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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 345}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{24}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{35}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   38,5  ~ \(\times\)  ~ 100
\item   4,12  ~ \(\times\)  ~ 10
\item   6,96  ~ \(\times\)  ~ 10
\item   0,01  ~ \(\times\)  ~ 100
\item   0,1  ~ \(\times\)  ~ 10
\item   8,08  ~ \(\times\)  ~ 100
\item   0,851  ~ \(\times\)  ~ 1 000
\item   13,7  ~ \(\times\)  ~ 1 000
\item   2,79  ~ \(\times\)  ~ 100
\item   255  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 537  ~ : ~ 1 000
\item   6 016  ~ : ~ 1 000
\item   1 345  ~ : ~ 1 000
\item   872,8  ~ : ~ 10
\item   80,96  ~ : ~ 1 000
\item   9,451  ~ : ~ 1 000
\item   45,33  ~ : ~ 1 000
\item   497,4  ~ : ~ 1 000
\item   252,1  ~ : ~ 100
\item   18,42  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,028  ~ \(\times\)  ~ ... ~ = ~ 28
\item   6,4  ~ \(\times\)  ~ ... ~ = ~ 64
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 0,33
\item   5,5  ~ \(\times\)  ~ ... ~ = ~ 55
\item   7,41  ~ \(\times\)  ~ ... ~ = ~ 741
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 7
\item   387  ~ \(\times\)  ~ ... ~ = ~ 3 870
\item   928  ~ \(\times\)  ~ ... ~ = ~ 928 000
\item   0,096  ~ \(\times\)  ~ ... ~ = ~ 0,96
\item   0,06  ~ \(\times\)  ~ ... ~ = ~ 6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 816  ~ \(\times\)  ~ 0,1
\item   1 922  ~ \(\times\)  ~ 0,01
\item   855,4  ~ \(\times\)  ~ 0,001
\item   4,56  ~ \(\times\)  ~ 0,1
\item   173,6  ~ \(\times\)  ~ 0,01
\item   12,51  ~ \(\times\)  ~ 0,01
\item   8,042  ~ \(\times\)  ~ 0,001
\item   182,8  ~ \(\times\)  ~ 0,1
\item   1,796  ~ \(\times\)  ~ 0,001
\item   799,7  ~ \(\times\)  ~ 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   6 047  ~ \(\times\)  ~ ... ~ = ~  6,047
\item   84,08  ~ \(\times\)  ~ ... ~ = ~  0,084 08
\item   5 371  ~ \(\times\)  ~ ... ~ = ~  5,371
\item   66,64  ~ \(\times\)  ~ ... ~ = ~  0,066 64
\item   74,7  ~ \(\times\)  ~ ... ~ = ~  0,747
\item   887,7  ~ \(\times\)  ~ ... ~ = ~  0,887 7
\item   1,956  ~ \(\times\)  ~ ... ~ = ~  0,195 6
\item   20,29  ~ \(\times\)  ~ ... ~ = ~  0,202 9
\item   53,91  ~ \(\times\)  ~ ... ~ = ~  0,053 91
\item   646,5  ~ \(\times\)  ~ ... ~ = ~  64,65
\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~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   510,02 ~dag~ = ...~kg
\item   584,47 ~daL~ = ...~cL
\item   499,32 ~cm~ = ...~mm
\item   5 161,5 ~L~ = ...~hL
\item   142,57 ~cg~ = ...~g
\item   8 011,9 ~kg~ = ...~hg
\item   5 815,5 ~hg~ = ...~dag
\item   6 802,4 ~L~ = ...~dL
\item   7 764,8 ~hm~ = ...~dm
\item   1 789,8 ~cg~ = ...~kg
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{320}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{24}{10}\) = \(\dfrac{240}{100}\)
\item   \(\dfrac{35}{100}\) = \(\dfrac{350}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   38,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 850}
\item   4,12  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 41,2}
\item   6,96  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 69,6}
\item   0,01  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1}
\item   0,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1}
\item   8,08  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 808}
\item   0,851  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 851}
\item   13,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 13 700}
\item   2,79  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 279}
\item   255  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 25 500}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 537 ~ : ~ 1 000 ~ = ~{\color{red} 2,537}
\item   6 016 ~ : ~ 1 000 ~ = ~{\color{red} 6,016}
\item   1 345 ~ : ~ 1 000 ~ = ~{\color{red} 1,345}
\item   872,8 ~ : ~ 10 ~ = ~{\color{red} 87,28}
\item   80,96 ~ : ~ 1 000 ~ = ~{\color{red} 0,080 96}
\item   9,451 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 451}
\item   45,33 ~ : ~ 1 000 ~ = ~{\color{red} 0,045 33}
\item   497,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,497 4}
\item   252,1 ~ : ~ 100 ~ = ~{\color{red} 2,521}
\item   18,42 ~ : ~ 10 ~ = ~{\color{red} 1,842}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,028 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~28
\item   6,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~64
\item   0,033 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,33
\item   5,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~55
\item   7,41 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~741
\item   0,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7
\item   387 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 870
\item   928 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~928 000
\item   0,096 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,96
\item   0,06 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 816 ~ \(\times\)  0,1 ~ = ~{\color{red} 381,6
}\item   1 922 ~ \(\times\)  0,01 ~ = ~{\color{red} 19,22
}\item   855,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,855 4
}\item   4,56 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,456
}\item   173,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,736
}\item   12,51 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,125 1
}\item   8,042 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 042
}\item   182,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 18,28
}\item   1,796 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 796
}\item   799,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,799 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   6 047 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,047
\item   84,08 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,084 08
\item   5 371 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,371
\item   66,64 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,066 64
\item   74,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,747
\item   887,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,887 7
\item   1,956 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,195 6
\item   20,29 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,202 9
\item   53,91 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,053 91
\item   646,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 64,65
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   510,02 ~dag~ = {\color{red}  5,100 2 }~kg
\item   584,47 ~daL~ = {\color{red}  584 470 }~cL
\item   499,32 ~cm~ = {\color{red}  4 993,2 }~mm
\item   5 161,5 ~L~ = {\color{red}  51,615 }~hL
\item   142,57 ~cg~ = {\color{red}  1,425 7 }~g
\item   8 011,9 ~kg~ = {\color{red}  80 119 }~hg
\item   5 815,5 ~hg~ = {\color{red}  58 155 }~dag
\item   6 802,4 ~L~ = {\color{red}  68 024 }~dL
\item   7 764,8 ~hm~ = {\color{red}  7 764 800 }~dm
\item   1 789,8 ~cg~ = {\color{red}  0,017 898 }~kg
\end{itemize}
\end{multicols}
\end{document}
