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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 293}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{75}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   429  ~ \(\times\)  ~ 100
\item   0,034  ~ \(\times\)  ~ 1 000
\item   97,7  ~ \(\times\)  ~ 10
\item   83,2  ~ \(\times\)  ~ 100
\item   109  ~ \(\times\)  ~ 1 000
\item   0,053  ~ \(\times\)  ~ 10
\item   0,207  ~ \(\times\)  ~ 10
\item   0,569  ~ \(\times\)  ~ 10
\item   0,028  ~ \(\times\)  ~ 100
\item   59  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   657,2  ~ : ~ 1 000
\item   962,7  ~ : ~ 1 000
\item   222,9  ~ : ~ 10
\item   5 814  ~ : ~ 1 000
\item   3,956  ~ : ~ 10
\item   457,7  ~ : ~ 10
\item   6,124  ~ : ~ 1 000
\item   1 288  ~ : ~ 10
\item   72,96  ~ : ~ 10
\item   43,95  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,13  ~ \(\times\)  ~ ... ~ = ~ 4 130
\item   0,741  ~ \(\times\)  ~ ... ~ = ~ 74,1
\item   61,1  ~ \(\times\)  ~ ... ~ = ~ 6 110
\item   151  ~ \(\times\)  ~ ... ~ = ~ 151 000
\item   58,9  ~ \(\times\)  ~ ... ~ = ~ 589
\item   0,012  ~ \(\times\)  ~ ... ~ = ~ 1,2
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 0,6
\item   2,37  ~ \(\times\)  ~ ... ~ = ~ 2 370
\item   85  ~ \(\times\)  ~ ... ~ = ~ 850
\item   8,65  ~ \(\times\)  ~ ... ~ = ~ 86,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,01  ~ \(\times\)  ~ 0,1
\item   6,263  ~ \(\times\)  ~ 0,1
\item   5,644  ~ \(\times\)  ~ 0,001
\item   42,97  ~ \(\times\)  ~ 0,01
\item   4,645  ~ \(\times\)  ~ 0,1
\item   3 456  ~ \(\times\)  ~ 0,1
\item   242,2  ~ \(\times\)  ~ 0,001
\item   371,6  ~ \(\times\)  ~ 0,1
\item   10,55  ~ \(\times\)  ~ 0,001
\item   3 431  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,189  ~ \(\times\)  ~ ... ~ = ~  0,118 9
\item   6,057  ~ \(\times\)  ~ ... ~ = ~  0,006 057
\item   84,77  ~ \(\times\)  ~ ... ~ = ~  8,477
\item   880,6  ~ \(\times\)  ~ ... ~ = ~  8,806
\item   438,4  ~ \(\times\)  ~ ... ~ = ~  4,384
\item   8 626  ~ \(\times\)  ~ ... ~ = ~  8,626
\item   503,1  ~ \(\times\)  ~ ... ~ = ~  5,031
\item   43,63  ~ \(\times\)  ~ ... ~ = ~  0,436 3
\item   8 975  ~ \(\times\)  ~ ... ~ = ~  8,975
\item   9 252  ~ \(\times\)  ~ ... ~ = ~  9,252
\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~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 482,6 ~g~ = ...~dag
\item   712,45 ~dag~ = ...~g
\item   490,64 ~mL~ = ...~L
\item   298,98 ~hg~ = ...~mg
\item   3 212,5 ~g~ = ...~cg
\item   9 377,4 ~mg~ = ...~cg
\item   8 260,6 ~hL~ = ...~cL
\item   7 490,6 ~km~ = ...~m
\item   249,97 ~hm~ = ...~m
\item   762,47 ~m~ = ...~dam
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{2500}{100}\) = \(\dfrac{250}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{75}{10}\) = \(\dfrac{750}{100}\)
\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   429  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 42 900}
\item   0,034  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 34}
\item   97,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 977}
\item   83,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 320}
\item   109  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 109 000}
\item   0,053  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,53}
\item   0,207  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,07}
\item   0,569  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,69}
\item   0,028  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,8}
\item   59  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 59 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   657,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,657 2}
\item   962,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,962 7}
\item   222,9 ~ : ~ 10 ~ = ~{\color{red} 22,29}
\item   5 814 ~ : ~ 1 000 ~ = ~{\color{red} 5,814}
\item   3,956 ~ : ~ 10 ~ = ~{\color{red} 0,395 6}
\item   457,7 ~ : ~ 10 ~ = ~{\color{red} 45,77}
\item   6,124 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 124}
\item   1 288 ~ : ~ 10 ~ = ~{\color{red} 128,8}
\item   72,96 ~ : ~ 10 ~ = ~{\color{red} 7,296}
\item   43,95 ~ : ~ 10 ~ = ~{\color{red} 4,395}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,13 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 130
\item   0,741 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~74,1
\item   61,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 110
\item   151 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~151 000
\item   58,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~589
\item   0,012 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1,2
\item   0,06 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,6
\item   2,37 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 370
\item   85 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~850
\item   8,65 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~86,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   78,01 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,801
}\item   6,263 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,626 3
}\item   5,644 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 644
}\item   42,97 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,429 7
}\item   4,645 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,464 5
}\item   3 456 ~ \(\times\)  0,1 ~ = ~{\color{red} 345,6
}\item   242,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,242 2
}\item   371,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 37,16
}\item   10,55 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,010 55
}\item   3 431 ~ \(\times\)  0,1 ~ = ~{\color{red} 343,1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,189 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,118 9
\item   6,057 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 057
\item   84,77 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,477
\item   880,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,806
\item   438,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,384
\item   8 626 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,626
\item   503,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,031
\item   43,63 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,436 3
\item   8 975 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,975
\item   9 252 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,252
\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~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 482,6 ~g~ = {\color{red}  248,26 }~dag
\item   712,45 ~dag~ = {\color{red}  7 124,5 }~g
\item   490,64 ~mL~ = {\color{red}  0,490 64 }~L
\item   298,98 ~hg~ = {\color{red}  29 898 000 }~mg
\item   3 212,5 ~g~ = {\color{red}  321 250 }~cg
\item   9 377,4 ~mg~ = {\color{red}  937,74 }~cg
\item   8 260,6 ~hL~ = {\color{red}  82 606 000 }~cL
\item   7 490,6 ~km~ = {\color{red}  7 490 600 }~m
\item   249,97 ~hm~ = {\color{red}  24 997 }~m
\item   762,47 ~m~ = {\color{red}  76,247 }~dam
\end{itemize}
\end{multicols}
\end{document}
