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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 382}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   790  ~ \(\times\)  ~ 100
\item   0,604  ~ \(\times\)  ~ 1 000
\item   1,8  ~ \(\times\)  ~ 100
\item   905  ~ \(\times\)  ~ 1 000
\item   46,9  ~ \(\times\)  ~ 1 000
\item   71,7  ~ \(\times\)  ~ 100
\item   0,038  ~ \(\times\)  ~ 1 000
\item   95,2  ~ \(\times\)  ~ 100
\item   20,1  ~ \(\times\)  ~ 10
\item   97,5  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,26  ~ : ~ 100
\item   4 612  ~ : ~ 1 000
\item   6 242  ~ : ~ 100
\item   9,67  ~ : ~ 10
\item   9,875  ~ : ~ 10
\item   246,6  ~ : ~ 10
\item   3,649  ~ : ~ 10
\item   94,43  ~ : ~ 10
\item   2 267  ~ : ~ 100
\item   24,96  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,34  ~ \(\times\)  ~ ... ~ = ~ 83,4
\item   45,5  ~ \(\times\)  ~ ... ~ = ~ 455
\item   33,6  ~ \(\times\)  ~ ... ~ = ~ 3 360
\item   0,484  ~ \(\times\)  ~ ... ~ = ~ 484
\item   5,3  ~ \(\times\)  ~ ... ~ = ~ 530
\item   5,3  ~ \(\times\)  ~ ... ~ = ~ 5 300
\item   41,6  ~ \(\times\)  ~ ... ~ = ~ 4 160
\item   8,21  ~ \(\times\)  ~ ... ~ = ~ 82,1
\item   903  ~ \(\times\)  ~ ... ~ = ~ 9 030
\item   88,1  ~ \(\times\)  ~ ... ~ = ~ 88 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 757  ~ \(\times\)  ~ 0,001
\item   2,131  ~ \(\times\)  ~ 0,001
\item   747,9  ~ \(\times\)  ~ 0,001
\item   92,8  ~ \(\times\)  ~ 0,01
\item   9,187  ~ \(\times\)  ~ 0,1
\item   7,452  ~ \(\times\)  ~ 0,01
\item   153,8  ~ \(\times\)  ~ 0,1
\item   18,77  ~ \(\times\)  ~ 0,001
\item   9,267  ~ \(\times\)  ~ 0,1
\item   6 945  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   882,1  ~ \(\times\)  ~ ... ~ = ~  8,821
\item   5 783  ~ \(\times\)  ~ ... ~ = ~  57,83
\item   5 895  ~ \(\times\)  ~ ... ~ = ~  589,5
\item   3,74  ~ \(\times\)  ~ ... ~ = ~  0,037 4
\item   6 283  ~ \(\times\)  ~ ... ~ = ~  6,283
\item   22,89  ~ \(\times\)  ~ ... ~ = ~  2,289
\item   5 611  ~ \(\times\)  ~ ... ~ = ~  561,1
\item   8 079  ~ \(\times\)  ~ ... ~ = ~  8,079
\item   4,838  ~ \(\times\)  ~ ... ~ = ~  0,483 8
\item   93,61  ~ \(\times\)  ~ ... ~ = ~  0,936 1
\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 ~m~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 116,9 ~cg~ = ...~dg
\item   981,39 ~mL~ = ...~kL
\item   687,08 ~cL~ = ...~hL
\item   168,65 ~daL~ = ...~kL
\item   728,49 ~cL~ = ...~dL
\item   6 517 ~hg~ = ...~cg
\item   4 690,1 ~cg~ = ...~hg
\item   694,65 ~hL~ = ...~kL
\item   2 927,2 ~mL~ = ...~dL
\item   4 014,6 ~cm~ = ...~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   1 = \(\dfrac{10}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{2800}{100}\) = \(\dfrac{280}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{390}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{760}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   790  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 79 000}
\item   0,604  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 604}
\item   1,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 180}
\item   905  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 905 000}
\item   46,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 46 900}
\item   71,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 170}
\item   0,038  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 38}
\item   95,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 520}
\item   20,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 201}
\item   97,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 975}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,26 ~ : ~ 100 ~ = ~{\color{red} 0,692 6}
\item   4 612 ~ : ~ 1 000 ~ = ~{\color{red} 4,612}
\item   6 242 ~ : ~ 100 ~ = ~{\color{red} 62,42}
\item   9,67 ~ : ~ 10 ~ = ~{\color{red} 0,967}
\item   9,875 ~ : ~ 10 ~ = ~{\color{red} 0,987 5}
\item   246,6 ~ : ~ 10 ~ = ~{\color{red} 24,66}
\item   3,649 ~ : ~ 10 ~ = ~{\color{red} 0,364 9}
\item   94,43 ~ : ~ 10 ~ = ~{\color{red} 9,443}
\item   2 267 ~ : ~ 100 ~ = ~{\color{red} 22,67}
\item   24,96 ~ : ~ 10 ~ = ~{\color{red} 2,496}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~83,4
\item   45,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~455
\item   33,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 360
\item   0,484 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~484
\item   5,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~530
\item   5,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 300
\item   41,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 160
\item   8,21 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~82,1
\item   903 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 030
\item   88,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~88 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 757 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,757
}\item   2,131 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 131
}\item   747,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,747 9
}\item   92,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,928
}\item   9,187 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,918 7
}\item   7,452 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,074 52
}\item   153,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 15,38
}\item   18,77 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,018 77
}\item   9,267 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,926 7
}\item   6 945 ~ \(\times\)  0,01 ~ = ~{\color{red} 69,45
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   882,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,821
\item   5 783 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 57,83
\item   5 895 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 589,5
\item   3,74 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,037 4
\item   6 283 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,283
\item   22,89 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,289
\item   5 611 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 561,1
\item   8 079 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,079
\item   4,838 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,483 8
\item   93,61 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,936 1
\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 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ 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   3 116,9 ~cg~ = {\color{red}  311,69 }~dg
\item   981,39 ~mL~ = {\color{red}  0,000 981 39 }~kL
\item   687,08 ~cL~ = {\color{red}  0,068 708 }~hL
\item   168,65 ~daL~ = {\color{red}  1,686 5 }~kL
\item   728,49 ~cL~ = {\color{red}  72,849 }~dL
\item   6 517 ~hg~ = {\color{red}  65 170 000 }~cg
\item   4 690,1 ~cg~ = {\color{red}  0,469 01 }~hg
\item   694,65 ~hL~ = {\color{red}  69,465 }~kL
\item   2 927,2 ~mL~ = {\color{red}  29,272 }~dL
\item   4 014,6 ~cm~ = {\color{red}  0,401 46 }~hm
\end{itemize}
\end{multicols}
\end{document}
