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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 246}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{67}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,8  ~ \(\times\)  ~ 100
\item   0,096  ~ \(\times\)  ~ 1 000
\item   832  ~ \(\times\)  ~ 1 000
\item   9,5  ~ \(\times\)  ~ 10
\item   5,25  ~ \(\times\)  ~ 100
\item   152  ~ \(\times\)  ~ 10
\item   39  ~ \(\times\)  ~ 10
\item   729  ~ \(\times\)  ~ 10
\item   0,82  ~ \(\times\)  ~ 1 000
\item   0,018  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 344  ~ : ~ 100
\item   875,1  ~ : ~ 10
\item   212,7  ~ : ~ 100
\item   3 614  ~ : ~ 10
\item   7 006  ~ : ~ 10
\item   732,5  ~ : ~ 100
\item   8,928  ~ : ~ 1 000
\item   8,919  ~ : ~ 10
\item   77,09  ~ : ~ 100
\item   6 434  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,11  ~ \(\times\)  ~ ... ~ = ~ 2 110
\item   37,4  ~ \(\times\)  ~ ... ~ = ~ 3 740
\item   182  ~ \(\times\)  ~ ... ~ = ~ 18 200
\item   8,07  ~ \(\times\)  ~ ... ~ = ~ 80,7
\item   34,8  ~ \(\times\)  ~ ... ~ = ~ 3 480
\item   0,133  ~ \(\times\)  ~ ... ~ = ~ 133
\item   0,076  ~ \(\times\)  ~ ... ~ = ~ 76
\item   17,3  ~ \(\times\)  ~ ... ~ = ~ 17 300
\item   0,964  ~ \(\times\)  ~ ... ~ = ~ 964
\item   450  ~ \(\times\)  ~ ... ~ = ~ 4 500
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,412  ~ \(\times\)  ~ 0,001
\item   4 798  ~ \(\times\)  ~ 0,01
\item   641,4  ~ \(\times\)  ~ 0,001
\item   1,649  ~ \(\times\)  ~ 0,01
\item   2,701  ~ \(\times\)  ~ 0,1
\item   4,384  ~ \(\times\)  ~ 0,1
\item   4,141  ~ \(\times\)  ~ 0,001
\item   1 004  ~ \(\times\)  ~ 0,01
\item   4 786  ~ \(\times\)  ~ 0,1
\item   425,1  ~ \(\times\)  ~ 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   19,72  ~ \(\times\)  ~ ... ~ = ~  0,019 72
\item   93,42  ~ \(\times\)  ~ ... ~ = ~  0,934 2
\item   53,62  ~ \(\times\)  ~ ... ~ = ~  5,362
\item   709,1  ~ \(\times\)  ~ ... ~ = ~  7,091
\item   37,8  ~ \(\times\)  ~ ... ~ = ~  0,378
\item   8,57  ~ \(\times\)  ~ ... ~ = ~  0,085 7
\item   8,454  ~ \(\times\)  ~ ... ~ = ~  0,008 454
\item   8 656  ~ \(\times\)  ~ ... ~ = ~  865,6
\item   97,53  ~ \(\times\)  ~ ... ~ = ~  9,753
\item   2,255  ~ \(\times\)  ~ ... ~ = ~  0,002 255
\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~ = ...~m
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~m~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 485 ~dag~ = ...~mg
\item   4 941,7 ~g~ = ...~kg
\item   636,35 ~dm~ = ...~hm
\item   244,11 ~m~ = ...~dam
\item   6 045,8 ~kg~ = ...~hg
\item   613,42 ~km~ = ...~cm
\item   3 274,7 ~daL~ = ...~mL
\item   3 883 ~kL~ = ...~hL
\item   9 411,8 ~hg~ = ...~dag
\item   5 065,6 ~mg~ = ...~dag
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{560}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{67}{10}\) = \(\dfrac{670}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{330}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 980}
\item   0,096  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 96}
\item   832  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 832 000}
\item   9,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 95}
\item   5,25  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 525}
\item   152  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 520}
\item   39  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 390}
\item   729  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 290}
\item   0,82  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 820}
\item   0,018  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 344 ~ : ~ 100 ~ = ~{\color{red} 73,44}
\item   875,1 ~ : ~ 10 ~ = ~{\color{red} 87,51}
\item   212,7 ~ : ~ 100 ~ = ~{\color{red} 2,127}
\item   3 614 ~ : ~ 10 ~ = ~{\color{red} 361,4}
\item   7 006 ~ : ~ 10 ~ = ~{\color{red} 700,6}
\item   732,5 ~ : ~ 100 ~ = ~{\color{red} 7,325}
\item   8,928 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 928}
\item   8,919 ~ : ~ 10 ~ = ~{\color{red} 0,891 9}
\item   77,09 ~ : ~ 100 ~ = ~{\color{red} 0,770 9}
\item   6 434 ~ : ~ 10 ~ = ~{\color{red} 643,4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,11 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 110
\item   37,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 740
\item   182 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~18 200
\item   8,07 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~80,7
\item   34,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 480
\item   0,133 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~133
\item   0,076 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~76
\item   17,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~17 300
\item   0,964 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~964
\item   450 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 500
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,412 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 412
}\item   4 798 ~ \(\times\)  0,01 ~ = ~{\color{red} 47,98
}\item   641,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,641 4
}\item   1,649 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,016 49
}\item   2,701 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,270 1
}\item   4,384 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,438 4
}\item   4,141 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 141
}\item   1 004 ~ \(\times\)  0,01 ~ = ~{\color{red} 10,04
}\item   4 786 ~ \(\times\)  0,1 ~ = ~{\color{red} 478,6
}\item   425,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,425 1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   19,72 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,019 72
\item   93,42 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,934 2
\item   53,62 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,362
\item   709,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,091
\item   37,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,378
\item   8,57 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,085 7
\item   8,454 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 454
\item   8 656 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 865,6
\item   97,53 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,753
\item   2,255 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 255
\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}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 485 ~dag~ = {\color{red}  34 850 000 }~mg
\item   4 941,7 ~g~ = {\color{red}  4,941 7 }~kg
\item   636,35 ~dm~ = {\color{red}  0,636 35 }~hm
\item   244,11 ~m~ = {\color{red}  24,411 }~dam
\item   6 045,8 ~kg~ = {\color{red}  60 458 }~hg
\item   613,42 ~km~ = {\color{red}  61 342 000 }~cm
\item   3 274,7 ~daL~ = {\color{red}  32 747 000 }~mL
\item   3 883 ~kL~ = {\color{red}  38 830 }~hL
\item   9 411,8 ~hg~ = {\color{red}  94 118 }~dag
\item   5 065,6 ~mg~ = {\color{red}  0,506 56 }~dag
\end{itemize}
\end{multicols}
\end{document}
