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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 160}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{86}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,074  ~ \(\times\)  ~ 100
\item   56  ~ \(\times\)  ~ 1 000
\item   0,448  ~ \(\times\)  ~ 10
\item   296  ~ \(\times\)  ~ 100
\item   5,7  ~ \(\times\)  ~ 10
\item   0,452  ~ \(\times\)  ~ 1 000
\item   0,386  ~ \(\times\)  ~ 100
\item   8,61  ~ \(\times\)  ~ 100
\item   97  ~ \(\times\)  ~ 10
\item   0,078  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   473,8  ~ : ~ 100
\item   137,1  ~ : ~ 10
\item   2,634  ~ : ~ 100
\item   5 194  ~ : ~ 100
\item   96,86  ~ : ~ 100
\item   476  ~ : ~ 1 000
\item   3 562  ~ : ~ 1 000
\item   7,453  ~ : ~ 10
\item   87,54  ~ : ~ 1 000
\item   2 143  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   30  ~ \(\times\)  ~ ... ~ = ~ 300
\item   803  ~ \(\times\)  ~ ... ~ = ~ 803 000
\item   18,7  ~ \(\times\)  ~ ... ~ = ~ 187
\item   0,688  ~ \(\times\)  ~ ... ~ = ~ 6,88
\item   694  ~ \(\times\)  ~ ... ~ = ~ 6 940
\item   853  ~ \(\times\)  ~ ... ~ = ~ 85 300
\item   710  ~ \(\times\)  ~ ... ~ = ~ 710 000
\item   94,8  ~ \(\times\)  ~ ... ~ = ~ 94 800
\item   46  ~ \(\times\)  ~ ... ~ = ~ 460
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 591  ~ \(\times\)  ~ 0,1
\item   951,8  ~ \(\times\)  ~ 0,01
\item   8,497  ~ \(\times\)  ~ 0,01
\item   72,47  ~ \(\times\)  ~ 0,01
\item   24,71  ~ \(\times\)  ~ 0,001
\item   7 970  ~ \(\times\)  ~ 0,001
\item   483,1  ~ \(\times\)  ~ 0,01
\item   72,15  ~ \(\times\)  ~ 0,001
\item   760,9  ~ \(\times\)  ~ 0,001
\item   12,11  ~ \(\times\)  ~ 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   90,17  ~ \(\times\)  ~ ... ~ = ~  9,017
\item   4 788  ~ \(\times\)  ~ ... ~ = ~  47,88
\item   3 096  ~ \(\times\)  ~ ... ~ = ~  30,96
\item   5,53  ~ \(\times\)  ~ ... ~ = ~  0,553
\item   2,273  ~ \(\times\)  ~ ... ~ = ~  0,227 3
\item   8,078  ~ \(\times\)  ~ ... ~ = ~  0,008 078
\item   435,4  ~ \(\times\)  ~ ... ~ = ~  0,435 4
\item   739,4  ~ \(\times\)  ~ ... ~ = ~  73,94
\item   8,078  ~ \(\times\)  ~ ... ~ = ~  0,807 8
\item   276,6  ~ \(\times\)  ~ ... ~ = ~  2,766
\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 ~dm~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~m~ = ...~km
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   608,99 ~dg~ = ...~hg
\item   5 507,3 ~daL~ = ...~hL
\item   329,63 ~daL~ = ...~kL
\item   6 877,8 ~mm~ = ...~km
\item   870,67 ~km~ = ...~dm
\item   682,65 ~mg~ = ...~hg
\item   9 744,7 ~m~ = ...~dm
\item   544,11 ~dm~ = ...~hm
\item   5 913,2 ~g~ = ...~dg
\item   3 504,4 ~mL~ = ...~hL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{6200}{100}\) = \(\dfrac{620}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{86}{10}\) = \(\dfrac{860}{100}\)
\item   \(\dfrac{55}{100}\) = \(\dfrac{550}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,074  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,4}
\item   56  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 56 000}
\item   0,448  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,48}
\item   296  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 29 600}
\item   5,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 57}
\item   0,452  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 452}
\item   0,386  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 38,6}
\item   8,61  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 861}
\item   97  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 970}
\item   0,078  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 78}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   473,8 ~ : ~ 100 ~ = ~{\color{red} 4,738}
\item   137,1 ~ : ~ 10 ~ = ~{\color{red} 13,71}
\item   2,634 ~ : ~ 100 ~ = ~{\color{red} 0,026 34}
\item   5 194 ~ : ~ 100 ~ = ~{\color{red} 51,94}
\item   96,86 ~ : ~ 100 ~ = ~{\color{red} 0,968 6}
\item   476 ~ : ~ 1 000 ~ = ~{\color{red} 0,476}
\item   3 562 ~ : ~ 1 000 ~ = ~{\color{red} 3,562}
\item   7,453 ~ : ~ 10 ~ = ~{\color{red} 0,745 3}
\item   87,54 ~ : ~ 1 000 ~ = ~{\color{red} 0,087 54}
\item   2 143 ~ : ~ 100 ~ = ~{\color{red} 21,43}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,004 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,4
\item   30 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~300
\item   803 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~803 000
\item   18,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~187
\item   0,688 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,88
\item   694 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 940
\item   853 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~85 300
\item   710 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~710 000
\item   94,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~94 800
\item   46 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~460
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 591 ~ \(\times\)  0,1 ~ = ~{\color{red} 759,1
}\item   951,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,518
}\item   8,497 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,084 97
}\item   72,47 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,724 7
}\item   24,71 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,024 71
}\item   7 970 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,97
}\item   483,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,831
}\item   72,15 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,072 15
}\item   760,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,760 9
}\item   12,11 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,211
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,17 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,017
\item   4 788 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 47,88
\item   3 096 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 30,96
\item   5,53 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,553
\item   2,273 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,227 3
\item   8,078 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 078
\item   435,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,435 4
\item   739,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 73,94
\item   8,078 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,807 8
\item   276,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,766
\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 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   608,99 ~dg~ = {\color{red}  0,608 99 }~hg
\item   5 507,3 ~daL~ = {\color{red}  550,73 }~hL
\item   329,63 ~daL~ = {\color{red}  3,296 3 }~kL
\item   6 877,8 ~mm~ = {\color{red}  0,006 877 8 }~km
\item   870,67 ~km~ = {\color{red}  8 706 700 }~dm
\item   682,65 ~mg~ = {\color{red}  0,006 826 5 }~hg
\item   9 744,7 ~m~ = {\color{red}  97 447 }~dm
\item   544,11 ~dm~ = {\color{red}  0,544 11 }~hm
\item   5 913,2 ~g~ = {\color{red}  59 132 }~dg
\item   3 504,4 ~mL~ = {\color{red}  0,035 044 }~hL
\end{itemize}
\end{multicols}
\end{document}
