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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 19}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{61}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,5  ~ \(\times\)  ~ 1 000
\item   0,016  ~ \(\times\)  ~ 100
\item   1,19  ~ \(\times\)  ~ 100
\item   3,44  ~ \(\times\)  ~ 10
\item   8  ~ \(\times\)  ~ 100
\item   0,003  ~ \(\times\)  ~ 1 000
\item   215  ~ \(\times\)  ~ 10
\item   0,013  ~ \(\times\)  ~ 100
\item   406  ~ \(\times\)  ~ 10
\item   433  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,588  ~ : ~ 100
\item   73,14  ~ : ~ 1 000
\item   833  ~ : ~ 1 000
\item   675,9  ~ : ~ 1 000
\item   9 547  ~ : ~ 10
\item   649,5  ~ : ~ 10
\item   2,307  ~ : ~ 10
\item   9,066  ~ : ~ 10
\item   7,547  ~ : ~ 1 000
\item   2,063  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,14  ~ \(\times\)  ~ ... ~ = ~ 514
\item   0,093  ~ \(\times\)  ~ ... ~ = ~ 0,93
\item   920  ~ \(\times\)  ~ ... ~ = ~ 9 200
\item   102  ~ \(\times\)  ~ ... ~ = ~ 10 200
\item   0,394  ~ \(\times\)  ~ ... ~ = ~ 3,94
\item   7,01  ~ \(\times\)  ~ ... ~ = ~ 70,1
\item   4,96  ~ \(\times\)  ~ ... ~ = ~ 496
\item   4,22  ~ \(\times\)  ~ ... ~ = ~ 4 220
\item   0,184  ~ \(\times\)  ~ ... ~ = ~ 18,4
\item   3,17  ~ \(\times\)  ~ ... ~ = ~ 3 170
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   843  ~ \(\times\)  ~ 0,1
\item   5,2  ~ \(\times\)  ~ 0,1
\item   7 686  ~ \(\times\)  ~ 0,01
\item   8,387  ~ \(\times\)  ~ 0,001
\item   36,5  ~ \(\times\)  ~ 0,01
\item   4 603  ~ \(\times\)  ~ 0,1
\item   217,1  ~ \(\times\)  ~ 0,01
\item   4,784  ~ \(\times\)  ~ 0,1
\item   3,423  ~ \(\times\)  ~ 0,001
\item   1,214  ~ \(\times\)  ~ 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   2 610  ~ \(\times\)  ~ ... ~ = ~  26,1
\item   4 848  ~ \(\times\)  ~ ... ~ = ~  4,848
\item   90,41  ~ \(\times\)  ~ ... ~ = ~  0,904 1
\item   35,51  ~ \(\times\)  ~ ... ~ = ~  0,035 51
\item   5 301  ~ \(\times\)  ~ ... ~ = ~  530,1
\item   470,3  ~ \(\times\)  ~ ... ~ = ~  47,03
\item   33,3  ~ \(\times\)  ~ ... ~ = ~  0,033 3
\item   773,5  ~ \(\times\)  ~ ... ~ = ~  7,735
\item   85,02  ~ \(\times\)  ~ ... ~ = ~  0,085 02
\item   51,15  ~ \(\times\)  ~ ... ~ = ~  0,051 15
\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 ~hm~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   838,76 ~dg~ = ...~kg
\item   805,5 ~mm~ = ...~dam
\item   3 558,1 ~kL~ = ...~dL
\item   3 474,2 ~hm~ = ...~mm
\item   5 748,7 ~g~ = ...~dag
\item   135,9 ~hm~ = ...~dam
\item   6 247,2 ~hg~ = ...~kg
\item   5 096,1 ~dg~ = ...~hg
\item   308,85 ~L~ = ...~mL
\item   2 268,8 ~kg~ = ...~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   1 = \(\dfrac{10}{10}\)
\item   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{7600}{100}\) = \(\dfrac{760}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{61}{10}\) = \(\dfrac{610}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{550}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 500}
\item   0,016  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,6}
\item   1,19  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 119}
\item   3,44  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 34,4}
\item   8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 800}
\item   0,003  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3}
\item   215  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 150}
\item   0,013  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,3}
\item   406  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 060}
\item   433  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 330}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,588 ~ : ~ 100 ~ = ~{\color{red} 0,095 88}
\item   73,14 ~ : ~ 1 000 ~ = ~{\color{red} 0,073 14}
\item   833 ~ : ~ 1 000 ~ = ~{\color{red} 0,833}
\item   675,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,675 9}
\item   9 547 ~ : ~ 10 ~ = ~{\color{red} 954,7}
\item   649,5 ~ : ~ 10 ~ = ~{\color{red} 64,95}
\item   2,307 ~ : ~ 10 ~ = ~{\color{red} 0,230 7}
\item   9,066 ~ : ~ 10 ~ = ~{\color{red} 0,906 6}
\item   7,547 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 547}
\item   2,063 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 063}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,14 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~514
\item   0,093 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,93
\item   920 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 200
\item   102 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~10 200
\item   0,394 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,94
\item   7,01 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~70,1
\item   4,96 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~496
\item   4,22 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 220
\item   0,184 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~18,4
\item   3,17 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 170
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   843 ~ \(\times\)  0,1 ~ = ~{\color{red} 84,3
}\item   5,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,52
}\item   7 686 ~ \(\times\)  0,01 ~ = ~{\color{red} 76,86
}\item   8,387 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 387
}\item   36,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,365
}\item   4 603 ~ \(\times\)  0,1 ~ = ~{\color{red} 460,3
}\item   217,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,171
}\item   4,784 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,478 4
}\item   3,423 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 423
}\item   1,214 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 214
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 610 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 26,1
\item   4 848 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,848
\item   90,41 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,904 1
\item   35,51 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,035 51
\item   5 301 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 530,1
\item   470,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 47,03
\item   33,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,033 3
\item   773,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,735
\item   85,02 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,085 02
\item   51,15 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,051 15
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   838,76 ~dg~ = {\color{red}  0,083 876 }~kg
\item   805,5 ~mm~ = {\color{red}  0,080 55 }~dam
\item   3 558,1 ~kL~ = {\color{red}  35 581 000 }~dL
\item   3 474,2 ~hm~ = {\color{red}  347 420 000 }~mm
\item   5 748,7 ~g~ = {\color{red}  574,87 }~dag
\item   135,9 ~hm~ = {\color{red}  1 359 }~dam
\item   6 247,2 ~hg~ = {\color{red}  624,72 }~kg
\item   5 096,1 ~dg~ = {\color{red}  5,096 1 }~hg
\item   308,85 ~L~ = {\color{red}  308 850 }~mL
\item   2 268,8 ~kg~ = {\color{red}  2 268 800 000 }~mg
\end{itemize}
\end{multicols}
\end{document}
