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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 36}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{21}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{11}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   52,3  ~ \(\times\)  ~ 10
\item   0,284  ~ \(\times\)  ~ 100
\item   5,82  ~ \(\times\)  ~ 1 000
\item   0,009  ~ \(\times\)  ~ 100
\item   0,856  ~ \(\times\)  ~ 100
\item   0,362  ~ \(\times\)  ~ 10
\item   41  ~ \(\times\)  ~ 10
\item   0,535  ~ \(\times\)  ~ 1 000
\item   79,2  ~ \(\times\)  ~ 1 000
\item   31  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   98,21  ~ : ~ 1 000
\item   909,9  ~ : ~ 10
\item   9,831  ~ : ~ 100
\item   237,2  ~ : ~ 100
\item   619,3  ~ : ~ 100
\item   4 298  ~ : ~ 10
\item   8,411  ~ : ~ 1 000
\item   84,2  ~ : ~ 100
\item   148,5  ~ : ~ 100
\item   343  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,4  ~ \(\times\)  ~ ... ~ = ~ 740
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 0,45
\item   0,648  ~ \(\times\)  ~ ... ~ = ~ 64,8
\item   50,9  ~ \(\times\)  ~ ... ~ = ~ 50 900
\item   5,86  ~ \(\times\)  ~ ... ~ = ~ 58,6
\item   0,11  ~ \(\times\)  ~ ... ~ = ~ 1,1
\item   2,38  ~ \(\times\)  ~ ... ~ = ~ 23,8
\item   80  ~ \(\times\)  ~ ... ~ = ~ 800
\item   562  ~ \(\times\)  ~ ... ~ = ~ 56 200
\item   9,36  ~ \(\times\)  ~ ... ~ = ~ 936
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 936  ~ \(\times\)  ~ 0,001
\item   5 018  ~ \(\times\)  ~ 0,01
\item   0,66  ~ \(\times\)  ~ 0,001
\item   1,411  ~ \(\times\)  ~ 0,001
\item   20,24  ~ \(\times\)  ~ 0,01
\item   625,5  ~ \(\times\)  ~ 0,01
\item   539,8  ~ \(\times\)  ~ 0,1
\item   4,724  ~ \(\times\)  ~ 0,01
\item   185,2  ~ \(\times\)  ~ 0,1
\item   2,167  ~ \(\times\)  ~ 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   51,88  ~ \(\times\)  ~ ... ~ = ~  0,051 88
\item   7 475  ~ \(\times\)  ~ ... ~ = ~  7,475
\item   2,909  ~ \(\times\)  ~ ... ~ = ~  0,290 9
\item   9,85  ~ \(\times\)  ~ ... ~ = ~  0,985
\item   822,8  ~ \(\times\)  ~ ... ~ = ~  8,228
\item   1,692  ~ \(\times\)  ~ ... ~ = ~  0,016 92
\item   24,33  ~ \(\times\)  ~ ... ~ = ~  0,243 3
\item   5 139  ~ \(\times\)  ~ ... ~ = ~  51,39
\item   6,995  ~ \(\times\)  ~ ... ~ = ~  0,006 995
\item   6,956  ~ \(\times\)  ~ ... ~ = ~  0,695 6
\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 ~dm~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   322,94 ~g~ = ...~hg
\item   8 597 ~hL~ = ...~kL
\item   3 263,9 ~hm~ = ...~m
\item   982,6 ~km~ = ...~hm
\item   731,98 ~hm~ = ...~mm
\item   687 ~hg~ = ...~kg
\item   337,99 ~kg~ = ...~mg
\item   3 442,7 ~L~ = ...~hL
\item   697,14 ~mg~ = ...~dag
\item   571,54 ~kL~ = ...~mL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{130}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{21}{10}\) = \(\dfrac{210}{100}\)
\item   \(\dfrac{11}{100}\) = \(\dfrac{110}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   52,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 523}
\item   0,284  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 28,4}
\item   5,82  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 820}
\item   0,009  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,9}
\item   0,856  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 85,6}
\item   0,362  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,62}
\item   41  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 410}
\item   0,535  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 535}
\item   79,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 79 200}
\item   31  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 100}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   98,21 ~ : ~ 1 000 ~ = ~{\color{red} 0,098 21}
\item   909,9 ~ : ~ 10 ~ = ~{\color{red} 90,99}
\item   9,831 ~ : ~ 100 ~ = ~{\color{red} 0,098 31}
\item   237,2 ~ : ~ 100 ~ = ~{\color{red} 2,372}
\item   619,3 ~ : ~ 100 ~ = ~{\color{red} 6,193}
\item   4 298 ~ : ~ 10 ~ = ~{\color{red} 429,8}
\item   8,411 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 411}
\item   84,2 ~ : ~ 100 ~ = ~{\color{red} 0,842}
\item   148,5 ~ : ~ 100 ~ = ~{\color{red} 1,485}
\item   343 ~ : ~ 10 ~ = ~{\color{red} 34,3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~740
\item   0,045 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,45
\item   0,648 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~64,8
\item   50,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~50 900
\item   5,86 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~58,6
\item   0,11 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,1
\item   2,38 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~23,8
\item   80 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~800
\item   562 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~56 200
\item   9,36 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~936
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 936 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,936
}\item   5 018 ~ \(\times\)  0,01 ~ = ~{\color{red} 50,18
}\item   0,66 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 66
}\item   1,411 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 411
}\item   20,24 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,202 4
}\item   625,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,255
}\item   539,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 53,98
}\item   4,724 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,047 24
}\item   185,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 18,52
}\item   2,167 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 167
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,88 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,051 88
\item   7 475 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,475
\item   2,909 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,290 9
\item   9,85 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,985
\item   822,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,228
\item   1,692 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,016 92
\item   24,33 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,243 3
\item   5 139 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 51,39
\item   6,995 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 995
\item   6,956 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,695 6
\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 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   322,94 ~g~ = {\color{red}  3,229 4 }~hg
\item   8 597 ~hL~ = {\color{red}  859,7 }~kL
\item   3 263,9 ~hm~ = {\color{red}  326 390 }~m
\item   982,6 ~km~ = {\color{red}  9 826 }~hm
\item   731,98 ~hm~ = {\color{red}  73 198 000 }~mm
\item   687 ~hg~ = {\color{red}  68,7 }~kg
\item   337,99 ~kg~ = {\color{red}  337 990 000 }~mg
\item   3 442,7 ~L~ = {\color{red}  34,427 }~hL
\item   697,14 ~mg~ = {\color{red}  0,069 714 }~dag
\item   571,54 ~kL~ = {\color{red}  571 540 000 }~mL
\end{itemize}
\end{multicols}
\end{document}
