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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 138}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{77}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,92  ~ \(\times\)  ~ 10
\item   19,8  ~ \(\times\)  ~ 100
\item   1,81  ~ \(\times\)  ~ 1 000
\item   74,3  ~ \(\times\)  ~ 10
\item   0,724  ~ \(\times\)  ~ 1 000
\item   10,1  ~ \(\times\)  ~ 1 000
\item   23,8  ~ \(\times\)  ~ 100
\item   0,3  ~ \(\times\)  ~ 10
\item   6,3  ~ \(\times\)  ~ 100
\item   0,623  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   22,88  ~ : ~ 100
\item   8 701  ~ : ~ 1 000
\item   6 515  ~ : ~ 1 000
\item   6 268  ~ : ~ 1 000
\item   8 333  ~ : ~ 10
\item   8,297  ~ : ~ 10
\item   677  ~ : ~ 1 000
\item   9,672  ~ : ~ 10
\item   559,6  ~ : ~ 10
\item   5 182  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,77  ~ \(\times\)  ~ ... ~ = ~ 77,7
\item   17,3  ~ \(\times\)  ~ ... ~ = ~ 173
\item   1,08  ~ \(\times\)  ~ ... ~ = ~ 108
\item   2,98  ~ \(\times\)  ~ ... ~ = ~ 29,8
\item   6,03  ~ \(\times\)  ~ ... ~ = ~ 603
\item   0,633  ~ \(\times\)  ~ ... ~ = ~ 63,3
\item   2,47  ~ \(\times\)  ~ ... ~ = ~ 2 470
\item   0,551  ~ \(\times\)  ~ ... ~ = ~ 55,1
\item   0,865  ~ \(\times\)  ~ ... ~ = ~ 86,5
\item   0,44  ~ \(\times\)  ~ ... ~ = ~ 440
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,422  ~ \(\times\)  ~ 0,001
\item   0,682  ~ \(\times\)  ~ 0,01
\item   511,8  ~ \(\times\)  ~ 0,001
\item   3 852  ~ \(\times\)  ~ 0,1
\item   1,304  ~ \(\times\)  ~ 0,01
\item   18,99  ~ \(\times\)  ~ 0,001
\item   129,6  ~ \(\times\)  ~ 0,1
\item   491  ~ \(\times\)  ~ 0,001
\item   7,576  ~ \(\times\)  ~ 0,01
\item   692,5  ~ \(\times\)  ~ 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   8,209  ~ \(\times\)  ~ ... ~ = ~  0,082 09
\item   540,6  ~ \(\times\)  ~ ... ~ = ~  54,06
\item   9,145  ~ \(\times\)  ~ ... ~ = ~  0,009 145
\item   6 709  ~ \(\times\)  ~ ... ~ = ~  670,9
\item   5,807  ~ \(\times\)  ~ ... ~ = ~  0,005 807
\item   692,2  ~ \(\times\)  ~ ... ~ = ~  0,692 2
\item   6,512  ~ \(\times\)  ~ ... ~ = ~  0,065 12
\item   9,846  ~ \(\times\)  ~ ... ~ = ~  0,984 6
\item   1,554  ~ \(\times\)  ~ ... ~ = ~  0,155 4
\item   3,427  ~ \(\times\)  ~ ... ~ = ~  0,342 7
\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 ~cm~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   940,76 ~km~ = ...~hm
\item   4 309,9 ~dag~ = ...~dg
\item   348,63 ~hL~ = ...~dL
\item   450,18 ~mL~ = ...~dL
\item   6 674,1 ~hm~ = ...~mm
\item   3 800,7 ~dL~ = ...~L
\item   9 628,8 ~L~ = ...~mL
\item   3 537,8 ~g~ = ...~kg
\item   554,03 ~hg~ = ...~kg
\item   3 358,3 ~m~ = ...~cm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{6800}{100}\) = \(\dfrac{680}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{370}{100}\)
\item   \(\dfrac{77}{100}\) = \(\dfrac{770}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,92  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 89,2}
\item   19,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 980}
\item   1,81  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 810}
\item   74,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 743}
\item   0,724  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 724}
\item   10,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 10 100}
\item   23,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 380}
\item   0,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3}
\item   6,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 630}
\item   0,623  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 623}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   22,88 ~ : ~ 100 ~ = ~{\color{red} 0,228 8}
\item   8 701 ~ : ~ 1 000 ~ = ~{\color{red} 8,701}
\item   6 515 ~ : ~ 1 000 ~ = ~{\color{red} 6,515}
\item   6 268 ~ : ~ 1 000 ~ = ~{\color{red} 6,268}
\item   8 333 ~ : ~ 10 ~ = ~{\color{red} 833,3}
\item   8,297 ~ : ~ 10 ~ = ~{\color{red} 0,829 7}
\item   677 ~ : ~ 1 000 ~ = ~{\color{red} 0,677}
\item   9,672 ~ : ~ 10 ~ = ~{\color{red} 0,967 2}
\item   559,6 ~ : ~ 10 ~ = ~{\color{red} 55,96}
\item   5 182 ~ : ~ 10 ~ = ~{\color{red} 518,2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,77 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~77,7
\item   17,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~173
\item   1,08 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~108
\item   2,98 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~29,8
\item   6,03 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~603
\item   0,633 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~63,3
\item   2,47 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 470
\item   0,551 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~55,1
\item   0,865 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~86,5
\item   0,44 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~440
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,422 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 422
}\item   0,682 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,006 82
}\item   511,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,511 8
}\item   3 852 ~ \(\times\)  0,1 ~ = ~{\color{red} 385,2
}\item   1,304 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,013 04
}\item   18,99 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,018 99
}\item   129,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 12,96
}\item   491 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,491
}\item   7,576 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,075 76
}\item   692,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,692 5
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,209 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,082 09
\item   540,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 54,06
\item   9,145 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 145
\item   6 709 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 670,9
\item   5,807 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 807
\item   692,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,692 2
\item   6,512 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,065 12
\item   9,846 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,984 6
\item   1,554 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,155 4
\item   3,427 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,342 7
\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 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   940,76 ~km~ = {\color{red}  9 407,6 }~hm
\item   4 309,9 ~dag~ = {\color{red}  430 990 }~dg
\item   348,63 ~hL~ = {\color{red}  348 630 }~dL
\item   450,18 ~mL~ = {\color{red}  4,501 8 }~dL
\item   6 674,1 ~hm~ = {\color{red}  667 410 000 }~mm
\item   3 800,7 ~dL~ = {\color{red}  380,07 }~L
\item   9 628,8 ~L~ = {\color{red}  9 628 800 }~mL
\item   3 537,8 ~g~ = {\color{red}  3,537 8 }~kg
\item   554,03 ~hg~ = {\color{red}  55,403 }~kg
\item   3 358,3 ~m~ = {\color{red}  335 830 }~cm
\end{itemize}
\end{multicols}
\end{document}
