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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 307}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,45  ~ \(\times\)  ~ 10
\item   0,706  ~ \(\times\)  ~ 1 000
\item   93,6  ~ \(\times\)  ~ 1 000
\item   362  ~ \(\times\)  ~ 10
\item   0,698  ~ \(\times\)  ~ 1 000
\item   0,313  ~ \(\times\)  ~ 1 000
\item   702  ~ \(\times\)  ~ 10
\item   35,3  ~ \(\times\)  ~ 1 000
\item   26,2  ~ \(\times\)  ~ 100
\item   0,018  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26,98  ~ : ~ 100
\item   5 896  ~ : ~ 10
\item   3,57  ~ : ~ 10
\item   78,22  ~ : ~ 10
\item   730,8  ~ : ~ 1 000
\item   26,9  ~ : ~ 10
\item   187,2  ~ : ~ 100
\item   48,61  ~ : ~ 1 000
\item   3,374  ~ : ~ 10
\item   48,14  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,85  ~ \(\times\)  ~ ... ~ = ~ 8,5
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 67
\item   0,021  ~ \(\times\)  ~ ... ~ = ~ 0,21
\item   622  ~ \(\times\)  ~ ... ~ = ~ 62 200
\item   17,8  ~ \(\times\)  ~ ... ~ = ~ 17 800
\item   324  ~ \(\times\)  ~ ... ~ = ~ 3 240
\item   9,34  ~ \(\times\)  ~ ... ~ = ~ 93,4
\item   1,5  ~ \(\times\)  ~ ... ~ = ~ 1 500
\item   85,2  ~ \(\times\)  ~ ... ~ = ~ 8 520
\item   104  ~ \(\times\)  ~ ... ~ = ~ 10 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   63,96  ~ \(\times\)  ~ 0,1
\item   174,9  ~ \(\times\)  ~ 0,001
\item   51,03  ~ \(\times\)  ~ 0,001
\item   5,936  ~ \(\times\)  ~ 0,1
\item   2,588  ~ \(\times\)  ~ 0,1
\item   392,7  ~ \(\times\)  ~ 0,1
\item   65,96  ~ \(\times\)  ~ 0,01
\item   260,6  ~ \(\times\)  ~ 0,01
\item   6,819  ~ \(\times\)  ~ 0,001
\item   4,077  ~ \(\times\)  ~ 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   369,8  ~ \(\times\)  ~ ... ~ = ~  0,369 8
\item   2,529  ~ \(\times\)  ~ ... ~ = ~  0,025 29
\item   5,108  ~ \(\times\)  ~ ... ~ = ~  0,005 108
\item   581,7  ~ \(\times\)  ~ ... ~ = ~  5,817
\item   5 172  ~ \(\times\)  ~ ... ~ = ~  51,72
\item   31,8  ~ \(\times\)  ~ ... ~ = ~  0,318
\item   77,2  ~ \(\times\)  ~ ... ~ = ~  0,772
\item   960,9  ~ \(\times\)  ~ ... ~ = ~  0,960 9
\item   13,68  ~ \(\times\)  ~ ... ~ = ~  0,136 8
\item   455,2  ~ \(\times\)  ~ ... ~ = ~  4,552
\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~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 068,3 ~cm~ = ...~m
\item   7 167,8 ~kg~ = ...~g
\item   448,46 ~hm~ = ...~dam
\item   5 066,3 ~mm~ = ...~cm
\item   1 298,6 ~dg~ = ...~g
\item   3 632,3 ~dam~ = ...~dm
\item   8 697,7 ~kg~ = ...~hg
\item   2 831,7 ~km~ = ...~m
\item   347,94 ~dL~ = ...~hL
\item   330,51 ~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   9 = \(\dfrac{90}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{990}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{770}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{720}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,45  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 44,5}
\item   0,706  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 706}
\item   93,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 93 600}
\item   362  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 620}
\item   0,698  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 698}
\item   0,313  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 313}
\item   702  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 020}
\item   35,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 35 300}
\item   26,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 620}
\item   0,018  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,18}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26,98 ~ : ~ 100 ~ = ~{\color{red} 0,269 8}
\item   5 896 ~ : ~ 10 ~ = ~{\color{red} 589,6}
\item   3,57 ~ : ~ 10 ~ = ~{\color{red} 0,357}
\item   78,22 ~ : ~ 10 ~ = ~{\color{red} 7,822}
\item   730,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,730 8}
\item   26,9 ~ : ~ 10 ~ = ~{\color{red} 2,69}
\item   187,2 ~ : ~ 100 ~ = ~{\color{red} 1,872}
\item   48,61 ~ : ~ 1 000 ~ = ~{\color{red} 0,048 61}
\item   3,374 ~ : ~ 10 ~ = ~{\color{red} 0,337 4}
\item   48,14 ~ : ~ 10 ~ = ~{\color{red} 4,814}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,85 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,5
\item   0,067 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~67
\item   0,021 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,21
\item   622 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~62 200
\item   17,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~17 800
\item   324 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 240
\item   9,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~93,4
\item   1,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 500
\item   85,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 520
\item   104 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~10 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   63,96 ~ \(\times\)  0,1 ~ = ~{\color{red} 6,396
}\item   174,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,174 9
}\item   51,03 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,051 03
}\item   5,936 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,593 6
}\item   2,588 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,258 8
}\item   392,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 39,27
}\item   65,96 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,659 6
}\item   260,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,606
}\item   6,819 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 819
}\item   4,077 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,407 7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   369,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,369 8
\item   2,529 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,025 29
\item   5,108 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 108
\item   581,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,817
\item   5 172 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 51,72
\item   31,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,318
\item   77,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,772
\item   960,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,960 9
\item   13,68 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,136 8
\item   455,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,552
\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~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 068,3 ~cm~ = {\color{red}  40,683 }~m
\item   7 167,8 ~kg~ = {\color{red}  7 167 800 }~g
\item   448,46 ~hm~ = {\color{red}  4 484,6 }~dam
\item   5 066,3 ~mm~ = {\color{red}  506,63 }~cm
\item   1 298,6 ~dg~ = {\color{red}  129,86 }~g
\item   3 632,3 ~dam~ = {\color{red}  363 230 }~dm
\item   8 697,7 ~kg~ = {\color{red}  86 977 }~hg
\item   2 831,7 ~km~ = {\color{red}  2 831 700 }~m
\item   347,94 ~dL~ = {\color{red}  0,347 94 }~hL
\item   330,51 ~cm~ = {\color{red}  33,051 }~dm
\end{itemize}
\end{multicols}
\end{document}
