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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 55}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3000}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{21}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   318  ~ \(\times\)  ~ 100
\item   0,946  ~ \(\times\)  ~ 1 000
\item   0,403  ~ \(\times\)  ~ 1 000
\item   4,24  ~ \(\times\)  ~ 1 000
\item   0,984  ~ \(\times\)  ~ 1 000
\item   800  ~ \(\times\)  ~ 1 000
\item   272  ~ \(\times\)  ~ 10
\item   534  ~ \(\times\)  ~ 1 000
\item   48,4  ~ \(\times\)  ~ 10
\item   39,6  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,325  ~ : ~ 10
\item   381,4  ~ : ~ 100
\item   28,87  ~ : ~ 100
\item   237  ~ : ~ 100
\item   51,88  ~ : ~ 100
\item   342,8  ~ : ~ 100
\item   297,1  ~ : ~ 10
\item   516,4  ~ : ~ 100
\item   35,31  ~ : ~ 1 000
\item   2,233  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,061  ~ \(\times\)  ~ ... ~ = ~ 61
\item   0,118  ~ \(\times\)  ~ ... ~ = ~ 118
\item   921  ~ \(\times\)  ~ ... ~ = ~ 92 100
\item   0,66  ~ \(\times\)  ~ ... ~ = ~ 66
\item   3,3  ~ \(\times\)  ~ ... ~ = ~ 33
\item   0,009  ~ \(\times\)  ~ ... ~ = ~ 0,9
\item   0,818  ~ \(\times\)  ~ ... ~ = ~ 81,8
\item   507  ~ \(\times\)  ~ ... ~ = ~ 50 700
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 2,8
\item   1,36  ~ \(\times\)  ~ ... ~ = ~ 13,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,528  ~ \(\times\)  ~ 0,01
\item   977  ~ \(\times\)  ~ 0,001
\item   4 635  ~ \(\times\)  ~ 0,1
\item   5,922  ~ \(\times\)  ~ 0,01
\item   5 889  ~ \(\times\)  ~ 0,1
\item   591,7  ~ \(\times\)  ~ 0,01
\item   5,466  ~ \(\times\)  ~ 0,001
\item   4,876  ~ \(\times\)  ~ 0,01
\item   813  ~ \(\times\)  ~ 0,001
\item   415,9  ~ \(\times\)  ~ 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   35,2  ~ \(\times\)  ~ ... ~ = ~  0,352
\item   9,618  ~ \(\times\)  ~ ... ~ = ~  0,961 8
\item   889  ~ \(\times\)  ~ ... ~ = ~  0,889
\item   83,71  ~ \(\times\)  ~ ... ~ = ~  8,371
\item   796,6  ~ \(\times\)  ~ ... ~ = ~  0,796 6
\item   6 858  ~ \(\times\)  ~ ... ~ = ~  68,58
\item   33,18  ~ \(\times\)  ~ ... ~ = ~  3,318
\item   8 526  ~ \(\times\)  ~ ... ~ = ~  8,526
\item   3,726  ~ \(\times\)  ~ ... ~ = ~  0,003 726
\item   789,7  ~ \(\times\)  ~ ... ~ = ~  7,897
\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 ~cm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 805,4 ~hm~ = ...~km
\item   9 828,4 ~km~ = ...~dam
\item   694,87 ~dm~ = ...~km
\item   8 358,7 ~hm~ = ...~cm
\item   8 317,2 ~dL~ = ...~hL
\item   357,26 ~cL~ = ...~kL
\item   577,31 ~kg~ = ...~dag
\item   161,39 ~dm~ = ...~mm
\item   853,11 ~cg~ = ...~dag
\item   120,71 ~dam~ = ...~hm
\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   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{3000}{100}\) = \(\dfrac{300}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{21}{10}\) = \(\dfrac{210}{100}\)
\item   \(\dfrac{34}{100}\) = \(\dfrac{340}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   318  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 31 800}
\item   0,946  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 946}
\item   0,403  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 403}
\item   4,24  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 240}
\item   0,984  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 984}
\item   800  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 800 000}
\item   272  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 720}
\item   534  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 534 000}
\item   48,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 484}
\item   39,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 396}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,325 ~ : ~ 10 ~ = ~{\color{red} 0,832 5}
\item   381,4 ~ : ~ 100 ~ = ~{\color{red} 3,814}
\item   28,87 ~ : ~ 100 ~ = ~{\color{red} 0,288 7}
\item   237 ~ : ~ 100 ~ = ~{\color{red} 2,37}
\item   51,88 ~ : ~ 100 ~ = ~{\color{red} 0,518 8}
\item   342,8 ~ : ~ 100 ~ = ~{\color{red} 3,428}
\item   297,1 ~ : ~ 10 ~ = ~{\color{red} 29,71}
\item   516,4 ~ : ~ 100 ~ = ~{\color{red} 5,164}
\item   35,31 ~ : ~ 1 000 ~ = ~{\color{red} 0,035 31}
\item   2,233 ~ : ~ 100 ~ = ~{\color{red} 0,022 33}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,061 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~61
\item   0,118 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~118
\item   921 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~92 100
\item   0,66 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~66
\item   3,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~33
\item   0,009 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,9
\item   0,818 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~81,8
\item   507 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~50 700
\item   0,028 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,8
\item   1,36 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~13,6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,528 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,065 28
}\item   977 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,977
}\item   4 635 ~ \(\times\)  0,1 ~ = ~{\color{red} 463,5
}\item   5,922 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,059 22
}\item   5 889 ~ \(\times\)  0,1 ~ = ~{\color{red} 588,9
}\item   591,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,917
}\item   5,466 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 466
}\item   4,876 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,048 76
}\item   813 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,813
}\item   415,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,415 9
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   35,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,352
\item   9,618 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,961 8
\item   889 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,889
\item   83,71 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,371
\item   796,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,796 6
\item   6 858 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 68,58
\item   33,18 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,318
\item   8 526 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,526
\item   3,726 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 726
\item   789,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,897
\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 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 805,4 ~hm~ = {\color{red}  380,54 }~km
\item   9 828,4 ~km~ = {\color{red}  982 840 }~dam
\item   694,87 ~dm~ = {\color{red}  0,069 487 }~km
\item   8 358,7 ~hm~ = {\color{red}  83 587 000 }~cm
\item   8 317,2 ~dL~ = {\color{red}  8,317 2 }~hL
\item   357,26 ~cL~ = {\color{red}  0,003 572 6 }~kL
\item   577,31 ~kg~ = {\color{red}  57 731 }~dag
\item   161,39 ~dm~ = {\color{red}  16 139 }~mm
\item   853,11 ~cg~ = {\color{red}  0,853 11 }~dag
\item   120,71 ~dam~ = {\color{red}  12,071 }~hm
\end{itemize}
\end{multicols}
\end{document}
