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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 71}

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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   \(\dfrac{4400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,7  ~ \(\times\)  ~ 1 000
\item   0,007  ~ \(\times\)  ~ 10
\item   525  ~ \(\times\)  ~ 1 000
\item   5,48  ~ \(\times\)  ~ 100
\item   78,7  ~ \(\times\)  ~ 100
\item   67,1  ~ \(\times\)  ~ 10
\item   0,037  ~ \(\times\)  ~ 10
\item   0,041  ~ \(\times\)  ~ 10
\item   1,61  ~ \(\times\)  ~ 100
\item   465  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   44,3  ~ : ~ 1 000
\item   252,1  ~ : ~ 10
\item   84,86  ~ : ~ 100
\item   9 576  ~ : ~ 100
\item   585,3  ~ : ~ 100
\item   580  ~ : ~ 10
\item   4 188  ~ : ~ 100
\item   2,38  ~ : ~ 100
\item   81,93  ~ : ~ 100
\item   165,5  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64,5  ~ \(\times\)  ~ ... ~ = ~ 645
\item   0,598  ~ \(\times\)  ~ ... ~ = ~ 59,8
\item   5,68  ~ \(\times\)  ~ ... ~ = ~ 568
\item   0,011  ~ \(\times\)  ~ ... ~ = ~ 11
\item   273  ~ \(\times\)  ~ ... ~ = ~ 2 730
\item   87,4  ~ \(\times\)  ~ ... ~ = ~ 874
\item   4,92  ~ \(\times\)  ~ ... ~ = ~ 4 920
\item   0,087  ~ \(\times\)  ~ ... ~ = ~ 87
\item   8,96  ~ \(\times\)  ~ ... ~ = ~ 89,6
\item   28,5  ~ \(\times\)  ~ ... ~ = ~ 285
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,288  ~ \(\times\)  ~ 0,1
\item   2 205  ~ \(\times\)  ~ 0,1
\item   73,19  ~ \(\times\)  ~ 0,01
\item   70,68  ~ \(\times\)  ~ 0,01
\item   62,6  ~ \(\times\)  ~ 0,001
\item   8,056  ~ \(\times\)  ~ 0,1
\item   678,3  ~ \(\times\)  ~ 0,01
\item   50,64  ~ \(\times\)  ~ 0,001
\item   323  ~ \(\times\)  ~ 0,01
\item   7 068  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,66  ~ \(\times\)  ~ ... ~ = ~  0,041 66
\item   2,586  ~ \(\times\)  ~ ... ~ = ~  0,002 586
\item   95,1  ~ \(\times\)  ~ ... ~ = ~  0,095 1
\item   7 915  ~ \(\times\)  ~ ... ~ = ~  79,15
\item   6 343  ~ \(\times\)  ~ ... ~ = ~  6,343
\item   88,63  ~ \(\times\)  ~ ... ~ = ~  0,886 3
\item   91,11  ~ \(\times\)  ~ ... ~ = ~  0,091 11
\item   4,62  ~ \(\times\)  ~ ... ~ = ~  0,046 2
\item   5,359  ~ \(\times\)  ~ ... ~ = ~  0,005 359
\item   42,4  ~ \(\times\)  ~ ... ~ = ~  0,042 4
\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 ~km~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   368,44 ~mg~ = ...~dg
\item   4 567,2 ~g~ = ...~mg
\item   934,88 ~kL~ = ...~daL
\item   482,48 ~g~ = ...~hg
\item   408,62 ~km~ = ...~m
\item   2 988,7 ~kg~ = ...~g
\item   617,16 ~dag~ = ...~dg
\item   892 ~g~ = ...~dg
\item   3 142 ~mm~ = ...~km
\item   9 151,6 ~mg~ = ...~g
\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   \(\dfrac{4400}{100}\) = \(\dfrac{440}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{360}{100}\)
\item   \(\dfrac{44}{100}\) = \(\dfrac{440}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 700}
\item   0,007  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,07}
\item   525  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 525 000}
\item   5,48  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 548}
\item   78,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 870}
\item   67,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 671}
\item   0,037  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,37}
\item   0,041  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,41}
\item   1,61  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 161}
\item   465  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 465 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   44,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,044 3}
\item   252,1 ~ : ~ 10 ~ = ~{\color{red} 25,21}
\item   84,86 ~ : ~ 100 ~ = ~{\color{red} 0,848 6}
\item   9 576 ~ : ~ 100 ~ = ~{\color{red} 95,76}
\item   585,3 ~ : ~ 100 ~ = ~{\color{red} 5,853}
\item   580 ~ : ~ 10 ~ = ~{\color{red} 58}
\item   4 188 ~ : ~ 100 ~ = ~{\color{red} 41,88}
\item   2,38 ~ : ~ 100 ~ = ~{\color{red} 0,023 8}
\item   81,93 ~ : ~ 100 ~ = ~{\color{red} 0,819 3}
\item   165,5 ~ : ~ 100 ~ = ~{\color{red} 1,655}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   64,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~645
\item   0,598 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~59,8
\item   5,68 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~568
\item   0,011 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~11
\item   273 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2 730
\item   87,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~874
\item   4,92 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 920
\item   0,087 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~87
\item   8,96 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~89,6
\item   28,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~285
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,288 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,828 8
}\item   2 205 ~ \(\times\)  0,1 ~ = ~{\color{red} 220,5
}\item   73,19 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,731 9
}\item   70,68 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,706 8
}\item   62,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,062 6
}\item   8,056 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,805 6
}\item   678,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,783
}\item   50,64 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,050 64
}\item   323 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,23
}\item   7 068 ~ \(\times\)  0,01 ~ = ~{\color{red} 70,68
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   41,66 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,041 66
\item   2,586 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 586
\item   95,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,095 1
\item   7 915 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 79,15
\item   6 343 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,343
\item   88,63 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,886 3
\item   91,11 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,091 11
\item   4,62 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,046 2
\item   5,359 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 359
\item   42,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,042 4
\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 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\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   368,44 ~mg~ = {\color{red}  3,684 4 }~dg
\item   4 567,2 ~g~ = {\color{red}  4 567 200 }~mg
\item   934,88 ~kL~ = {\color{red}  93 488 }~daL
\item   482,48 ~g~ = {\color{red}  4,824 8 }~hg
\item   408,62 ~km~ = {\color{red}  408 620 }~m
\item   2 988,7 ~kg~ = {\color{red}  2 988 700 }~g
\item   617,16 ~dag~ = {\color{red}  61 716 }~dg
\item   892 ~g~ = {\color{red}  8 920 }~dg
\item   3 142 ~mm~ = {\color{red}  0,003 142 }~km
\item   9 151,6 ~mg~ = {\color{red}  9,151 6 }~g
\end{itemize}
\end{multicols}
\end{document}
