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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 218}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{53}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{37}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   884  ~ \(\times\)  ~ 1 000
\item   7,64  ~ \(\times\)  ~ 100
\item   2,09  ~ \(\times\)  ~ 100
\item   61,1  ~ \(\times\)  ~ 10
\item   0,066  ~ \(\times\)  ~ 1 000
\item   0,482  ~ \(\times\)  ~ 10
\item   65,5  ~ \(\times\)  ~ 1 000
\item   0,5  ~ \(\times\)  ~ 10
\item   14,7  ~ \(\times\)  ~ 10
\item   0,962  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,748  ~ : ~ 1 000
\item   43,03  ~ : ~ 10
\item   8,54  ~ : ~ 10
\item   4 878  ~ : ~ 10
\item   4 454  ~ : ~ 1 000
\item   260,8  ~ : ~ 10
\item   9,812  ~ : ~ 100
\item   1,088  ~ : ~ 10
\item   677  ~ : ~ 10
\item   19,51  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,049  ~ \(\times\)  ~ ... ~ = ~ 0,49
\item   61,3  ~ \(\times\)  ~ ... ~ = ~ 613
\item   0,794  ~ \(\times\)  ~ ... ~ = ~ 7,94
\item   4,79  ~ \(\times\)  ~ ... ~ = ~ 479
\item   8,94  ~ \(\times\)  ~ ... ~ = ~ 8 940
\item   0,322  ~ \(\times\)  ~ ... ~ = ~ 322
\item   35  ~ \(\times\)  ~ ... ~ = ~ 35 000
\item   31,4  ~ \(\times\)  ~ ... ~ = ~ 3 140
\item   0,495  ~ \(\times\)  ~ ... ~ = ~ 49,5
\item   1,75  ~ \(\times\)  ~ ... ~ = ~ 17,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 713  ~ \(\times\)  ~ 0,01
\item   7 214  ~ \(\times\)  ~ 0,01
\item   336,2  ~ \(\times\)  ~ 0,01
\item   634,9  ~ \(\times\)  ~ 0,01
\item   3 699  ~ \(\times\)  ~ 0,001
\item   9 833  ~ \(\times\)  ~ 0,01
\item   165  ~ \(\times\)  ~ 0,1
\item   0,69  ~ \(\times\)  ~ 0,1
\item   895,3  ~ \(\times\)  ~ 0,001
\item   5 592  ~ \(\times\)  ~ 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   8,518  ~ \(\times\)  ~ ... ~ = ~  0,008 518
\item   1,178  ~ \(\times\)  ~ ... ~ = ~  0,011 78
\item   81,63  ~ \(\times\)  ~ ... ~ = ~  0,081 63
\item   380,6  ~ \(\times\)  ~ ... ~ = ~  0,380 6
\item   3,132  ~ \(\times\)  ~ ... ~ = ~  0,003 132
\item   346,1  ~ \(\times\)  ~ ... ~ = ~  34,61
\item   5 386  ~ \(\times\)  ~ ... ~ = ~  53,86
\item   3,225  ~ \(\times\)  ~ ... ~ = ~  0,003 225
\item   3,187  ~ \(\times\)  ~ ... ~ = ~  0,031 87
\item   8,919  ~ \(\times\)  ~ ... ~ = ~  0,891 9
\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~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 216,1 ~mL~ = ...~hL
\item   4 942,6 ~dm~ = ...~m
\item   2 024,7 ~hm~ = ...~km
\item   211,41 ~daL~ = ...~mL
\item   414,71 ~km~ = ...~mm
\item   673,27 ~hg~ = ...~g
\item   598,84 ~hg~ = ...~cg
\item   2 306,4 ~dm~ = ...~hm
\item   801,86 ~dL~ = ...~L
\item   472,59 ~cm~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{2400}{100}\) = \(\dfrac{240}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{53}{10}\) = \(\dfrac{530}{100}\)
\item   \(\dfrac{37}{100}\) = \(\dfrac{370}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   884  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 884 000}
\item   7,64  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 764}
\item   2,09  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 209}
\item   61,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 611}
\item   0,066  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 66}
\item   0,482  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,82}
\item   65,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 65 500}
\item   0,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5}
\item   14,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 147}
\item   0,962  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,62}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,748 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 748}
\item   43,03 ~ : ~ 10 ~ = ~{\color{red} 4,303}
\item   8,54 ~ : ~ 10 ~ = ~{\color{red} 0,854}
\item   4 878 ~ : ~ 10 ~ = ~{\color{red} 487,8}
\item   4 454 ~ : ~ 1 000 ~ = ~{\color{red} 4,454}
\item   260,8 ~ : ~ 10 ~ = ~{\color{red} 26,08}
\item   9,812 ~ : ~ 100 ~ = ~{\color{red} 0,098 12}
\item   1,088 ~ : ~ 10 ~ = ~{\color{red} 0,108 8}
\item   677 ~ : ~ 10 ~ = ~{\color{red} 67,7}
\item   19,51 ~ : ~ 10 ~ = ~{\color{red} 1,951}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,049 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,49
\item   61,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~613
\item   0,794 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,94
\item   4,79 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~479
\item   8,94 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 940
\item   0,322 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~322
\item   35 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~35 000
\item   31,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 140
\item   0,495 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~49,5
\item   1,75 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~17,5
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 713 ~ \(\times\)  0,01 ~ = ~{\color{red} 87,13
}\item   7 214 ~ \(\times\)  0,01 ~ = ~{\color{red} 72,14
}\item   336,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,362
}\item   634,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,349
}\item   3 699 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,699
}\item   9 833 ~ \(\times\)  0,01 ~ = ~{\color{red} 98,33
}\item   165 ~ \(\times\)  0,1 ~ = ~{\color{red} 16,5
}\item   0,69 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,069
}\item   895,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,895 3
}\item   5 592 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,592
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,518 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 518
\item   1,178 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,011 78
\item   81,63 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,081 63
\item   380,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,380 6
\item   3,132 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 132
\item   346,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 34,61
\item   5 386 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 53,86
\item   3,225 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 225
\item   3,187 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,031 87
\item   8,919 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,891 9
\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~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 216,1 ~mL~ = {\color{red}  0,032 161 }~hL
\item   4 942,6 ~dm~ = {\color{red}  494,26 }~m
\item   2 024,7 ~hm~ = {\color{red}  202,47 }~km
\item   211,41 ~daL~ = {\color{red}  2 114 100 }~mL
\item   414,71 ~km~ = {\color{red}  414 710 000 }~mm
\item   673,27 ~hg~ = {\color{red}  67 327 }~g
\item   598,84 ~hg~ = {\color{red}  5 988 400 }~cg
\item   2 306,4 ~dm~ = {\color{red}  2,306 4 }~hm
\item   801,86 ~dL~ = {\color{red}  80,186 }~L
\item   472,59 ~cm~ = {\color{red}  47,259 }~dm
\end{itemize}
\end{multicols}
\end{document}
