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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 348}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,01  ~ \(\times\)  ~ 10
\item   0,959  ~ \(\times\)  ~ 10
\item   4,59  ~ \(\times\)  ~ 1 000
\item   1,81  ~ \(\times\)  ~ 10
\item   0,003  ~ \(\times\)  ~ 1 000
\item   467  ~ \(\times\)  ~ 100
\item   0,234  ~ \(\times\)  ~ 100
\item   96  ~ \(\times\)  ~ 10
\item   0,762  ~ \(\times\)  ~ 100
\item   0,088  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   324,9  ~ : ~ 10
\item   6 033  ~ : ~ 100
\item   1,965  ~ : ~ 100
\item   315,5  ~ : ~ 10
\item   9 702  ~ : ~ 10
\item   8,767  ~ : ~ 1 000
\item   0,65  ~ : ~ 10
\item   37,86  ~ : ~ 100
\item   3,193  ~ : ~ 1 000
\item   8 105  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   27  ~ \(\times\)  ~ ... ~ = ~ 270
\item   468  ~ \(\times\)  ~ ... ~ = ~ 4 680
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 0,33
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   0,904  ~ \(\times\)  ~ ... ~ = ~ 9,04
\item   0,76  ~ \(\times\)  ~ ... ~ = ~ 76
\item   8,91  ~ \(\times\)  ~ ... ~ = ~ 891
\item   868  ~ \(\times\)  ~ ... ~ = ~ 86 800
\item   0,084  ~ \(\times\)  ~ ... ~ = ~ 0,84
\item   0,219  ~ \(\times\)  ~ ... ~ = ~ 2,19
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 668  ~ \(\times\)  ~ 0,001
\item   6 259  ~ \(\times\)  ~ 0,1
\item   864,9  ~ \(\times\)  ~ 0,1
\item   4 872  ~ \(\times\)  ~ 0,01
\item   5,902  ~ \(\times\)  ~ 0,1
\item   461,1  ~ \(\times\)  ~ 0,001
\item   409,3  ~ \(\times\)  ~ 0,01
\item   407,5  ~ \(\times\)  ~ 0,1
\item   23,32  ~ \(\times\)  ~ 0,1
\item   8,706  ~ \(\times\)  ~ 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   20,8  ~ \(\times\)  ~ ... ~ = ~  0,020 8
\item   125,6  ~ \(\times\)  ~ ... ~ = ~  0,125 6
\item   874,2  ~ \(\times\)  ~ ... ~ = ~  0,874 2
\item   2,849  ~ \(\times\)  ~ ... ~ = ~  0,284 9
\item   9 278  ~ \(\times\)  ~ ... ~ = ~  92,78
\item   86,2  ~ \(\times\)  ~ ... ~ = ~  0,862
\item   36,18  ~ \(\times\)  ~ ... ~ = ~  0,361 8
\item   1,005  ~ \(\times\)  ~ ... ~ = ~  0,100 5
\item   59,57  ~ \(\times\)  ~ ... ~ = ~  5,957
\item   727  ~ \(\times\)  ~ ... ~ = ~  0,727
\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~ = ...~dam
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   962,16 ~hL~ = ...~mL
\item   906,15 ~mm~ = ...~dam
\item   305,37 ~km~ = ...~dm
\item   4 931,3 ~kg~ = ...~cg
\item   221,36 ~cg~ = ...~mg
\item   1 212,3 ~cg~ = ...~hg
\item   4 460,3 ~m~ = ...~dam
\item   6 815,3 ~daL~ = ...~hL
\item   271,72 ~hL~ = ...~L
\item   767,47 ~m~ = ...~hm
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{3800}{100}\) = \(\dfrac{380}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{690}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{570}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,01  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,1}
\item   0,959  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,59}
\item   4,59  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 590}
\item   1,81  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 18,1}
\item   0,003  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3}
\item   467  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 46 700}
\item   0,234  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 23,4}
\item   96  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 960}
\item   0,762  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 76,2}
\item   0,088  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 88}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   324,9 ~ : ~ 10 ~ = ~{\color{red} 32,49}
\item   6 033 ~ : ~ 100 ~ = ~{\color{red} 60,33}
\item   1,965 ~ : ~ 100 ~ = ~{\color{red} 0,019 65}
\item   315,5 ~ : ~ 10 ~ = ~{\color{red} 31,55}
\item   9 702 ~ : ~ 10 ~ = ~{\color{red} 970,2}
\item   8,767 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 767}
\item   0,65 ~ : ~ 10 ~ = ~{\color{red} 0,065}
\item   37,86 ~ : ~ 100 ~ = ~{\color{red} 0,378 6}
\item   3,193 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 193}
\item   8 105 ~ : ~ 10 ~ = ~{\color{red} 810,5}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   27 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~270
\item   468 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 680
\item   0,033 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,33
\item   0,004 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,4
\item   0,904 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,04
\item   0,76 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~76
\item   8,91 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~891
\item   868 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~86 800
\item   0,084 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,84
\item   0,219 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,19
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 668 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,668
}\item   6 259 ~ \(\times\)  0,1 ~ = ~{\color{red} 625,9
}\item   864,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 86,49
}\item   4 872 ~ \(\times\)  0,01 ~ = ~{\color{red} 48,72
}\item   5,902 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,590 2
}\item   461,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,461 1
}\item   409,3 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,093
}\item   407,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 40,75
}\item   23,32 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,332
}\item   8,706 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 706
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,020 8
\item   125,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,125 6
\item   874,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,874 2
\item   2,849 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,284 9
\item   9 278 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 92,78
\item   86,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,862
\item   36,18 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,361 8
\item   1,005 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,100 5
\item   59,57 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,957
\item   727 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,727
\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~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   962,16 ~hL~ = {\color{red}  96 216 000 }~mL
\item   906,15 ~mm~ = {\color{red}  0,090 615 }~dam
\item   305,37 ~km~ = {\color{red}  3 053 700 }~dm
\item   4 931,3 ~kg~ = {\color{red}  493 130 000 }~cg
\item   221,36 ~cg~ = {\color{red}  2 213,6 }~mg
\item   1 212,3 ~cg~ = {\color{red}  0,121 23 }~hg
\item   4 460,3 ~m~ = {\color{red}  446,03 }~dam
\item   6 815,3 ~daL~ = {\color{red}  681,53 }~hL
\item   271,72 ~hL~ = {\color{red}  27 172 }~L
\item   767,47 ~m~ = {\color{red}  7,674 7 }~hm
\end{itemize}
\end{multicols}
\end{document}
