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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 231}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,022  ~ \(\times\)  ~ 100
\item   0,434  ~ \(\times\)  ~ 100
\item   0,074  ~ \(\times\)  ~ 1 000
\item   0,31  ~ \(\times\)  ~ 10
\item   594  ~ \(\times\)  ~ 10
\item   89,5  ~ \(\times\)  ~ 100
\item   2,81  ~ \(\times\)  ~ 100
\item   15  ~ \(\times\)  ~ 1 000
\item   0,083  ~ \(\times\)  ~ 100
\item   716  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 502  ~ : ~ 1 000
\item   954  ~ : ~ 10
\item   57,54  ~ : ~ 10
\item   4,194  ~ : ~ 10
\item   53,21  ~ : ~ 1 000
\item   2,69  ~ : ~ 100
\item   6 317  ~ : ~ 1 000
\item   2,897  ~ : ~ 100
\item   41,23  ~ : ~ 1 000
\item   53,65  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,56  ~ \(\times\)  ~ ... ~ = ~ 35,6
\item   514  ~ \(\times\)  ~ ... ~ = ~ 5 140
\item   4,34  ~ \(\times\)  ~ ... ~ = ~ 43,4
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 6,3
\item   347  ~ \(\times\)  ~ ... ~ = ~ 3 470
\item   473  ~ \(\times\)  ~ ... ~ = ~ 473 000
\item   2,41  ~ \(\times\)  ~ ... ~ = ~ 2 410
\item   0,693  ~ \(\times\)  ~ ... ~ = ~ 69,3
\item   33,4  ~ \(\times\)  ~ ... ~ = ~ 33 400
\item   0,586  ~ \(\times\)  ~ ... ~ = ~ 5,86
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   508,5  ~ \(\times\)  ~ 0,001
\item   5 214  ~ \(\times\)  ~ 0,1
\item   2 832  ~ \(\times\)  ~ 0,001
\item   4,12  ~ \(\times\)  ~ 0,001
\item   53,56  ~ \(\times\)  ~ 0,01
\item   30,32  ~ \(\times\)  ~ 0,1
\item   3 970  ~ \(\times\)  ~ 0,001
\item   8 560  ~ \(\times\)  ~ 0,01
\item   6,929  ~ \(\times\)  ~ 0,01
\item   64,84  ~ \(\times\)  ~ 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   5,75  ~ \(\times\)  ~ ... ~ = ~  0,005 75
\item   1 386  ~ \(\times\)  ~ ... ~ = ~  138,6
\item   2,56  ~ \(\times\)  ~ ... ~ = ~  0,256
\item   3 399  ~ \(\times\)  ~ ... ~ = ~  339,9
\item   9 178  ~ \(\times\)  ~ ... ~ = ~  9,178
\item   9 448  ~ \(\times\)  ~ ... ~ = ~  9,448
\item   5 908  ~ \(\times\)  ~ ... ~ = ~  59,08
\item   295,7  ~ \(\times\)  ~ ... ~ = ~  2,957
\item   9,383  ~ \(\times\)  ~ ... ~ = ~  0,093 83
\item   6,938  ~ \(\times\)  ~ ... ~ = ~  0,693 8
\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 ~dm~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   374,5 ~cm~ = ...~hm
\item   6 062 ~kL~ = ...~mL
\item   4 269,8 ~m~ = ...~hm
\item   8 173,1 ~cL~ = ...~mL
\item   278,84 ~cL~ = ...~kL
\item   7 787,7 ~L~ = ...~kL
\item   7 744,8 ~dag~ = ...~dg
\item   5 290,5 ~hg~ = ...~cg
\item   479,62 ~hm~ = ...~dam
\item   499,77 ~dg~ = ...~cg
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{5900}{100}\) = \(\dfrac{590}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{400}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,022  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,2}
\item   0,434  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 43,4}
\item   0,074  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 74}
\item   0,31  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,1}
\item   594  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5 940}
\item   89,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 950}
\item   2,81  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 281}
\item   15  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 15 000}
\item   0,083  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,3}
\item   716  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 716 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 502 ~ : ~ 1 000 ~ = ~{\color{red} 7,502}
\item   954 ~ : ~ 10 ~ = ~{\color{red} 95,4}
\item   57,54 ~ : ~ 10 ~ = ~{\color{red} 5,754}
\item   4,194 ~ : ~ 10 ~ = ~{\color{red} 0,419 4}
\item   53,21 ~ : ~ 1 000 ~ = ~{\color{red} 0,053 21}
\item   2,69 ~ : ~ 100 ~ = ~{\color{red} 0,026 9}
\item   6 317 ~ : ~ 1 000 ~ = ~{\color{red} 6,317}
\item   2,897 ~ : ~ 100 ~ = ~{\color{red} 0,028 97}
\item   41,23 ~ : ~ 1 000 ~ = ~{\color{red} 0,041 23}
\item   53,65 ~ : ~ 10 ~ = ~{\color{red} 5,365}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,56 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~35,6
\item   514 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 140
\item   4,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~43,4
\item   0,063 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,3
\item   347 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 470
\item   473 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~473 000
\item   2,41 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 410
\item   0,693 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~69,3
\item   33,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33 400
\item   0,586 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,86
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   508,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,508 5
}\item   5 214 ~ \(\times\)  0,1 ~ = ~{\color{red} 521,4
}\item   2 832 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,832
}\item   4,12 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 12
}\item   53,56 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,535 6
}\item   30,32 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,032
}\item   3 970 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,97
}\item   8 560 ~ \(\times\)  0,01 ~ = ~{\color{red} 85,6
}\item   6,929 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,069 29
}\item   64,84 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,648 4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,75 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 75
\item   1 386 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 138,6
\item   2,56 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,256
\item   3 399 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 339,9
\item   9 178 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,178
\item   9 448 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,448
\item   5 908 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 59,08
\item   295,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,957
\item   9,383 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,093 83
\item   6,938 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,693 8
\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 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   374,5 ~cm~ = {\color{red}  0,037 45 }~hm
\item   6 062 ~kL~ = {\color{red}  6 062 000 000 }~mL
\item   4 269,8 ~m~ = {\color{red}  42,698 }~hm
\item   8 173,1 ~cL~ = {\color{red}  81 731 }~mL
\item   278,84 ~cL~ = {\color{red}  0,002 788 4 }~kL
\item   7 787,7 ~L~ = {\color{red}  7,787 7 }~kL
\item   7 744,8 ~dag~ = {\color{red}  774 480 }~dg
\item   5 290,5 ~hg~ = {\color{red}  52 905 000 }~cg
\item   479,62 ~hm~ = {\color{red}  4 796,2 }~dam
\item   499,77 ~dg~ = {\color{red}  4 997,7 }~cg
\end{itemize}
\end{multicols}
\end{document}
