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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 302}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{15}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   41,6  ~ \(\times\)  ~ 1 000
\item   0,802  ~ \(\times\)  ~ 100
\item   800  ~ \(\times\)  ~ 1 000
\item   0,068  ~ \(\times\)  ~ 10
\item   66,3  ~ \(\times\)  ~ 1 000
\item   0,014  ~ \(\times\)  ~ 10
\item   0,07  ~ \(\times\)  ~ 10
\item   8,92  ~ \(\times\)  ~ 100
\item   0,878  ~ \(\times\)  ~ 100
\item   0,556  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   484,4  ~ : ~ 10
\item   11,12  ~ : ~ 10
\item   69,03  ~ : ~ 10
\item   4,762  ~ : ~ 1 000
\item   417,4  ~ : ~ 10
\item   4 164  ~ : ~ 10
\item   7,853  ~ : ~ 10
\item   8,621  ~ : ~ 10
\item   4 829  ~ : ~ 100
\item   375,9  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   276  ~ \(\times\)  ~ ... ~ = ~ 2 760
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 88
\item   0,153  ~ \(\times\)  ~ ... ~ = ~ 153
\item   56  ~ \(\times\)  ~ ... ~ = ~ 5 600
\item   50  ~ \(\times\)  ~ ... ~ = ~ 50 000
\item   0,955  ~ \(\times\)  ~ ... ~ = ~ 9,55
\item   0,378  ~ \(\times\)  ~ ... ~ = ~ 37,8
\item   1,64  ~ \(\times\)  ~ ... ~ = ~ 1 640
\item   7,35  ~ \(\times\)  ~ ... ~ = ~ 735
\item   0,833  ~ \(\times\)  ~ ... ~ = ~ 8,33
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   25,81  ~ \(\times\)  ~ 0,01
\item   5,219  ~ \(\times\)  ~ 0,001
\item   2,312  ~ \(\times\)  ~ 0,001
\item   3,552  ~ \(\times\)  ~ 0,001
\item   604,9  ~ \(\times\)  ~ 0,01
\item   924,7  ~ \(\times\)  ~ 0,01
\item   1,063  ~ \(\times\)  ~ 0,1
\item   89,53  ~ \(\times\)  ~ 0,01
\item   38,68  ~ \(\times\)  ~ 0,01
\item   1,123  ~ \(\times\)  ~ 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   1,987  ~ \(\times\)  ~ ... ~ = ~  0,198 7
\item   1 678  ~ \(\times\)  ~ ... ~ = ~  167,8
\item   71,44  ~ \(\times\)  ~ ... ~ = ~  0,071 44
\item   2 134  ~ \(\times\)  ~ ... ~ = ~  213,4
\item   7,144  ~ \(\times\)  ~ ... ~ = ~  0,007 144
\item   33,47  ~ \(\times\)  ~ ... ~ = ~  0,033 47
\item   23,21  ~ \(\times\)  ~ ... ~ = ~  0,023 21
\item   7,619  ~ \(\times\)  ~ ... ~ = ~  0,761 9
\item   31,21  ~ \(\times\)  ~ ... ~ = ~  0,312 1
\item   94,5  ~ \(\times\)  ~ ... ~ = ~  0,945
\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 ~dam~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 272,3 ~dg~ = ...~g
\item   8 851,8 ~mm~ = ...~cm
\item   878,17 ~dg~ = ...~kg
\item   836,94 ~kg~ = ...~dag
\item   969,78 ~g~ = ...~mg
\item   4 078,5 ~mL~ = ...~cL
\item   4 969,4 ~km~ = ...~dm
\item   2 477,2 ~mL~ = ...~hL
\item   2 655,9 ~dag~ = ...~hg
\item   2 628,5 ~hm~ = ...~mm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{7100}{100}\) = \(\dfrac{710}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{15}{10}\) = \(\dfrac{150}{100}\)
\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   41,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 41 600}
\item   0,802  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80,2}
\item   800  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 800 000}
\item   0,068  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,68}
\item   66,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 66 300}
\item   0,014  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,14}
\item   0,07  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,7}
\item   8,92  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 892}
\item   0,878  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 87,8}
\item   0,556  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 55,6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   484,4 ~ : ~ 10 ~ = ~{\color{red} 48,44}
\item   11,12 ~ : ~ 10 ~ = ~{\color{red} 1,112}
\item   69,03 ~ : ~ 10 ~ = ~{\color{red} 6,903}
\item   4,762 ~ : ~ 1 000 ~ = ~{\color{red} 0,004 762}
\item   417,4 ~ : ~ 10 ~ = ~{\color{red} 41,74}
\item   4 164 ~ : ~ 10 ~ = ~{\color{red} 416,4}
\item   7,853 ~ : ~ 10 ~ = ~{\color{red} 0,785 3}
\item   8,621 ~ : ~ 10 ~ = ~{\color{red} 0,862 1}
\item   4 829 ~ : ~ 100 ~ = ~{\color{red} 48,29}
\item   375,9 ~ : ~ 10 ~ = ~{\color{red} 37,59}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   276 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 760
\item   0,088 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~88
\item   0,153 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~153
\item   56 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 600
\item   50 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~50 000
\item   0,955 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,55
\item   0,378 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~37,8
\item   1,64 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 640
\item   7,35 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~735
\item   0,833 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,33
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   25,81 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,258 1
}\item   5,219 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 219
}\item   2,312 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 312
}\item   3,552 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 552
}\item   604,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,049
}\item   924,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,247
}\item   1,063 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,106 3
}\item   89,53 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,895 3
}\item   38,68 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,386 8
}\item   1,123 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 123
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,987 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,198 7
\item   1 678 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 167,8
\item   71,44 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,071 44
\item   2 134 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 213,4
\item   7,144 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 144
\item   33,47 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,033 47
\item   23,21 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,023 21
\item   7,619 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,761 9
\item   31,21 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,312 1
\item   94,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,945
\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 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 272,3 ~dg~ = {\color{red}  227,23 }~g
\item   8 851,8 ~mm~ = {\color{red}  885,18 }~cm
\item   878,17 ~dg~ = {\color{red}  0,087 817 }~kg
\item   836,94 ~kg~ = {\color{red}  83 694 }~dag
\item   969,78 ~g~ = {\color{red}  969 780 }~mg
\item   4 078,5 ~mL~ = {\color{red}  407,85 }~cL
\item   4 969,4 ~km~ = {\color{red}  49 694 000 }~dm
\item   2 477,2 ~mL~ = {\color{red}  0,024 772 }~hL
\item   2 655,9 ~dag~ = {\color{red}  265,59 }~hg
\item   2 628,5 ~hm~ = {\color{red}  262 850 000 }~mm
\end{itemize}
\end{multicols}
\end{document}
