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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 143}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,094  ~ \(\times\)  ~ 100
\item   0,015  ~ \(\times\)  ~ 10
\item   789  ~ \(\times\)  ~ 1 000
\item   0,311  ~ \(\times\)  ~ 10
\item   0,03  ~ \(\times\)  ~ 100
\item   0,04  ~ \(\times\)  ~ 10
\item   6,51  ~ \(\times\)  ~ 100
\item   0,381  ~ \(\times\)  ~ 10
\item   4,46  ~ \(\times\)  ~ 10
\item   0,026  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,302  ~ : ~ 10
\item   3 900  ~ : ~ 1 000
\item   799,2  ~ : ~ 1 000
\item   59,09  ~ : ~ 100
\item   9,505  ~ : ~ 100
\item   2 267  ~ : ~ 10
\item   2,477  ~ : ~ 10
\item   2,644  ~ : ~ 10
\item   61,26  ~ : ~ 10
\item   4 891  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,475  ~ \(\times\)  ~ ... ~ = ~ 4,75
\item   0,537  ~ \(\times\)  ~ ... ~ = ~ 537
\item   81  ~ \(\times\)  ~ ... ~ = ~ 810
\item   463  ~ \(\times\)  ~ ... ~ = ~ 4 630
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 95
\item   0,511  ~ \(\times\)  ~ ... ~ = ~ 5,11
\item   735  ~ \(\times\)  ~ ... ~ = ~ 73 500
\item   0,238  ~ \(\times\)  ~ ... ~ = ~ 2,38
\item   1,68  ~ \(\times\)  ~ ... ~ = ~ 16,8
\item   42,7  ~ \(\times\)  ~ ... ~ = ~ 42 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,005  ~ \(\times\)  ~ 0,001
\item   297,2  ~ \(\times\)  ~ 0,001
\item   5 038  ~ \(\times\)  ~ 0,001
\item   479,5  ~ \(\times\)  ~ 0,1
\item   55,52  ~ \(\times\)  ~ 0,01
\item   17,05  ~ \(\times\)  ~ 0,01
\item   8 352  ~ \(\times\)  ~ 0,1
\item   89,43  ~ \(\times\)  ~ 0,1
\item   520,5  ~ \(\times\)  ~ 0,01
\item   82,17  ~ \(\times\)  ~ 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   489,3  ~ \(\times\)  ~ ... ~ = ~  4,893
\item   5 540  ~ \(\times\)  ~ ... ~ = ~  55,4
\item   313,7  ~ \(\times\)  ~ ... ~ = ~  0,313 7
\item   1 421  ~ \(\times\)  ~ ... ~ = ~  1,421
\item   933,3  ~ \(\times\)  ~ ... ~ = ~  0,933 3
\item   5,206  ~ \(\times\)  ~ ... ~ = ~  0,520 6
\item   5 934  ~ \(\times\)  ~ ... ~ = ~  59,34
\item   5 537  ~ \(\times\)  ~ ... ~ = ~  553,7
\item   791,5  ~ \(\times\)  ~ ... ~ = ~  7,915
\item   571,2  ~ \(\times\)  ~ ... ~ = ~  0,571 2
\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 ~hm~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 197,6 ~hL~ = ...~kL
\item   5 029,6 ~g~ = ...~dag
\item   508,77 ~g~ = ...~cg
\item   531,87 ~L~ = ...~kL
\item   250,84 ~dm~ = ...~hm
\item   8 828,7 ~mm~ = ...~km
\item   571,36 ~m~ = ...~km
\item   1 986,3 ~km~ = ...~dm
\item   1 801,9 ~hg~ = ...~dag
\item   3 954,1 ~m~ = ...~mm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{130}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{29}{10}\) = \(\dfrac{290}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{420}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,094  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,4}
\item   0,015  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,15}
\item   789  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 789 000}
\item   0,311  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,11}
\item   0,03  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3}
\item   0,04  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,4}
\item   6,51  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 651}
\item   0,381  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,81}
\item   4,46  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 44,6}
\item   0,026  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,302 ~ : ~ 10 ~ = ~{\color{red} 0,330 2}
\item   3 900 ~ : ~ 1 000 ~ = ~{\color{red} 3,9}
\item   799,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,799 2}
\item   59,09 ~ : ~ 100 ~ = ~{\color{red} 0,590 9}
\item   9,505 ~ : ~ 100 ~ = ~{\color{red} 0,095 05}
\item   2 267 ~ : ~ 10 ~ = ~{\color{red} 226,7}
\item   2,477 ~ : ~ 10 ~ = ~{\color{red} 0,247 7}
\item   2,644 ~ : ~ 10 ~ = ~{\color{red} 0,264 4}
\item   61,26 ~ : ~ 10 ~ = ~{\color{red} 6,126}
\item   4 891 ~ : ~ 10 ~ = ~{\color{red} 489,1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,475 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,75
\item   0,537 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~537
\item   81 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~810
\item   463 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 630
\item   0,095 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~95
\item   0,511 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,11
\item   735 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~73 500
\item   0,238 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,38
\item   1,68 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~16,8
\item   42,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~42 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,005 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 005
}\item   297,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,297 2
}\item   5 038 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,038
}\item   479,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 47,95
}\item   55,52 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,555 2
}\item   17,05 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,170 5
}\item   8 352 ~ \(\times\)  0,1 ~ = ~{\color{red} 835,2
}\item   89,43 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,943
}\item   520,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,205
}\item   82,17 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,821 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   489,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,893
\item   5 540 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 55,4
\item   313,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,313 7
\item   1 421 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,421
\item   933,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,933 3
\item   5,206 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,520 6
\item   5 934 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 59,34
\item   5 537 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 553,7
\item   791,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,915
\item   571,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,571 2
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 197,6 ~hL~ = {\color{red}  319,76 }~kL
\item   5 029,6 ~g~ = {\color{red}  502,96 }~dag
\item   508,77 ~g~ = {\color{red}  50 877 }~cg
\item   531,87 ~L~ = {\color{red}  0,531 87 }~kL
\item   250,84 ~dm~ = {\color{red}  0,250 84 }~hm
\item   8 828,7 ~mm~ = {\color{red}  0,008 828 7 }~km
\item   571,36 ~m~ = {\color{red}  0,571 36 }~km
\item   1 986,3 ~km~ = {\color{red}  19 863 000 }~dm
\item   1 801,9 ~hg~ = {\color{red}  18 019 }~dag
\item   3 954,1 ~m~ = {\color{red}  3 954 100 }~mm
\end{itemize}
\end{multicols}
\end{document}
