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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 282}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{51}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{30}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   136  ~ \(\times\)  ~ 10
\item   0,034  ~ \(\times\)  ~ 1 000
\item   0,334  ~ \(\times\)  ~ 1 000
\item   0,596  ~ \(\times\)  ~ 1 000
\item   0,064  ~ \(\times\)  ~ 100
\item   0,015  ~ \(\times\)  ~ 100
\item   1,78  ~ \(\times\)  ~ 1 000
\item   4,03  ~ \(\times\)  ~ 100
\item   40,8  ~ \(\times\)  ~ 100
\item   0,721  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   478,7  ~ : ~ 100
\item   2 695  ~ : ~ 100
\item   38,22  ~ : ~ 1 000
\item   97,87  ~ : ~ 100
\item   3,363  ~ : ~ 1 000
\item   60,5  ~ : ~ 1 000
\item   389,3  ~ : ~ 1 000
\item   4,633  ~ : ~ 100
\item   483,5  ~ : ~ 10
\item   9 149  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42,4  ~ \(\times\)  ~ ... ~ = ~ 4 240
\item   660  ~ \(\times\)  ~ ... ~ = ~ 66 000
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 3,2
\item   136  ~ \(\times\)  ~ ... ~ = ~ 13 600
\item   0,492  ~ \(\times\)  ~ ... ~ = ~ 49,2
\item   10,5  ~ \(\times\)  ~ ... ~ = ~ 105
\item   91,2  ~ \(\times\)  ~ ... ~ = ~ 912
\item   0,31  ~ \(\times\)  ~ ... ~ = ~ 31
\item   0,267  ~ \(\times\)  ~ ... ~ = ~ 2,67
\item   0,099  ~ \(\times\)  ~ ... ~ = ~ 99
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 397  ~ \(\times\)  ~ 0,001
\item   15,66  ~ \(\times\)  ~ 0,01
\item   6 077  ~ \(\times\)  ~ 0,1
\item   8 056  ~ \(\times\)  ~ 0,01
\item   6,631  ~ \(\times\)  ~ 0,001
\item   773,2  ~ \(\times\)  ~ 0,001
\item   52,89  ~ \(\times\)  ~ 0,001
\item   79,69  ~ \(\times\)  ~ 0,001
\item   5,522  ~ \(\times\)  ~ 0,1
\item   147,5  ~ \(\times\)  ~ 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   46,3  ~ \(\times\)  ~ ... ~ = ~  0,046 3
\item   8 521  ~ \(\times\)  ~ ... ~ = ~  85,21
\item   231,3  ~ \(\times\)  ~ ... ~ = ~  0,231 3
\item   98,65  ~ \(\times\)  ~ ... ~ = ~  0,986 5
\item   7 595  ~ \(\times\)  ~ ... ~ = ~  75,95
\item   767,8  ~ \(\times\)  ~ ... ~ = ~  76,78
\item   6,722  ~ \(\times\)  ~ ... ~ = ~  0,672 2
\item   83,43  ~ \(\times\)  ~ ... ~ = ~  8,343
\item   8 720  ~ \(\times\)  ~ ... ~ = ~  872
\item   12,5  ~ \(\times\)  ~ ... ~ = ~  0,125
\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 ~hm~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   459,04 ~kL~ = ...~dL
\item   395,72 ~kg~ = ...~cg
\item   438,23 ~g~ = ...~hg
\item   9 528,5 ~dm~ = ...~mm
\item   160,72 ~cL~ = ...~kL
\item   462,29 ~kL~ = ...~L
\item   7 677,8 ~dg~ = ...~dag
\item   309,21 ~L~ = ...~kL
\item   9 937,2 ~m~ = ...~cm
\item   824,38 ~m~ = ...~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   1 = \(\dfrac{10}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{9800}{100}\) = \(\dfrac{980}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{51}{10}\) = \(\dfrac{510}{100}\)
\item   \(\dfrac{30}{100}\) = \(\dfrac{300}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   136  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 360}
\item   0,034  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 34}
\item   0,334  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 334}
\item   0,596  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 596}
\item   0,064  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,4}
\item   0,015  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,5}
\item   1,78  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 780}
\item   4,03  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 403}
\item   40,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 080}
\item   0,721  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 72,1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   478,7 ~ : ~ 100 ~ = ~{\color{red} 4,787}
\item   2 695 ~ : ~ 100 ~ = ~{\color{red} 26,95}
\item   38,22 ~ : ~ 1 000 ~ = ~{\color{red} 0,038 22}
\item   97,87 ~ : ~ 100 ~ = ~{\color{red} 0,978 7}
\item   3,363 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 363}
\item   60,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,060 5}
\item   389,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,389 3}
\item   4,633 ~ : ~ 100 ~ = ~{\color{red} 0,046 33}
\item   483,5 ~ : ~ 10 ~ = ~{\color{red} 48,35}
\item   9 149 ~ : ~ 1 000 ~ = ~{\color{red} 9,149}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 240
\item   660 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~66 000
\item   0,032 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,2
\item   136 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~13 600
\item   0,492 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~49,2
\item   10,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~105
\item   91,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~912
\item   0,31 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~31
\item   0,267 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,67
\item   0,099 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~99
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 397 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,397
}\item   15,66 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,156 6
}\item   6 077 ~ \(\times\)  0,1 ~ = ~{\color{red} 607,7
}\item   8 056 ~ \(\times\)  0,01 ~ = ~{\color{red} 80,56
}\item   6,631 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 631
}\item   773,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,773 2
}\item   52,89 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,052 89
}\item   79,69 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,079 69
}\item   5,522 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,552 2
}\item   147,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 14,75
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   46,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,046 3
\item   8 521 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 85,21
\item   231,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,231 3
\item   98,65 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,986 5
\item   7 595 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 75,95
\item   767,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 76,78
\item   6,722 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,672 2
\item   83,43 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,343
\item   8 720 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 872
\item   12,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,125
\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 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   459,04 ~kL~ = {\color{red}  4 590 400 }~dL
\item   395,72 ~kg~ = {\color{red}  39 572 000 }~cg
\item   438,23 ~g~ = {\color{red}  4,382 3 }~hg
\item   9 528,5 ~dm~ = {\color{red}  952 850 }~mm
\item   160,72 ~cL~ = {\color{red}  0,001 607 2 }~kL
\item   462,29 ~kL~ = {\color{red}  462 290 }~L
\item   7 677,8 ~dg~ = {\color{red}  76,778 }~dag
\item   309,21 ~L~ = {\color{red}  0,309 21 }~kL
\item   9 937,2 ~m~ = {\color{red}  993 720 }~cm
\item   824,38 ~m~ = {\color{red}  8 243,8 }~dm
\end{itemize}
\end{multicols}
\end{document}
