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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 37}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{67}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   817  ~ \(\times\)  ~ 1 000
\item   0,048  ~ \(\times\)  ~ 100
\item   0,956  ~ \(\times\)  ~ 1 000
\item   0,442  ~ \(\times\)  ~ 10
\item   828  ~ \(\times\)  ~ 10
\item   432  ~ \(\times\)  ~ 1 000
\item   3,04  ~ \(\times\)  ~ 1 000
\item   0,73  ~ \(\times\)  ~ 1 000
\item   5,85  ~ \(\times\)  ~ 1 000
\item   0,073  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   872,9  ~ : ~ 1 000
\item   6 932  ~ : ~ 10
\item   2,25  ~ : ~ 10
\item   960,4  ~ : ~ 10
\item   54,07  ~ : ~ 1 000
\item   2 710  ~ : ~ 1 000
\item   32,2  ~ : ~ 1 000
\item   520,5  ~ : ~ 1 000
\item   5 044  ~ : ~ 100
\item   456,7  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,5  ~ \(\times\)  ~ ... ~ = ~ 1 550
\item   641  ~ \(\times\)  ~ ... ~ = ~ 64 100
\item   468  ~ \(\times\)  ~ ... ~ = ~ 468 000
\item   673  ~ \(\times\)  ~ ... ~ = ~ 67 300
\item   67,3  ~ \(\times\)  ~ ... ~ = ~ 673
\item   46,2  ~ \(\times\)  ~ ... ~ = ~ 4 620
\item   368  ~ \(\times\)  ~ ... ~ = ~ 3 680
\item   161  ~ \(\times\)  ~ ... ~ = ~ 161 000
\item   0,017  ~ \(\times\)  ~ ... ~ = ~ 17
\item   0,026  ~ \(\times\)  ~ ... ~ = ~ 2,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 867  ~ \(\times\)  ~ 0,001
\item   30,47  ~ \(\times\)  ~ 0,1
\item   3 565  ~ \(\times\)  ~ 0,001
\item   2,818  ~ \(\times\)  ~ 0,001
\item   8 629  ~ \(\times\)  ~ 0,01
\item   4 644  ~ \(\times\)  ~ 0,001
\item   98,5  ~ \(\times\)  ~ 0,1
\item   6,676  ~ \(\times\)  ~ 0,01
\item   120,6  ~ \(\times\)  ~ 0,1
\item   5 188  ~ \(\times\)  ~ 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   3,941  ~ \(\times\)  ~ ... ~ = ~  0,003 941
\item   82,44  ~ \(\times\)  ~ ... ~ = ~  0,082 44
\item   4 684  ~ \(\times\)  ~ ... ~ = ~  4,684
\item   33,25  ~ \(\times\)  ~ ... ~ = ~  0,033 25
\item   1,75  ~ \(\times\)  ~ ... ~ = ~  0,001 75
\item   8 541  ~ \(\times\)  ~ ... ~ = ~  85,41
\item   9,796  ~ \(\times\)  ~ ... ~ = ~  0,979 6
\item   55,52  ~ \(\times\)  ~ ... ~ = ~  5,552
\item   6 022  ~ \(\times\)  ~ ... ~ = ~  60,22
\item   8 075  ~ \(\times\)  ~ ... ~ = ~  80,75
\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 ~m~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 269,1 ~hg~ = ...~mg
\item   816,1 ~m~ = ...~km
\item   470,77 ~kg~ = ...~dg
\item   4 433 ~dg~ = ...~cg
\item   8 054,2 ~m~ = ...~cm
\item   962,48 ~hg~ = ...~dag
\item   606,3 ~mm~ = ...~km
\item   8 195 ~hg~ = ...~g
\item   378,94 ~dm~ = ...~dam
\item   711,7 ~dm~ = ...~cm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{9100}{100}\) = \(\dfrac{910}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{67}{10}\) = \(\dfrac{670}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{780}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   817  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 817 000}
\item   0,048  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,8}
\item   0,956  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 956}
\item   0,442  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,42}
\item   828  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 280}
\item   432  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 432 000}
\item   3,04  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 040}
\item   0,73  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 730}
\item   5,85  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 850}
\item   0,073  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,73}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   872,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,872 9}
\item   6 932 ~ : ~ 10 ~ = ~{\color{red} 693,2}
\item   2,25 ~ : ~ 10 ~ = ~{\color{red} 0,225}
\item   960,4 ~ : ~ 10 ~ = ~{\color{red} 96,04}
\item   54,07 ~ : ~ 1 000 ~ = ~{\color{red} 0,054 07}
\item   2 710 ~ : ~ 1 000 ~ = ~{\color{red} 2,71}
\item   32,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,032 2}
\item   520,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,520 5}
\item   5 044 ~ : ~ 100 ~ = ~{\color{red} 50,44}
\item   456,7 ~ : ~ 100 ~ = ~{\color{red} 4,567}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 550
\item   641 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~64 100
\item   468 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~468 000
\item   673 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~67 300
\item   67,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~673
\item   46,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 620
\item   368 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 680
\item   161 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~161 000
\item   0,017 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~17
\item   0,026 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 867 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,867
}\item   30,47 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,047
}\item   3 565 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,565
}\item   2,818 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 818
}\item   8 629 ~ \(\times\)  0,01 ~ = ~{\color{red} 86,29
}\item   4 644 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,644
}\item   98,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,85
}\item   6,676 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,066 76
}\item   120,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 12,06
}\item   5 188 ~ \(\times\)  0,1 ~ = ~{\color{red} 518,8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,941 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 941
\item   82,44 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,082 44
\item   4 684 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,684
\item   33,25 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,033 25
\item   1,75 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 75
\item   8 541 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 85,41
\item   9,796 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,979 6
\item   55,52 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,552
\item   6 022 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 60,22
\item   8 075 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 80,75
\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 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 269,1 ~hg~ = {\color{red}  626 910 000 }~mg
\item   816,1 ~m~ = {\color{red}  0,816 1 }~km
\item   470,77 ~kg~ = {\color{red}  4 707 700 }~dg
\item   4 433 ~dg~ = {\color{red}  44 330 }~cg
\item   8 054,2 ~m~ = {\color{red}  805 420 }~cm
\item   962,48 ~hg~ = {\color{red}  9 624,8 }~dag
\item   606,3 ~mm~ = {\color{red}  0,000 606 3 }~km
\item   8 195 ~hg~ = {\color{red}  819 500 }~g
\item   378,94 ~dm~ = {\color{red}  3,789 4 }~dam
\item   711,7 ~dm~ = {\color{red}  7 117 }~cm
\end{itemize}
\end{multicols}
\end{document}
