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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 103}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{88}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{26}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,679  ~ \(\times\)  ~ 100
\item   9,2  ~ \(\times\)  ~ 1 000
\item   0,13  ~ \(\times\)  ~ 10
\item   14,4  ~ \(\times\)  ~ 1 000
\item   856  ~ \(\times\)  ~ 10
\item   239  ~ \(\times\)  ~ 1 000
\item   0,014  ~ \(\times\)  ~ 1 000
\item   30,9  ~ \(\times\)  ~ 1 000
\item   0,043  ~ \(\times\)  ~ 1 000
\item   0,697  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   948  ~ : ~ 10
\item   614,8  ~ : ~ 1 000
\item   3,681  ~ : ~ 100
\item   471  ~ : ~ 1 000
\item   763,1  ~ : ~ 1 000
\item   86,77  ~ : ~ 10
\item   799,1  ~ : ~ 10
\item   69,84  ~ : ~ 10
\item   79,85  ~ : ~ 10
\item   15,76  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   692  ~ \(\times\)  ~ ... ~ = ~ 692 000
\item   793  ~ \(\times\)  ~ ... ~ = ~ 793 000
\item   4,01  ~ \(\times\)  ~ ... ~ = ~ 40,1
\item   0,572  ~ \(\times\)  ~ ... ~ = ~ 572
\item   0,644  ~ \(\times\)  ~ ... ~ = ~ 64,4
\item   0,847  ~ \(\times\)  ~ ... ~ = ~ 84,7
\item   776  ~ \(\times\)  ~ ... ~ = ~ 7 760
\item   464  ~ \(\times\)  ~ ... ~ = ~ 46 400
\item   6,71  ~ \(\times\)  ~ ... ~ = ~ 67,1
\item   56,5  ~ \(\times\)  ~ ... ~ = ~ 56 500
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   399,6  ~ \(\times\)  ~ 0,1
\item   642,9  ~ \(\times\)  ~ 0,001
\item   1,483  ~ \(\times\)  ~ 0,1
\item   7,922  ~ \(\times\)  ~ 0,01
\item   155,9  ~ \(\times\)  ~ 0,001
\item   6,78  ~ \(\times\)  ~ 0,01
\item   3 901  ~ \(\times\)  ~ 0,01
\item   5,171  ~ \(\times\)  ~ 0,1
\item   30,81  ~ \(\times\)  ~ 0,01
\item   8 777  ~ \(\times\)  ~ 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   80,79  ~ \(\times\)  ~ ... ~ = ~  8,079
\item   5 545  ~ \(\times\)  ~ ... ~ = ~  554,5
\item   639,2  ~ \(\times\)  ~ ... ~ = ~  6,392
\item   71,25  ~ \(\times\)  ~ ... ~ = ~  0,712 5
\item   89,5  ~ \(\times\)  ~ ... ~ = ~  0,895
\item   42,31  ~ \(\times\)  ~ ... ~ = ~  0,042 31
\item   0,655  ~ \(\times\)  ~ ... ~ = ~  0,000 655
\item   74,95  ~ \(\times\)  ~ ... ~ = ~  0,749 5
\item   241,6  ~ \(\times\)  ~ ... ~ = ~  2,416
\item   7 373  ~ \(\times\)  ~ ... ~ = ~  737,3
\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~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   239,75 ~m~ = ...~dam
\item   640,9 ~hL~ = ...~daL
\item   8 229,2 ~mL~ = ...~dL
\item   173,67 ~cm~ = ...~mm
\item   920,78 ~cL~ = ...~dL
\item   5 702,3 ~mg~ = ...~hg
\item   269,62 ~cL~ = ...~L
\item   9 937 ~cg~ = ...~hg
\item   931,42 ~hm~ = ...~dam
\item   7 484,9 ~hg~ = ...~dag
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{9900}{100}\) = \(\dfrac{990}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{88}{10}\) = \(\dfrac{880}{100}\)
\item   \(\dfrac{26}{100}\) = \(\dfrac{260}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,679  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 67,9}
\item   9,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 200}
\item   0,13  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,3}
\item   14,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 14 400}
\item   856  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 560}
\item   239  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 239 000}
\item   0,014  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 14}
\item   30,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 30 900}
\item   0,043  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 43}
\item   0,697  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,97}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   948 ~ : ~ 10 ~ = ~{\color{red} 94,8}
\item   614,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,614 8}
\item   3,681 ~ : ~ 100 ~ = ~{\color{red} 0,036 81}
\item   471 ~ : ~ 1 000 ~ = ~{\color{red} 0,471}
\item   763,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,763 1}
\item   86,77 ~ : ~ 10 ~ = ~{\color{red} 8,677}
\item   799,1 ~ : ~ 10 ~ = ~{\color{red} 79,91}
\item   69,84 ~ : ~ 10 ~ = ~{\color{red} 6,984}
\item   79,85 ~ : ~ 10 ~ = ~{\color{red} 7,985}
\item   15,76 ~ : ~ 100 ~ = ~{\color{red} 0,157 6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   692 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~692 000
\item   793 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~793 000
\item   4,01 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~40,1
\item   0,572 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~572
\item   0,644 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~64,4
\item   0,847 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~84,7
\item   776 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 760
\item   464 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~46 400
\item   6,71 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~67,1
\item   56,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~56 500
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   399,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 39,96
}\item   642,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,642 9
}\item   1,483 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,148 3
}\item   7,922 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,079 22
}\item   155,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,155 9
}\item   6,78 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,067 8
}\item   3 901 ~ \(\times\)  0,01 ~ = ~{\color{red} 39,01
}\item   5,171 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,517 1
}\item   30,81 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,308 1
}\item   8 777 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,777
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   80,79 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,079
\item   5 545 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 554,5
\item   639,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,392
\item   71,25 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,712 5
\item   89,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,895
\item   42,31 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,042 31
\item   0,655 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 655
\item   74,95 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,749 5
\item   241,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,416
\item   7 373 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 737,3
\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~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\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   239,75 ~m~ = {\color{red}  23,975 }~dam
\item   640,9 ~hL~ = {\color{red}  6 409 }~daL
\item   8 229,2 ~mL~ = {\color{red}  82,292 }~dL
\item   173,67 ~cm~ = {\color{red}  1 736,7 }~mm
\item   920,78 ~cL~ = {\color{red}  92,078 }~dL
\item   5 702,3 ~mg~ = {\color{red}  0,057 023 }~hg
\item   269,62 ~cL~ = {\color{red}  2,696 2 }~L
\item   9 937 ~cg~ = {\color{red}  0,993 7 }~hg
\item   931,42 ~hm~ = {\color{red}  9 314,2 }~dam
\item   7 484,9 ~hg~ = {\color{red}  74 849 }~dag
\end{itemize}
\end{multicols}
\end{document}
