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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 82}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{33}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{32}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,05  ~ \(\times\)  ~ 10
\item   790  ~ \(\times\)  ~ 100
\item   0,049  ~ \(\times\)  ~ 10
\item   2,11  ~ \(\times\)  ~ 1 000
\item   87  ~ \(\times\)  ~ 10
\item   502  ~ \(\times\)  ~ 1 000
\item   3,42  ~ \(\times\)  ~ 100
\item   0,098  ~ \(\times\)  ~ 10
\item   866  ~ \(\times\)  ~ 10
\item   3,74  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,28  ~ : ~ 1 000
\item   7,329  ~ : ~ 100
\item   4,846  ~ : ~ 1 000
\item   4 247  ~ : ~ 100
\item   4 999  ~ : ~ 1 000
\item   41,15  ~ : ~ 10
\item   3 589  ~ : ~ 100
\item   2 125  ~ : ~ 1 000
\item   5 625  ~ : ~ 100
\item   6 869  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,037  ~ \(\times\)  ~ ... ~ = ~ 0,37
\item   696  ~ \(\times\)  ~ ... ~ = ~ 696 000
\item   0,903  ~ \(\times\)  ~ ... ~ = ~ 90,3
\item   985  ~ \(\times\)  ~ ... ~ = ~ 9 850
\item   0,541  ~ \(\times\)  ~ ... ~ = ~ 541
\item   0,039  ~ \(\times\)  ~ ... ~ = ~ 3,9
\item   0,88  ~ \(\times\)  ~ ... ~ = ~ 8,8
\item   0,698  ~ \(\times\)  ~ ... ~ = ~ 69,8
\item   0,411  ~ \(\times\)  ~ ... ~ = ~ 41,1
\item   635  ~ \(\times\)  ~ ... ~ = ~ 635 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,377  ~ \(\times\)  ~ 0,01
\item   4 079  ~ \(\times\)  ~ 0,1
\item   6,485  ~ \(\times\)  ~ 0,001
\item   567,1  ~ \(\times\)  ~ 0,1
\item   7,111  ~ \(\times\)  ~ 0,001
\item   23,87  ~ \(\times\)  ~ 0,01
\item   275,5  ~ \(\times\)  ~ 0,01
\item   764,2  ~ \(\times\)  ~ 0,001
\item   650,5  ~ \(\times\)  ~ 0,1
\item   4 170  ~ \(\times\)  ~ 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   5,547  ~ \(\times\)  ~ ... ~ = ~  0,055 47
\item   23,91  ~ \(\times\)  ~ ... ~ = ~  2,391
\item   7,282  ~ \(\times\)  ~ ... ~ = ~  0,007 282
\item   80,32  ~ \(\times\)  ~ ... ~ = ~  8,032
\item   1 980  ~ \(\times\)  ~ ... ~ = ~  1,98
\item   34,92  ~ \(\times\)  ~ ... ~ = ~  0,349 2
\item   8 295  ~ \(\times\)  ~ ... ~ = ~  8,295
\item   311,9  ~ \(\times\)  ~ ... ~ = ~  3,119
\item   7,56  ~ \(\times\)  ~ ... ~ = ~  0,007 56
\item   4,708  ~ \(\times\)  ~ ... ~ = ~  0,047 08
\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~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~hm~ = ...~km
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 124,9 ~mg~ = ...~cg
\item   181,93 ~dam~ = ...~mm
\item   9 545 ~dam~ = ...~m
\item   1 881,5 ~dm~ = ...~mm
\item   825,06 ~hL~ = ...~cL
\item   2 169,2 ~hg~ = ...~dg
\item   119,3 ~mL~ = ...~hL
\item   6 267 ~mL~ = ...~kL
\item   5 634,2 ~m~ = ...~dam
\item   7 163,9 ~mL~ = ...~dL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{750}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{33}{10}\) = \(\dfrac{330}{100}\)
\item   \(\dfrac{32}{100}\) = \(\dfrac{320}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,05  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 70,5}
\item   790  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 79 000}
\item   0,049  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,49}
\item   2,11  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 110}
\item   87  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 870}
\item   502  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 502 000}
\item   3,42  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 342}
\item   0,098  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,98}
\item   866  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 660}
\item   3,74  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 37,4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   89,28 ~ : ~ 1 000 ~ = ~{\color{red} 0,089 28}
\item   7,329 ~ : ~ 100 ~ = ~{\color{red} 0,073 29}
\item   4,846 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 846}
\item   4 247 ~ : ~ 100 ~ = ~{\color{red} 42,47}
\item   4 999 ~ : ~ 1 000 ~ = ~{\color{red} 4,999}
\item   41,15 ~ : ~ 10 ~ = ~{\color{red} 4,115}
\item   3 589 ~ : ~ 100 ~ = ~{\color{red} 35,89}
\item   2 125 ~ : ~ 1 000 ~ = ~{\color{red} 2,125}
\item   5 625 ~ : ~ 100 ~ = ~{\color{red} 56,25}
\item   6 869 ~ : ~ 100 ~ = ~{\color{red} 68,69}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,037 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,37
\item   696 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~696 000
\item   0,903 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~90,3
\item   985 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9 850
\item   0,541 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~541
\item   0,039 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,9
\item   0,88 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,8
\item   0,698 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~69,8
\item   0,411 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~41,1
\item   635 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~635 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,377 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,083 77
}\item   4 079 ~ \(\times\)  0,1 ~ = ~{\color{red} 407,9
}\item   6,485 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 485
}\item   567,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 56,71
}\item   7,111 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 111
}\item   23,87 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,238 7
}\item   275,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,755
}\item   764,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,764 2
}\item   650,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 65,05
}\item   4 170 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,17
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,547 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,055 47
\item   23,91 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,391
\item   7,282 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 282
\item   80,32 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,032
\item   1 980 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,98
\item   34,92 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,349 2
\item   8 295 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,295
\item   311,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,119
\item   7,56 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 56
\item   4,708 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,047 08
\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~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 124,9 ~mg~ = {\color{red}  412,49 }~cg
\item   181,93 ~dam~ = {\color{red}  1 819 300 }~mm
\item   9 545 ~dam~ = {\color{red}  95 450 }~m
\item   1 881,5 ~dm~ = {\color{red}  188 150 }~mm
\item   825,06 ~hL~ = {\color{red}  8 250 600 }~cL
\item   2 169,2 ~hg~ = {\color{red}  2 169 200 }~dg
\item   119,3 ~mL~ = {\color{red}  0,001 193 }~hL
\item   6 267 ~mL~ = {\color{red}  0,006 267 }~kL
\item   5 634,2 ~m~ = {\color{red}  563,42 }~dam
\item   7 163,9 ~mL~ = {\color{red}  71,639 }~dL
\end{itemize}
\end{multicols}
\end{document}
