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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 134}

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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   \(\dfrac{8200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{14}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{94}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,79  ~ \(\times\)  ~ 10
\item   40,6  ~ \(\times\)  ~ 100
\item   0,026  ~ \(\times\)  ~ 1 000
\item   475  ~ \(\times\)  ~ 10
\item   0,03  ~ \(\times\)  ~ 1 000
\item   8,31  ~ \(\times\)  ~ 100
\item   936  ~ \(\times\)  ~ 1 000
\item   6,04  ~ \(\times\)  ~ 1 000
\item   0,902  ~ \(\times\)  ~ 1 000
\item   7,38  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43,57  ~ : ~ 10
\item   8,65  ~ : ~ 1 000
\item   48,23  ~ : ~ 1 000
\item   5 487  ~ : ~ 10
\item   653,4  ~ : ~ 10
\item   2 353  ~ : ~ 10
\item   16,86  ~ : ~ 10
\item   44,23  ~ : ~ 100
\item   33,88  ~ : ~ 1 000
\item   2 625  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   86,1  ~ \(\times\)  ~ ... ~ = ~ 861
\item   0,039  ~ \(\times\)  ~ ... ~ = ~ 39
\item   0,01  ~ \(\times\)  ~ ... ~ = ~ 10
\item   854  ~ \(\times\)  ~ ... ~ = ~ 8 540
\item   647  ~ \(\times\)  ~ ... ~ = ~ 6 470
\item   42,2  ~ \(\times\)  ~ ... ~ = ~ 422
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 0,22
\item   0,08  ~ \(\times\)  ~ ... ~ = ~ 80
\item   0,094  ~ \(\times\)  ~ ... ~ = ~ 0,94
\item   64,5  ~ \(\times\)  ~ ... ~ = ~ 6 450
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,974  ~ \(\times\)  ~ 0,1
\item   5 298  ~ \(\times\)  ~ 0,1
\item   2,79  ~ \(\times\)  ~ 0,01
\item   8 596  ~ \(\times\)  ~ 0,1
\item   5 824  ~ \(\times\)  ~ 0,1
\item   5,835  ~ \(\times\)  ~ 0,1
\item   11,2  ~ \(\times\)  ~ 0,01
\item   39,53  ~ \(\times\)  ~ 0,01
\item   1 079  ~ \(\times\)  ~ 0,001
\item   7 759  ~ \(\times\)  ~ 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   4 252  ~ \(\times\)  ~ ... ~ = ~  4,252
\item   54,77  ~ \(\times\)  ~ ... ~ = ~  0,547 7
\item   7,339  ~ \(\times\)  ~ ... ~ = ~  0,073 39
\item   50,42  ~ \(\times\)  ~ ... ~ = ~  5,042
\item   7,562  ~ \(\times\)  ~ ... ~ = ~  0,007 562
\item   3,704  ~ \(\times\)  ~ ... ~ = ~  0,003 704
\item   80,71  ~ \(\times\)  ~ ... ~ = ~  0,807 1
\item   16,16  ~ \(\times\)  ~ ... ~ = ~  1,616
\item   6 622  ~ \(\times\)  ~ ... ~ = ~  6,622
\item   3 205  ~ \(\times\)  ~ ... ~ = ~  3,205
\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~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 530,7 ~daL~ = ...~hL
\item   9 801,1 ~kL~ = ...~dL
\item   744,68 ~hL~ = ...~mL
\item   722,51 ~hL~ = ...~dL
\item   9 477,6 ~cm~ = ...~dm
\item   973,52 ~kg~ = ...~g
\item   5 109,2 ~dag~ = ...~cg
\item   9 170,4 ~cm~ = ...~mm
\item   3 150,1 ~g~ = ...~kg
\item   711,48 ~m~ = ...~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   8 = \(\dfrac{80}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{8200}{100}\) = \(\dfrac{820}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{14}{10}\) = \(\dfrac{140}{100}\)
\item   \(\dfrac{94}{100}\) = \(\dfrac{940}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,79  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,9}
\item   40,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 060}
\item   0,026  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 26}
\item   475  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 750}
\item   0,03  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 30}
\item   8,31  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 831}
\item   936  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 936 000}
\item   6,04  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 040}
\item   0,902  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 902}
\item   7,38  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 380}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   43,57 ~ : ~ 10 ~ = ~{\color{red} 4,357}
\item   8,65 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 65}
\item   48,23 ~ : ~ 1 000 ~ = ~{\color{red} 0,048 23}
\item   5 487 ~ : ~ 10 ~ = ~{\color{red} 548,7}
\item   653,4 ~ : ~ 10 ~ = ~{\color{red} 65,34}
\item   2 353 ~ : ~ 10 ~ = ~{\color{red} 235,3}
\item   16,86 ~ : ~ 10 ~ = ~{\color{red} 1,686}
\item   44,23 ~ : ~ 100 ~ = ~{\color{red} 0,442 3}
\item   33,88 ~ : ~ 1 000 ~ = ~{\color{red} 0,033 88}
\item   2 625 ~ : ~ 100 ~ = ~{\color{red} 26,25}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   86,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~861
\item   0,039 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~39
\item   0,01 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~10
\item   854 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 540
\item   647 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 470
\item   42,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~422
\item   0,022 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,22
\item   0,08 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~80
\item   0,094 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,94
\item   64,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 450
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,974 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,597 4
}\item   5 298 ~ \(\times\)  0,1 ~ = ~{\color{red} 529,8
}\item   2,79 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,027 9
}\item   8 596 ~ \(\times\)  0,1 ~ = ~{\color{red} 859,6
}\item   5 824 ~ \(\times\)  0,1 ~ = ~{\color{red} 582,4
}\item   5,835 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,583 5
}\item   11,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,112
}\item   39,53 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,395 3
}\item   1 079 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,079
}\item   7 759 ~ \(\times\)  0,1 ~ = ~{\color{red} 775,9
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 252 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,252
\item   54,77 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,547 7
\item   7,339 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,073 39
\item   50,42 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,042
\item   7,562 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 562
\item   3,704 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 704
\item   80,71 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,807 1
\item   16,16 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,616
\item   6 622 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,622
\item   3 205 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,205
\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 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 530,7 ~daL~ = {\color{red}  253,07 }~hL
\item   9 801,1 ~kL~ = {\color{red}  98 011 000 }~dL
\item   744,68 ~hL~ = {\color{red}  74 468 000 }~mL
\item   722,51 ~hL~ = {\color{red}  722 510 }~dL
\item   9 477,6 ~cm~ = {\color{red}  947,76 }~dm
\item   973,52 ~kg~ = {\color{red}  973 520 }~g
\item   5 109,2 ~dag~ = {\color{red}  5 109 200 }~cg
\item   9 170,4 ~cm~ = {\color{red}  91 704 }~mm
\item   3 150,1 ~g~ = {\color{red}  3,150 1 }~kg
\item   711,48 ~m~ = {\color{red}  7,114 8 }~hm
\end{itemize}
\end{multicols}
\end{document}
