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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 306}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{63}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{59}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,07  ~ \(\times\)  ~ 10
\item   0,062  ~ \(\times\)  ~ 10
\item   8,96  ~ \(\times\)  ~ 10
\item   0,087  ~ \(\times\)  ~ 1 000
\item   0,062  ~ \(\times\)  ~ 1 000
\item   2,68  ~ \(\times\)  ~ 100
\item   0,21  ~ \(\times\)  ~ 10
\item   5,6  ~ \(\times\)  ~ 1 000
\item   0,006  ~ \(\times\)  ~ 1 000
\item   2,98  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,6  ~ : ~ 10
\item   73,8  ~ : ~ 1 000
\item   0,237  ~ : ~ 100
\item   85,86  ~ : ~ 10
\item   9 064  ~ : ~ 100
\item   836,1  ~ : ~ 10
\item   23,82  ~ : ~ 100
\item   9,557  ~ : ~ 10
\item   64,24  ~ : ~ 10
\item   57,39  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   122  ~ \(\times\)  ~ ... ~ = ~ 122 000
\item   68,6  ~ \(\times\)  ~ ... ~ = ~ 686
\item   15,8  ~ \(\times\)  ~ ... ~ = ~ 1 580
\item   238  ~ \(\times\)  ~ ... ~ = ~ 2 380
\item   75,2  ~ \(\times\)  ~ ... ~ = ~ 75 200
\item   0,094  ~ \(\times\)  ~ ... ~ = ~ 0,94
\item   0,092  ~ \(\times\)  ~ ... ~ = ~ 0,92
\item   34,2  ~ \(\times\)  ~ ... ~ = ~ 342
\item   2,97  ~ \(\times\)  ~ ... ~ = ~ 2 970
\item   73,3  ~ \(\times\)  ~ ... ~ = ~ 7 330
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   492,8  ~ \(\times\)  ~ 0,1
\item   6 691  ~ \(\times\)  ~ 0,1
\item   4 622  ~ \(\times\)  ~ 0,01
\item   161  ~ \(\times\)  ~ 0,01
\item   9,409  ~ \(\times\)  ~ 0,01
\item   83,26  ~ \(\times\)  ~ 0,01
\item   12,66  ~ \(\times\)  ~ 0,01
\item   94,06  ~ \(\times\)  ~ 0,01
\item   7,489  ~ \(\times\)  ~ 0,01
\item   1,628  ~ \(\times\)  ~ 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   8 836  ~ \(\times\)  ~ ... ~ = ~  88,36
\item   4,342  ~ \(\times\)  ~ ... ~ = ~  0,004 342
\item   6 332  ~ \(\times\)  ~ ... ~ = ~  63,32
\item   18,99  ~ \(\times\)  ~ ... ~ = ~  0,189 9
\item   12,62  ~ \(\times\)  ~ ... ~ = ~  0,126 2
\item   9 108  ~ \(\times\)  ~ ... ~ = ~  9,108
\item   82,46  ~ \(\times\)  ~ ... ~ = ~  0,082 46
\item   782  ~ \(\times\)  ~ ... ~ = ~  7,82
\item   30,46  ~ \(\times\)  ~ ... ~ = ~  0,304 6
\item   742,3  ~ \(\times\)  ~ ... ~ = ~  0,742 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 ~m~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 450,6 ~hg~ = ...~g
\item   446,09 ~dL~ = ...~daL
\item   530,89 ~mm~ = ...~m
\item   3 539,3 ~dag~ = ...~kg
\item   3 395,8 ~dam~ = ...~m
\item   510,9 ~cg~ = ...~dag
\item   4 650,7 ~dm~ = ...~m
\item   9 512,2 ~m~ = ...~km
\item   640,63 ~mm~ = ...~dam
\item   680,83 ~daL~ = ...~hL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{4600}{100}\) = \(\dfrac{460}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{63}{10}\) = \(\dfrac{630}{100}\)
\item   \(\dfrac{59}{100}\) = \(\dfrac{590}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,07  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,7}
\item   0,062  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,62}
\item   8,96  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 89,6}
\item   0,087  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 87}
\item   0,062  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 62}
\item   2,68  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 268}
\item   0,21  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,1}
\item   5,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 600}
\item   0,006  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6}
\item   2,98  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 298}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   66,6 ~ : ~ 10 ~ = ~{\color{red} 6,66}
\item   73,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,073 8}
\item   0,237 ~ : ~ 100 ~ = ~{\color{red} 0,002 37}
\item   85,86 ~ : ~ 10 ~ = ~{\color{red} 8,586}
\item   9 064 ~ : ~ 100 ~ = ~{\color{red} 90,64}
\item   836,1 ~ : ~ 10 ~ = ~{\color{red} 83,61}
\item   23,82 ~ : ~ 100 ~ = ~{\color{red} 0,238 2}
\item   9,557 ~ : ~ 10 ~ = ~{\color{red} 0,955 7}
\item   64,24 ~ : ~ 10 ~ = ~{\color{red} 6,424}
\item   57,39 ~ : ~ 1 000 ~ = ~{\color{red} 0,057 39}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   122 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~122 000
\item   68,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~686
\item   15,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 580
\item   238 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 380
\item   75,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~75 200
\item   0,094 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,94
\item   0,092 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,92
\item   34,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~342
\item   2,97 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 970
\item   73,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 330
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   492,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 49,28
}\item   6 691 ~ \(\times\)  0,1 ~ = ~{\color{red} 669,1
}\item   4 622 ~ \(\times\)  0,01 ~ = ~{\color{red} 46,22
}\item   161 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,61
}\item   9,409 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,094 09
}\item   83,26 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,832 6
}\item   12,66 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,126 6
}\item   94,06 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,940 6
}\item   7,489 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,074 89
}\item   1,628 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 628
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 836 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 88,36
\item   4,342 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 342
\item   6 332 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 63,32
\item   18,99 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,189 9
\item   12,62 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,126 2
\item   9 108 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,108
\item   82,46 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,082 46
\item   782 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,82
\item   30,46 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,304 6
\item   742,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,742 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 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 450,6 ~hg~ = {\color{red}  845 060 }~g
\item   446,09 ~dL~ = {\color{red}  4,460 9 }~daL
\item   530,89 ~mm~ = {\color{red}  0,530 89 }~m
\item   3 539,3 ~dag~ = {\color{red}  35,393 }~kg
\item   3 395,8 ~dam~ = {\color{red}  33 958 }~m
\item   510,9 ~cg~ = {\color{red}  0,510 9 }~dag
\item   4 650,7 ~dm~ = {\color{red}  465,07 }~m
\item   9 512,2 ~m~ = {\color{red}  9,512 2 }~km
\item   640,63 ~mm~ = {\color{red}  0,064 063 }~dam
\item   680,83 ~daL~ = {\color{red}  68,083 }~hL
\end{itemize}
\end{multicols}
\end{document}
