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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 247}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{71}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{17}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,45  ~ \(\times\)  ~ 10
\item   441  ~ \(\times\)  ~ 10
\item   2,1  ~ \(\times\)  ~ 1 000
\item   0,022  ~ \(\times\)  ~ 1 000
\item   0,044  ~ \(\times\)  ~ 1 000
\item   1,41  ~ \(\times\)  ~ 10
\item   927  ~ \(\times\)  ~ 1 000
\item   654  ~ \(\times\)  ~ 100
\item   0,07  ~ \(\times\)  ~ 10
\item   1,05  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 596  ~ : ~ 10
\item   61,34  ~ : ~ 10
\item   48,13  ~ : ~ 100
\item   0,334  ~ : ~ 1 000
\item   2,06  ~ : ~ 10
\item   34,59  ~ : ~ 1 000
\item   16,66  ~ : ~ 10
\item   86,28  ~ : ~ 10
\item   94,9  ~ : ~ 100
\item   0,922  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   712  ~ \(\times\)  ~ ... ~ = ~ 71 200
\item   11  ~ \(\times\)  ~ ... ~ = ~ 1 100
\item   134  ~ \(\times\)  ~ ... ~ = ~ 1 340
\item   96,1  ~ \(\times\)  ~ ... ~ = ~ 9 610
\item   0,029  ~ \(\times\)  ~ ... ~ = ~ 0,29
\item   632  ~ \(\times\)  ~ ... ~ = ~ 6 320
\item   6,87  ~ \(\times\)  ~ ... ~ = ~ 687
\item   590  ~ \(\times\)  ~ ... ~ = ~ 5 900
\item   76,5  ~ \(\times\)  ~ ... ~ = ~ 765
\item   0,077  ~ \(\times\)  ~ ... ~ = ~ 0,77
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   76,78  ~ \(\times\)  ~ 0,01
\item   674  ~ \(\times\)  ~ 0,001
\item   4,191  ~ \(\times\)  ~ 0,01
\item   9 501  ~ \(\times\)  ~ 0,01
\item   634,6  ~ \(\times\)  ~ 0,01
\item   556,8  ~ \(\times\)  ~ 0,001
\item   1,413  ~ \(\times\)  ~ 0,1
\item   1 113  ~ \(\times\)  ~ 0,1
\item   1 702  ~ \(\times\)  ~ 0,1
\item   374,1  ~ \(\times\)  ~ 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   468,7  ~ \(\times\)  ~ ... ~ = ~  4,687
\item   2 414  ~ \(\times\)  ~ ... ~ = ~  2,414
\item   72,86  ~ \(\times\)  ~ ... ~ = ~  0,072 86
\item   8,517  ~ \(\times\)  ~ ... ~ = ~  0,008 517
\item   28,12  ~ \(\times\)  ~ ... ~ = ~  2,812
\item   8,1  ~ \(\times\)  ~ ... ~ = ~  0,008 1
\item   808,4  ~ \(\times\)  ~ ... ~ = ~  0,808 4
\item   29,5  ~ \(\times\)  ~ ... ~ = ~  0,029 5
\item   428,5  ~ \(\times\)  ~ ... ~ = ~  4,285
\item   12,02  ~ \(\times\)  ~ ... ~ = ~  0,120 2
\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 ~km~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   757,02 ~L~ = ...~kL
\item   857,47 ~hL~ = ...~dL
\item   351,07 ~cg~ = ...~hg
\item   3 488,4 ~m~ = ...~cm
\item   4 595,4 ~hm~ = ...~km
\item   421,8 ~cg~ = ...~dg
\item   3 126,7 ~m~ = ...~dm
\item   6 715,3 ~hL~ = ...~daL
\item   277,63 ~dm~ = ...~cm
\item   5 352,9 ~mL~ = ...~kL
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{130}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{71}{10}\) = \(\dfrac{710}{100}\)
\item   \(\dfrac{17}{100}\) = \(\dfrac{170}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,45  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 64,5}
\item   441  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 410}
\item   2,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 100}
\item   0,022  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 22}
\item   0,044  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 44}
\item   1,41  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 14,1}
\item   927  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 927 000}
\item   654  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 65 400}
\item   0,07  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,7}
\item   1,05  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 105}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 596 ~ : ~ 10 ~ = ~{\color{red} 659,6}
\item   61,34 ~ : ~ 10 ~ = ~{\color{red} 6,134}
\item   48,13 ~ : ~ 100 ~ = ~{\color{red} 0,481 3}
\item   0,334 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 334}
\item   2,06 ~ : ~ 10 ~ = ~{\color{red} 0,206}
\item   34,59 ~ : ~ 1 000 ~ = ~{\color{red} 0,034 59}
\item   16,66 ~ : ~ 10 ~ = ~{\color{red} 1,666}
\item   86,28 ~ : ~ 10 ~ = ~{\color{red} 8,628}
\item   94,9 ~ : ~ 100 ~ = ~{\color{red} 0,949}
\item   0,922 ~ : ~ 100 ~ = ~{\color{red} 0,009 22}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   712 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~71 200
\item   11 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 100
\item   134 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 340
\item   96,1 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 610
\item   0,029 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,29
\item   632 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 320
\item   6,87 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~687
\item   590 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 900
\item   76,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~765
\item   0,077 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,77
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   76,78 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,767 8
}\item   674 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,674
}\item   4,191 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,041 91
}\item   9 501 ~ \(\times\)  0,01 ~ = ~{\color{red} 95,01
}\item   634,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 6,346
}\item   556,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,556 8
}\item   1,413 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,141 3
}\item   1 113 ~ \(\times\)  0,1 ~ = ~{\color{red} 111,3
}\item   1 702 ~ \(\times\)  0,1 ~ = ~{\color{red} 170,2
}\item   374,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 37,41
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   468,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,687
\item   2 414 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,414
\item   72,86 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,072 86
\item   8,517 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 517
\item   28,12 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,812
\item   8,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 1
\item   808,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,808 4
\item   29,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,029 5
\item   428,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,285
\item   12,02 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,120 2
\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 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   757,02 ~L~ = {\color{red}  0,757 02 }~kL
\item   857,47 ~hL~ = {\color{red}  857 470 }~dL
\item   351,07 ~cg~ = {\color{red}  0,035 107 }~hg
\item   3 488,4 ~m~ = {\color{red}  348 840 }~cm
\item   4 595,4 ~hm~ = {\color{red}  459,54 }~km
\item   421,8 ~cg~ = {\color{red}  42,18 }~dg
\item   3 126,7 ~m~ = {\color{red}  31 267 }~dm
\item   6 715,3 ~hL~ = {\color{red}  67 153 }~daL
\item   277,63 ~dm~ = {\color{red}  2 776,3 }~cm
\item   5 352,9 ~mL~ = {\color{red}  0,005 352 9 }~kL
\end{itemize}
\end{multicols}
\end{document}
