  ~ \(\times\)  ~ ... ~ = ~  0,658 8
\item   14,8  ~ \(\times\)  ~ ... ~ = ~  0,014 8
\item   22,88  ~ \(\times\)  ~ ... ~ = ~  0,022 88
\item   88,4  ~ \(\times\)  ~ ... ~ = ~  8,84
\item   66,8  ~ \(\times\)  ~ ... ~ = ~  0,066 8
\item   8 091  ~ \(\times\)  ~ ... ~ = ~  8,091
\item   4,552  ~ \(\times\)  ~ ... ~ = ~  0,004 552
\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 ~dm~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 963,1 ~L~ = ...~hL
\item   636,34 ~L~ = ...~mL
\item   484,43 ~mL~ = ...~hL
\item   761,65 ~dg~ = ...~g
\item   958,26 ~dL~ = ...~L
\item   3 284,4 ~dag~ = ...~g
\item   445,87 ~dm~ = ...~m
\item   306,45 ~g~ = ...~dag
\item   7 080,3 ~kL~ = ...~mL
\item   468,92 ~cg~ = ...~mg
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{3300}{100}\) = \(\dfrac{330}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{390}{100}\)
\item   \(\dfrac{48}{100}\) = \(\dfrac{480}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 38}
\item   591  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 910}
\item   0,017  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 17}
\item   0,319  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 319}
\item   4,23  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 423}
\item   0,84  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 84}
\item   64,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 641}
\item   532  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 532 000}
\item   1,05  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 105}
\item   1,19  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 11,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,746 ~ : ~ 10 ~ = ~{\color{red} 0,574 6}
\item   7,92 ~ : ~ 10 ~ = ~{\color{red} 0,792}
\item   319 ~ : ~ 100 ~ = ~{\color{red} 3,19}
\item   4 163 ~ : ~ 10 ~ = ~{\color{red} 416,3}
\item   7 250 ~ : ~ 1 000 ~ = ~{\color{red} 7,25}
\item   54,85 ~ : ~ 100 ~ = ~{\color{red} 0,548 5}
\item   753,3 ~ : ~ 10 ~ = ~{\color{red} 75,33}
\item   8,021 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 021}
\item   5 768 ~ : ~ 100 ~ = ~{\color{red} 57,68}
\item   2 677 ~ : ~ 10 ~ = ~{\color{red} 267,7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   913 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~913 000
\item   0,078 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~78
\item   0,058 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,8
\item   9,76 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 760
\item   0,212 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,12
\item   3,78 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~37,8
\item   86,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~86 700
\item   742 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74 200
\item   787 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~787 000
\item   0,647 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,47
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   243,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,243 8
}\item   1,89 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 89
}\item   11,34 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,134
}\item   0,211 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,002 11
}\item   302,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 30,23
}\item   4,678 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,046 78
}\item   11,63 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,011 63
}\item   8 090 ~ \(\times\)  0,01 ~ = ~{\color{red} 80,9
}\item   81,47 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,814 7
}\item   67,05 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,067 05
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 470 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 74,7
\item   423,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 42,32
\item   2 270 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 22,7
\item   65,88 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,658 8
\item   14,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,014 8
\item   22,88 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,022 88
\item   88,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,84
\item   66,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,066 8
\item   8 091 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,091
\item   4,552 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 552
\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 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 963,1 ~L~ = {\color{red}  59,631 }~hL
\item   636,34 ~L~ = {\color{red}  636 340 }~mL
\item   484,43 ~mL~ = {\color{red}  0,004 844 3 }~hL
\item   761,65 ~dg~ = {\color{red}  76,165 }~g
\item   958,26 ~dL~ = {\color{red}  95,826 }~L
\item   3 284,4 ~dag~ = {\color{red}  32 844 }~g
\item   445,87 ~dm~ = {\color{red}  44,587 }~m
\item   306,45 ~g~ = {\color{red}  30,645 }~dag
\item   7 080,3 ~kL~ = {\color{red}  7 080 300 000 }~mL
\item   468,92 ~cg~ = {\color{red}  4 689,2 }~mg
\end{itemize}
\end{multicols}
\end{document}
