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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 118}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{48}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,2  ~ \(\times\)  ~ 10
\item   0,631  ~ \(\times\)  ~ 1 000
\item   6,31  ~ \(\times\)  ~ 1 000
\item   0,083  ~ \(\times\)  ~ 10
\item   0,084  ~ \(\times\)  ~ 1 000
\item   0,075  ~ \(\times\)  ~ 10
\item   94,4  ~ \(\times\)  ~ 1 000
\item   0,144  ~ \(\times\)  ~ 100
\item   782  ~ \(\times\)  ~ 1 000
\item   877  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,94  ~ : ~ 1 000
\item   7,555  ~ : ~ 10
\item   746,7  ~ : ~ 100
\item   0,118  ~ : ~ 10
\item   7 665  ~ : ~ 10
\item   240,8  ~ : ~ 100
\item   658,9  ~ : ~ 10
\item   30,4  ~ : ~ 100
\item   2 330  ~ : ~ 100
\item   853,9  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   673  ~ \(\times\)  ~ ... ~ = ~ 6 730
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 0,62
\item   0,065  ~ \(\times\)  ~ ... ~ = ~ 6,5
\item   17,2  ~ \(\times\)  ~ ... ~ = ~ 17 200
\item   0,331  ~ \(\times\)  ~ ... ~ = ~ 3,31
\item   0,946  ~ \(\times\)  ~ ... ~ = ~ 946
\item   847  ~ \(\times\)  ~ ... ~ = ~ 847 000
\item   88,2  ~ \(\times\)  ~ ... ~ = ~ 882
\item   13,1  ~ \(\times\)  ~ ... ~ = ~ 131
\item   762  ~ \(\times\)  ~ ... ~ = ~ 762 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 771  ~ \(\times\)  ~ 0,001
\item   740,4  ~ \(\times\)  ~ 0,001
\item   756,5  ~ \(\times\)  ~ 0,01
\item   58,78  ~ \(\times\)  ~ 0,01
\item   3,138  ~ \(\times\)  ~ 0,1
\item   9 539  ~ \(\times\)  ~ 0,1
\item   2,18  ~ \(\times\)  ~ 0,001
\item   7 707  ~ \(\times\)  ~ 0,1
\item   8 052  ~ \(\times\)  ~ 0,01
\item   0,248  ~ \(\times\)  ~ 0,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   720,8  ~ \(\times\)  ~ ... ~ = ~  0,720 8
\item   3,162  ~ \(\times\)  ~ ... ~ = ~  0,031 62
\item   12,19  ~ \(\times\)  ~ ... ~ = ~  0,121 9
\item   70,44  ~ \(\times\)  ~ ... ~ = ~  0,070 44
\item   63,78  ~ \(\times\)  ~ ... ~ = ~  0,063 78
\item   6 430  ~ \(\times\)  ~ ... ~ = ~  6,43
\item   60,72  ~ \(\times\)  ~ ... ~ = ~  6,072
\item   5,653  ~ \(\times\)  ~ ... ~ = ~  0,565 3
\item   43,7  ~ \(\times\)  ~ ... ~ = ~  0,043 7
\item   8,944  ~ \(\times\)  ~ ... ~ = ~  0,008 944
\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 ~hm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~km~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   387,98 ~mm~ = ...~cm
\item   4 407 ~L~ = ...~mL
\item   944,44 ~mL~ = ...~kL
\item   1 318 ~dL~ = ...~cL
\item   9 118,9 ~cL~ = ...~mL
\item   530,44 ~daL~ = ...~dL
\item   4 295,7 ~hg~ = ...~g
\item   4 116,4 ~dL~ = ...~mL
\item   380,74 ~mL~ = ...~cL
\item   1 738,9 ~cg~ = ...~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   3 = \(\dfrac{30}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{230}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{48}{10}\) = \(\dfrac{480}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{130}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 32}
\item   0,631  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 631}
\item   6,31  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 310}
\item   0,083  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,83}
\item   0,084  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84}
\item   0,075  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,75}
\item   94,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 94 400}
\item   0,144  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 14,4}
\item   782  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 782 000}
\item   877  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 877 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   59,94 ~ : ~ 1 000 ~ = ~{\color{red} 0,059 94}
\item   7,555 ~ : ~ 10 ~ = ~{\color{red} 0,755 5}
\item   746,7 ~ : ~ 100 ~ = ~{\color{red} 7,467}
\item   0,118 ~ : ~ 10 ~ = ~{\color{red} 0,011 8}
\item   7 665 ~ : ~ 10 ~ = ~{\color{red} 766,5}
\item   240,8 ~ : ~ 100 ~ = ~{\color{red} 2,408}
\item   658,9 ~ : ~ 10 ~ = ~{\color{red} 65,89}
\item   30,4 ~ : ~ 100 ~ = ~{\color{red} 0,304}
\item   2 330 ~ : ~ 100 ~ = ~{\color{red} 23,3}
\item   853,9 ~ : ~ 10 ~ = ~{\color{red} 85,39}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   673 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 730
\item   0,062 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,62
\item   0,065 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6,5
\item   17,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~17 200
\item   0,331 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,31
\item   0,946 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~946
\item   847 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~847 000
\item   88,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~882
\item   13,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~131
\item   762 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~762 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 771 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,771
}\item   740,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,740 4
}\item   756,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,565
}\item   58,78 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,587 8
}\item   3,138 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,313 8
}\item   9 539 ~ \(\times\)  0,1 ~ = ~{\color{red} 953,9
}\item   2,18 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 18
}\item   7 707 ~ \(\times\)  0,1 ~ = ~{\color{red} 770,7
}\item   8 052 ~ \(\times\)  0,01 ~ = ~{\color{red} 80,52
}\item   0,248 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,024 8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   720,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,720 8
\item   3,162 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,031 62
\item   12,19 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,121 9
\item   70,44 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,070 44
\item   63,78 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,063 78
\item   6 430 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,43
\item   60,72 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,072
\item   5,653 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,565 3
\item   43,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,043 7
\item   8,944 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 944
\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 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   387,98 ~mm~ = {\color{red}  38,798 }~cm
\item   4 407 ~L~ = {\color{red}  4 407 000 }~mL
\item   944,44 ~mL~ = {\color{red}  0,000 944 44 }~kL
\item   1 318 ~dL~ = {\color{red}  13 180 }~cL
\item   9 118,9 ~cL~ = {\color{red}  91 189 }~mL
\item   530,44 ~daL~ = {\color{red}  53 044 }~dL
\item   4 295,7 ~hg~ = {\color{red}  429 570 }~g
\item   4 116,4 ~dL~ = {\color{red}  411 640 }~mL
\item   380,74 ~mL~ = {\color{red}  38,074 }~cL
\item   1 738,9 ~cg~ = {\color{red}  17,389 }~g
\end{itemize}
\end{multicols}
\end{document}
