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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 296}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{97}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,066  ~ \(\times\)  ~ 100
\item   91,5  ~ \(\times\)  ~ 10
\item   839  ~ \(\times\)  ~ 100
\item   76,6  ~ \(\times\)  ~ 1 000
\item   85,4  ~ \(\times\)  ~ 10
\item   0,043  ~ \(\times\)  ~ 100
\item   0,016  ~ \(\times\)  ~ 10
\item   699  ~ \(\times\)  ~ 10
\item   0,023  ~ \(\times\)  ~ 100
\item   0,93  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   882,4  ~ : ~ 1 000
\item   45,49  ~ : ~ 10
\item   9,321  ~ : ~ 1 000
\item   87,54  ~ : ~ 1 000
\item   71,89  ~ : ~ 100
\item   90,97  ~ : ~ 100
\item   37,35  ~ : ~ 10
\item   30,12  ~ : ~ 1 000
\item   894  ~ : ~ 10
\item   1,904  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,218  ~ \(\times\)  ~ ... ~ = ~ 21,8
\item   48,4  ~ \(\times\)  ~ ... ~ = ~ 484
\item   733  ~ \(\times\)  ~ ... ~ = ~ 7 330
\item   0,386  ~ \(\times\)  ~ ... ~ = ~ 386
\item   584  ~ \(\times\)  ~ ... ~ = ~ 5 840
\item   0,001  ~ \(\times\)  ~ ... ~ = ~ 0,1
\item   52,5  ~ \(\times\)  ~ ... ~ = ~ 52 500
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 6,4
\item   22,5  ~ \(\times\)  ~ ... ~ = ~ 225
\item   9,09  ~ \(\times\)  ~ ... ~ = ~ 909
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,17  ~ \(\times\)  ~ 0,001
\item   567,8  ~ \(\times\)  ~ 0,001
\item   23,89  ~ \(\times\)  ~ 0,1
\item   55,43  ~ \(\times\)  ~ 0,01
\item   83,49  ~ \(\times\)  ~ 0,001
\item   1,518  ~ \(\times\)  ~ 0,001
\item   3,152  ~ \(\times\)  ~ 0,1
\item   7,12  ~ \(\times\)  ~ 0,01
\item   4,456  ~ \(\times\)  ~ 0,01
\item   71,11  ~ \(\times\)  ~ 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   75,39  ~ \(\times\)  ~ ... ~ = ~  0,753 9
\item   7 712  ~ \(\times\)  ~ ... ~ = ~  77,12
\item   13,26  ~ \(\times\)  ~ ... ~ = ~  1,326
\item   9 234  ~ \(\times\)  ~ ... ~ = ~  923,4
\item   739,4  ~ \(\times\)  ~ ... ~ = ~  73,94
\item   772,4  ~ \(\times\)  ~ ... ~ = ~  77,24
\item   757,8  ~ \(\times\)  ~ ... ~ = ~  0,757 8
\item   590,9  ~ \(\times\)  ~ ... ~ = ~  0,590 9
\item   4 841  ~ \(\times\)  ~ ... ~ = ~  48,41
\item   27,67  ~ \(\times\)  ~ ... ~ = ~  0,027 67
\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 ~cm~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 353,3 ~dam~ = ...~m
\item   7 859,1 ~L~ = ...~dL
\item   1 153,4 ~m~ = ...~dam
\item   497,53 ~dg~ = ...~kg
\item   390,39 ~m~ = ...~km
\item   7 054,9 ~mL~ = ...~cL
\item   5 322,8 ~dg~ = ...~dag
\item   2 043,9 ~dL~ = ...~L
\item   785,6 ~kL~ = ...~daL
\item   5 215,6 ~hg~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{5800}{100}\) = \(\dfrac{580}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{97}{10}\) = \(\dfrac{970}{100}\)
\item   \(\dfrac{16}{100}\) = \(\dfrac{160}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,066  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6,6}
\item   91,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 915}
\item   839  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 83 900}
\item   76,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 76 600}
\item   85,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 854}
\item   0,043  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,3}
\item   0,016  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,16}
\item   699  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6 990}
\item   0,023  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,3}
\item   0,93  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 93}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   882,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,882 4}
\item   45,49 ~ : ~ 10 ~ = ~{\color{red} 4,549}
\item   9,321 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 321}
\item   87,54 ~ : ~ 1 000 ~ = ~{\color{red} 0,087 54}
\item   71,89 ~ : ~ 100 ~ = ~{\color{red} 0,718 9}
\item   90,97 ~ : ~ 100 ~ = ~{\color{red} 0,909 7}
\item   37,35 ~ : ~ 10 ~ = ~{\color{red} 3,735}
\item   30,12 ~ : ~ 1 000 ~ = ~{\color{red} 0,030 12}
\item   894 ~ : ~ 10 ~ = ~{\color{red} 89,4}
\item   1,904 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 904}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,218 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~21,8
\item   48,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~484
\item   733 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 330
\item   0,386 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~386
\item   584 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 840
\item   0,001 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,1
\item   52,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~52 500
\item   0,064 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,4
\item   22,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~225
\item   9,09 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~909
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,17 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,041 17
}\item   567,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,567 8
}\item   23,89 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,389
}\item   55,43 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,554 3
}\item   83,49 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,083 49
}\item   1,518 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 518
}\item   3,152 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,315 2
}\item   7,12 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,071 2
}\item   4,456 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,044 56
}\item   71,11 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,071 11
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   75,39 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,753 9
\item   7 712 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 77,12
\item   13,26 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,326
\item   9 234 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 923,4
\item   739,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 73,94
\item   772,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 77,24
\item   757,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,757 8
\item   590,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,590 9
\item   4 841 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 48,41
\item   27,67 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,027 67
\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 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 353,3 ~dam~ = {\color{red}  73 533 }~m
\item   7 859,1 ~L~ = {\color{red}  78 591 }~dL
\item   1 153,4 ~m~ = {\color{red}  115,34 }~dam
\item   497,53 ~dg~ = {\color{red}  0,049 753 }~kg
\item   390,39 ~m~ = {\color{red}  0,390 39 }~km
\item   7 054,9 ~mL~ = {\color{red}  705,49 }~cL
\item   5 322,8 ~dg~ = {\color{red}  53,228 }~dag
\item   2 043,9 ~dL~ = {\color{red}  204,39 }~L
\item   785,6 ~kL~ = {\color{red}  78 560 }~daL
\item   5 215,6 ~hg~ = {\color{red}  5 215 600 }~dg
\end{itemize}
\end{multicols}
\end{document}
