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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 368}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{24}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,063  ~ \(\times\)  ~ 1 000
\item   5,81  ~ \(\times\)  ~ 10
\item   9,05  ~ \(\times\)  ~ 100
\item   401  ~ \(\times\)  ~ 10
\item   0,77  ~ \(\times\)  ~ 100
\item   0,083  ~ \(\times\)  ~ 1 000
\item   0,438  ~ \(\times\)  ~ 10
\item   86,5  ~ \(\times\)  ~ 100
\item   94,9  ~ \(\times\)  ~ 10
\item   51,2  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,858  ~ : ~ 1 000
\item   4 352  ~ : ~ 10
\item   9,51  ~ : ~ 1 000
\item   6 553  ~ : ~ 1 000
\item   6 690  ~ : ~ 1 000
\item   94,56  ~ : ~ 10
\item   326,1  ~ : ~ 10
\item   7 625  ~ : ~ 1 000
\item   5,022  ~ : ~ 100
\item   64,78  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   70,3  ~ \(\times\)  ~ ... ~ = ~ 70 300
\item   167  ~ \(\times\)  ~ ... ~ = ~ 1 670
\item   4,91  ~ \(\times\)  ~ ... ~ = ~ 4 910
\item   0,594  ~ \(\times\)  ~ ... ~ = ~ 59,4
\item   0,063  ~ \(\times\)  ~ ... ~ = ~ 63
\item   7,93  ~ \(\times\)  ~ ... ~ = ~ 7 930
\item   0,345  ~ \(\times\)  ~ ... ~ = ~ 34,5
\item   874  ~ \(\times\)  ~ ... ~ = ~ 8 740
\item   3,97  ~ \(\times\)  ~ ... ~ = ~ 39,7
\item   82,3  ~ \(\times\)  ~ ... ~ = ~ 8 230
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   556,1  ~ \(\times\)  ~ 0,01
\item   62,3  ~ \(\times\)  ~ 0,001
\item   675  ~ \(\times\)  ~ 0,01
\item   2 728  ~ \(\times\)  ~ 0,001
\item   692  ~ \(\times\)  ~ 0,1
\item   532,8  ~ \(\times\)  ~ 0,001
\item   88,4  ~ \(\times\)  ~ 0,001
\item   569,8  ~ \(\times\)  ~ 0,001
\item   668,5  ~ \(\times\)  ~ 0,001
\item   8 417  ~ \(\times\)  ~ 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   3 066  ~ \(\times\)  ~ ... ~ = ~  306,6
\item   5,789  ~ \(\times\)  ~ ... ~ = ~  0,005 789
\item   65,97  ~ \(\times\)  ~ ... ~ = ~  0,659 7
\item   3 299  ~ \(\times\)  ~ ... ~ = ~  3,299
\item   875,5  ~ \(\times\)  ~ ... ~ = ~  8,755
\item   6,298  ~ \(\times\)  ~ ... ~ = ~  0,006 298
\item   7,094  ~ \(\times\)  ~ ... ~ = ~  0,709 4
\item   830,6  ~ \(\times\)  ~ ... ~ = ~  8,306
\item   3,723  ~ \(\times\)  ~ ... ~ = ~  0,372 3
\item   955  ~ \(\times\)  ~ ... ~ = ~  0,955
\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~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 578 ~daL~ = ...~hL
\item   6 628,7 ~dag~ = ...~g
\item   8 210,7 ~kg~ = ...~dg
\item   9 855,1 ~m~ = ...~mm
\item   510,09 ~mL~ = ...~kL
\item   8 782,4 ~dam~ = ...~mm
\item   807,81 ~hm~ = ...~m
\item   240,68 ~hg~ = ...~mg
\item   873,81 ~hg~ = ...~kg
\item   926,65 ~dg~ = ...~hg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{1500}{100}\) = \(\dfrac{150}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{24}{10}\) = \(\dfrac{240}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,063  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 63}
\item   5,81  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 58,1}
\item   9,05  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 905}
\item   401  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 010}
\item   0,77  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 77}
\item   0,083  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 83}
\item   0,438  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,38}
\item   86,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 650}
\item   94,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 949}
\item   51,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 51 200}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,858 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 858}
\item   4 352 ~ : ~ 10 ~ = ~{\color{red} 435,2}
\item   9,51 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 51}
\item   6 553 ~ : ~ 1 000 ~ = ~{\color{red} 6,553}
\item   6 690 ~ : ~ 1 000 ~ = ~{\color{red} 6,69}
\item   94,56 ~ : ~ 10 ~ = ~{\color{red} 9,456}
\item   326,1 ~ : ~ 10 ~ = ~{\color{red} 32,61}
\item   7 625 ~ : ~ 1 000 ~ = ~{\color{red} 7,625}
\item   5,022 ~ : ~ 100 ~ = ~{\color{red} 0,050 22}
\item   64,78 ~ : ~ 1 000 ~ = ~{\color{red} 0,064 78}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   70,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~70 300
\item   167 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 670
\item   4,91 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 910
\item   0,594 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~59,4
\item   0,063 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~63
\item   7,93 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 930
\item   0,345 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~34,5
\item   874 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 740
\item   3,97 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~39,7
\item   82,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 230
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   556,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,561
}\item   62,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,062 3
}\item   675 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,75
}\item   2 728 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,728
}\item   692 ~ \(\times\)  0,1 ~ = ~{\color{red} 69,2
}\item   532,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,532 8
}\item   88,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,088 4
}\item   569,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,569 8
}\item   668,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,668 5
}\item   8 417 ~ \(\times\)  0,01 ~ = ~{\color{red} 84,17
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 066 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 306,6
\item   5,789 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 789
\item   65,97 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,659 7
\item   3 299 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,299
\item   875,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,755
\item   6,298 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 298
\item   7,094 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,709 4
\item   830,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,306
\item   3,723 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,372 3
\item   955 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,955
\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~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 578 ~daL~ = {\color{red}  457,8 }~hL
\item   6 628,7 ~dag~ = {\color{red}  66 287 }~g
\item   8 210,7 ~kg~ = {\color{red}  82 107 000 }~dg
\item   9 855,1 ~m~ = {\color{red}  9 855 100 }~mm
\item   510,09 ~mL~ = {\color{red}  0,000 510 09 }~kL
\item   8 782,4 ~dam~ = {\color{red}  87 824 000 }~mm
\item   807,81 ~hm~ = {\color{red}  80 781 }~m
\item   240,68 ~hg~ = {\color{red}  24 068 000 }~mg
\item   873,81 ~hg~ = {\color{red}  87,381 }~kg
\item   926,65 ~dg~ = {\color{red}  0,926 65 }~hg
\end{itemize}
\end{multicols}
\end{document}
