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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 105}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{84}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,51  ~ \(\times\)  ~ 10
\item   8,79  ~ \(\times\)  ~ 10
\item   77,8  ~ \(\times\)  ~ 10
\item   0,684  ~ \(\times\)  ~ 100
\item   96,2  ~ \(\times\)  ~ 100
\item   0,639  ~ \(\times\)  ~ 100
\item   51,7  ~ \(\times\)  ~ 1 000
\item   0,02  ~ \(\times\)  ~ 100
\item   0,095  ~ \(\times\)  ~ 100
\item   0,71  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,08  ~ : ~ 1 000
\item   3,141  ~ : ~ 1 000
\item   8,37  ~ : ~ 1 000
\item   8,547  ~ : ~ 1 000
\item   4 829  ~ : ~ 1 000
\item   69,65  ~ : ~ 100
\item   440,3  ~ : ~ 10
\item   9,147  ~ : ~ 100
\item   5 943  ~ : ~ 1 000
\item   323,5  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   63,3  ~ \(\times\)  ~ ... ~ = ~ 6 330
\item   0,786  ~ \(\times\)  ~ ... ~ = ~ 78,6
\item   0,081  ~ \(\times\)  ~ ... ~ = ~ 81
\item   88,1  ~ \(\times\)  ~ ... ~ = ~ 88 100
\item   42  ~ \(\times\)  ~ ... ~ = ~ 42 000
\item   659  ~ \(\times\)  ~ ... ~ = ~ 65 900
\item   5,94  ~ \(\times\)  ~ ... ~ = ~ 594
\item   68,1  ~ \(\times\)  ~ ... ~ = ~ 68 100
\item   9,53  ~ \(\times\)  ~ ... ~ = ~ 953
\item   318  ~ \(\times\)  ~ ... ~ = ~ 3 180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,88  ~ \(\times\)  ~ 0,1
\item   72,52  ~ \(\times\)  ~ 0,1
\item   4 126  ~ \(\times\)  ~ 0,01
\item   368,1  ~ \(\times\)  ~ 0,1
\item   606,2  ~ \(\times\)  ~ 0,001
\item   859,4  ~ \(\times\)  ~ 0,001
\item   45,25  ~ \(\times\)  ~ 0,1
\item   8,085  ~ \(\times\)  ~ 0,1
\item   281,6  ~ \(\times\)  ~ 0,1
\item   9 566  ~ \(\times\)  ~ 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   73,24  ~ \(\times\)  ~ ... ~ = ~  7,324
\item   58,28  ~ \(\times\)  ~ ... ~ = ~  0,582 8
\item   34,4  ~ \(\times\)  ~ ... ~ = ~  0,344
\item   64,56  ~ \(\times\)  ~ ... ~ = ~  0,064 56
\item   184,9  ~ \(\times\)  ~ ... ~ = ~  18,49
\item   4 417  ~ \(\times\)  ~ ... ~ = ~  44,17
\item   117,8  ~ \(\times\)  ~ ... ~ = ~  11,78
\item   633  ~ \(\times\)  ~ ... ~ = ~  6,33
\item   16  ~ \(\times\)  ~ ... ~ = ~  0,016
\item   7,351  ~ \(\times\)  ~ ... ~ = ~  0,073 51
\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 ~hm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   737,68 ~kg~ = ...~mg
\item   8 083 ~kg~ = ...~dag
\item   2 278,8 ~kL~ = ...~dL
\item   4 613,5 ~daL~ = ...~mL
\item   8 177,9 ~dL~ = ...~mL
\item   679,52 ~g~ = ...~cg
\item   634,57 ~cL~ = ...~mL
\item   5 973,9 ~dm~ = ...~km
\item   197,41 ~daL~ = ...~kL
\item   237,02 ~hm~ = ...~dm
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{1100}{100}\) = \(\dfrac{110}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{780}{100}\)
\item   \(\dfrac{84}{100}\) = \(\dfrac{840}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,51  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 35,1}
\item   8,79  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 87,9}
\item   77,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 778}
\item   0,684  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 68,4}
\item   96,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 620}
\item   0,639  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 63,9}
\item   51,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 51 700}
\item   0,02  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2}
\item   0,095  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,5}
\item   0,71  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 710}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,08 ~ : ~ 1 000 ~ = ~{\color{red} 0,020 08}
\item   3,141 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 141}
\item   8,37 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 37}
\item   8,547 ~ : ~ 1 000 ~ = ~{\color{red} 0,008 547}
\item   4 829 ~ : ~ 1 000 ~ = ~{\color{red} 4,829}
\item   69,65 ~ : ~ 100 ~ = ~{\color{red} 0,696 5}
\item   440,3 ~ : ~ 10 ~ = ~{\color{red} 44,03}
\item   9,147 ~ : ~ 100 ~ = ~{\color{red} 0,091 47}
\item   5 943 ~ : ~ 1 000 ~ = ~{\color{red} 5,943}
\item   323,5 ~ : ~ 10 ~ = ~{\color{red} 32,35}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   63,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 330
\item   0,786 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~78,6
\item   0,081 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~81
\item   88,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~88 100
\item   42 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~42 000
\item   659 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~65 900
\item   5,94 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~594
\item   68,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~68 100
\item   9,53 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~953
\item   318 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,88 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,188
}\item   72,52 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,252
}\item   4 126 ~ \(\times\)  0,01 ~ = ~{\color{red} 41,26
}\item   368,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 36,81
}\item   606,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,606 2
}\item   859,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,859 4
}\item   45,25 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,525
}\item   8,085 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,808 5
}\item   281,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 28,16
}\item   9 566 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,566
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   73,24 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,324
\item   58,28 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,582 8
\item   34,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,344
\item   64,56 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,064 56
\item   184,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 18,49
\item   4 417 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 44,17
\item   117,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 11,78
\item   633 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,33
\item   16 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,016
\item   7,351 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,073 51
\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 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   737,68 ~kg~ = {\color{red}  737 680 000 }~mg
\item   8 083 ~kg~ = {\color{red}  808 300 }~dag
\item   2 278,8 ~kL~ = {\color{red}  22 788 000 }~dL
\item   4 613,5 ~daL~ = {\color{red}  46 135 000 }~mL
\item   8 177,9 ~dL~ = {\color{red}  817 790 }~mL
\item   679,52 ~g~ = {\color{red}  67 952 }~cg
\item   634,57 ~cL~ = {\color{red}  6 345,7 }~mL
\item   5 973,9 ~dm~ = {\color{red}  0,597 39 }~km
\item   197,41 ~daL~ = {\color{red}  1,974 1 }~kL
\item   237,02 ~hm~ = {\color{red}  237 020 }~dm
\end{itemize}
\end{multicols}
\end{document}
