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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 376}

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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   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   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{77}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,112  ~ \(\times\)  ~ 100
\item   0,019  ~ \(\times\)  ~ 10
\item   4,67  ~ \(\times\)  ~ 10
\item   0,032  ~ \(\times\)  ~ 1 000
\item   0,078  ~ \(\times\)  ~ 10
\item   0,241  ~ \(\times\)  ~ 10
\item   0,07  ~ \(\times\)  ~ 10
\item   0,01  ~ \(\times\)  ~ 10
\item   123  ~ \(\times\)  ~ 100
\item   0,069  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,27  ~ : ~ 10
\item   3 398  ~ : ~ 100
\item   9,96  ~ : ~ 1 000
\item   1,346  ~ : ~ 1 000
\item   33,51  ~ : ~ 100
\item   497,6  ~ : ~ 100
\item   460,4  ~ : ~ 100
\item   7,058  ~ : ~ 1 000
\item   389,3  ~ : ~ 10
\item   2,74  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 8,9
\item   62,1  ~ \(\times\)  ~ ... ~ = ~ 6 210
\item   0,012  ~ \(\times\)  ~ ... ~ = ~ 0,12
\item   5,91  ~ \(\times\)  ~ ... ~ = ~ 59,1
\item   378  ~ \(\times\)  ~ ... ~ = ~ 37 800
\item   0,057  ~ \(\times\)  ~ ... ~ = ~ 57
\item   73,6  ~ \(\times\)  ~ ... ~ = ~ 73 600
\item   3,12  ~ \(\times\)  ~ ... ~ = ~ 3 120
\item   4,92  ~ \(\times\)  ~ ... ~ = ~ 49,2
\item   924  ~ \(\times\)  ~ ... ~ = ~ 924 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,68  ~ \(\times\)  ~ 0,001
\item   8 945  ~ \(\times\)  ~ 0,001
\item   234,3  ~ \(\times\)  ~ 0,01
\item   356,4  ~ \(\times\)  ~ 0,001
\item   5,567  ~ \(\times\)  ~ 0,01
\item   94,79  ~ \(\times\)  ~ 0,001
\item   5 856  ~ \(\times\)  ~ 0,001
\item   616,7  ~ \(\times\)  ~ 0,001
\item   62,62  ~ \(\times\)  ~ 0,1
\item   3,907  ~ \(\times\)  ~ 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   4,789  ~ \(\times\)  ~ ... ~ = ~  0,047 89
\item   9 842  ~ \(\times\)  ~ ... ~ = ~  98,42
\item   88,14  ~ \(\times\)  ~ ... ~ = ~  0,881 4
\item   7,922  ~ \(\times\)  ~ ... ~ = ~  0,007 922
\item   2,432  ~ \(\times\)  ~ ... ~ = ~  0,002 432
\item   9 599  ~ \(\times\)  ~ ... ~ = ~  95,99
\item   49,91  ~ \(\times\)  ~ ... ~ = ~  4,991
\item   3 295  ~ \(\times\)  ~ ... ~ = ~  3,295
\item   6,431  ~ \(\times\)  ~ ... ~ = ~  0,643 1
\item   370,1  ~ \(\times\)  ~ ... ~ = ~  37,01
\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~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dm
\item   1 ~hm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 387 ~mL~ = ...~cL
\item   747,92 ~dg~ = ...~hg
\item   580,83 ~cg~ = ...~dag
\item   3 684 ~mL~ = ...~daL
\item   551,56 ~hg~ = ...~dg
\item   226,77 ~dL~ = ...~mL
\item   2 103,1 ~L~ = ...~hL
\item   2 730,2 ~g~ = ...~cg
\item   9 597,3 ~mg~ = ...~hg
\item   2 625 ~cg~ = ...~g
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{4800}{100}\) = \(\dfrac{480}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{960}{100}\)
\item   \(\dfrac{77}{100}\) = \(\dfrac{770}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,112  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 11,2}
\item   0,019  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,19}
\item   4,67  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 46,7}
\item   0,032  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32}
\item   0,078  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,78}
\item   0,241  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,41}
\item   0,07  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,7}
\item   0,01  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,1}
\item   123  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 12 300}
\item   0,069  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,27 ~ : ~ 10 ~ = ~{\color{red} 5,827}
\item   3 398 ~ : ~ 100 ~ = ~{\color{red} 33,98}
\item   9,96 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 96}
\item   1,346 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 346}
\item   33,51 ~ : ~ 100 ~ = ~{\color{red} 0,335 1}
\item   497,6 ~ : ~ 100 ~ = ~{\color{red} 4,976}
\item   460,4 ~ : ~ 100 ~ = ~{\color{red} 4,604}
\item   7,058 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 058}
\item   389,3 ~ : ~ 10 ~ = ~{\color{red} 38,93}
\item   2,74 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 74}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,089 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,9
\item   62,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 210
\item   0,012 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,12
\item   5,91 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~59,1
\item   378 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~37 800
\item   0,057 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~57
\item   73,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~73 600
\item   3,12 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 120
\item   4,92 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~49,2
\item   924 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~924 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,68 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 68
}\item   8 945 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,945
}\item   234,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,343
}\item   356,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,356 4
}\item   5,567 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,055 67
}\item   94,79 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,094 79
}\item   5 856 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,856
}\item   616,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,616 7
}\item   62,62 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,262
}\item   3,907 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 907
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,789 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,047 89
\item   9 842 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 98,42
\item   88,14 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,881 4
\item   7,922 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 922
\item   2,432 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 432
\item   9 599 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 95,99
\item   49,91 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,991
\item   3 295 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,295
\item   6,431 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,643 1
\item   370,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 37,01
\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~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 387 ~mL~ = {\color{red}  338,7 }~cL
\item   747,92 ~dg~ = {\color{red}  0,747 92 }~hg
\item   580,83 ~cg~ = {\color{red}  0,580 83 }~dag
\item   3 684 ~mL~ = {\color{red}  0,368 4 }~daL
\item   551,56 ~hg~ = {\color{red}  551 560 }~dg
\item   226,77 ~dL~ = {\color{red}  22 677 }~mL
\item   2 103,1 ~L~ = {\color{red}  21,031 }~hL
\item   2 730,2 ~g~ = {\color{red}  273 020 }~cg
\item   9 597,3 ~mg~ = {\color{red}  0,095 973 }~hg
\item   2 625 ~cg~ = {\color{red}  26,25 }~g
\end{itemize}
\end{multicols}
\end{document}
