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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 367}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   \(\dfrac{40}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{11}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,68  ~ \(\times\)  ~ 100
\item   0,047  ~ \(\times\)  ~ 10
\item   6,9  ~ \(\times\)  ~ 10
\item   4,74  ~ \(\times\)  ~ 100
\item   6,18  ~ \(\times\)  ~ 100
\item   93,6  ~ \(\times\)  ~ 100
\item   15,7  ~ \(\times\)  ~ 1 000
\item   0,309  ~ \(\times\)  ~ 10
\item   9,5  ~ \(\times\)  ~ 10
\item   0,009  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,8  ~ : ~ 100
\item   2,18  ~ : ~ 1 000
\item   481,6  ~ : ~ 1 000
\item   9 079  ~ : ~ 1 000
\item   1,204  ~ : ~ 100
\item   5 344  ~ : ~ 10
\item   8,741  ~ : ~ 10
\item   796,5  ~ : ~ 10
\item   4 458  ~ : ~ 100
\item   1,359  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 43
\item   0,02  ~ \(\times\)  ~ ... ~ = ~ 20
\item   897  ~ \(\times\)  ~ ... ~ = ~ 897 000
\item   5,29  ~ \(\times\)  ~ ... ~ = ~ 529
\item   224  ~ \(\times\)  ~ ... ~ = ~ 22 400
\item   85,6  ~ \(\times\)  ~ ... ~ = ~ 85 600
\item   63,1  ~ \(\times\)  ~ ... ~ = ~ 631
\item   0,052  ~ \(\times\)  ~ ... ~ = ~ 0,52
\item   7,95  ~ \(\times\)  ~ ... ~ = ~ 7 950
\item   4,91  ~ \(\times\)  ~ ... ~ = ~ 491
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 436  ~ \(\times\)  ~ 0,1
\item   705,8  ~ \(\times\)  ~ 0,001
\item   302,2  ~ \(\times\)  ~ 0,001
\item   6 659  ~ \(\times\)  ~ 0,01
\item   2 941  ~ \(\times\)  ~ 0,1
\item   9 839  ~ \(\times\)  ~ 0,01
\item   368,2  ~ \(\times\)  ~ 0,1
\item   12,35  ~ \(\times\)  ~ 0,1
\item   20,2  ~ \(\times\)  ~ 0,01
\item   5 653  ~ \(\times\)  ~ 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   9,298  ~ \(\times\)  ~ ... ~ = ~  0,009 298
\item   65,86  ~ \(\times\)  ~ ... ~ = ~  0,065 86
\item   6,12  ~ \(\times\)  ~ ... ~ = ~  0,612
\item   90,54  ~ \(\times\)  ~ ... ~ = ~  0,090 54
\item   65,85  ~ \(\times\)  ~ ... ~ = ~  6,585
\item   145,7  ~ \(\times\)  ~ ... ~ = ~  1,457
\item   4,725  ~ \(\times\)  ~ ... ~ = ~  0,472 5
\item   6 635  ~ \(\times\)  ~ ... ~ = ~  66,35
\item   3,434  ~ \(\times\)  ~ ... ~ = ~  0,034 34
\item   960,1  ~ \(\times\)  ~ ... ~ = ~  0,960 1
\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 ~km~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 684,3 ~dag~ = ...~hg
\item   214,65 ~cg~ = ...~dg
\item   7 830,9 ~cg~ = ...~mg
\item   531,87 ~mL~ = ...~hL
\item   758,19 ~daL~ = ...~L
\item   267,05 ~dm~ = ...~cm
\item   825,26 ~m~ = ...~dm
\item   9 212,9 ~hm~ = ...~dam
\item   5 773,9 ~mL~ = ...~cL
\item   976,13 ~g~ = ...~dg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{130}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{40}{10}\) = \(\dfrac{400}{100}\)
\item   \(\dfrac{11}{100}\) = \(\dfrac{110}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,68  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 768}
\item   0,047  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,47}
\item   6,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 69}
\item   4,74  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 474}
\item   6,18  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 618}
\item   93,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 360}
\item   15,7  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 15 700}
\item   0,309  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,09}
\item   9,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 95}
\item   0,009  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,8 ~ : ~ 100 ~ = ~{\color{red} 0,518}
\item   2,18 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 18}
\item   481,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,481 6}
\item   9 079 ~ : ~ 1 000 ~ = ~{\color{red} 9,079}
\item   1,204 ~ : ~ 100 ~ = ~{\color{red} 0,012 04}
\item   5 344 ~ : ~ 10 ~ = ~{\color{red} 534,4}
\item   8,741 ~ : ~ 10 ~ = ~{\color{red} 0,874 1}
\item   796,5 ~ : ~ 10 ~ = ~{\color{red} 79,65}
\item   4 458 ~ : ~ 100 ~ = ~{\color{red} 44,58}
\item   1,359 ~ : ~ 100 ~ = ~{\color{red} 0,013 59}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,043 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43
\item   0,02 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~20
\item   897 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~897 000
\item   5,29 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~529
\item   224 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22 400
\item   85,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~85 600
\item   63,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~631
\item   0,052 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,52
\item   7,95 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 950
\item   4,91 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~491
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 436 ~ \(\times\)  0,1 ~ = ~{\color{red} 243,6
}\item   705,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,705 8
}\item   302,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,302 2
}\item   6 659 ~ \(\times\)  0,01 ~ = ~{\color{red} 66,59
}\item   2 941 ~ \(\times\)  0,1 ~ = ~{\color{red} 294,1
}\item   9 839 ~ \(\times\)  0,01 ~ = ~{\color{red} 98,39
}\item   368,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 36,82
}\item   12,35 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,235
}\item   20,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,202
}\item   5 653 ~ \(\times\)  0,1 ~ = ~{\color{red} 565,3
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,298 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 298
\item   65,86 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,065 86
\item   6,12 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,612
\item   90,54 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,090 54
\item   65,85 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,585
\item   145,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,457
\item   4,725 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,472 5
\item   6 635 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 66,35
\item   3,434 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,034 34
\item   960,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,960 1
\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 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 684,3 ~dag~ = {\color{red}  368,43 }~hg
\item   214,65 ~cg~ = {\color{red}  21,465 }~dg
\item   7 830,9 ~cg~ = {\color{red}  78 309 }~mg
\item   531,87 ~mL~ = {\color{red}  0,005 318 7 }~hL
\item   758,19 ~daL~ = {\color{red}  7 581,9 }~L
\item   267,05 ~dm~ = {\color{red}  2 670,5 }~cm
\item   825,26 ~m~ = {\color{red}  8 252,6 }~dm
\item   9 212,9 ~hm~ = {\color{red}  92 129 }~dam
\item   5 773,9 ~mL~ = {\color{red}  577,39 }~cL
\item   976,13 ~g~ = {\color{red}  9 761,3 }~dg
\end{itemize}
\end{multicols}
\end{document}
