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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 156}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{30}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17  ~ \(\times\)  ~ 1 000
\item   0,583  ~ \(\times\)  ~ 100
\item   34,5  ~ \(\times\)  ~ 10
\item   16,8  ~ \(\times\)  ~ 10
\item   457  ~ \(\times\)  ~ 1 000
\item   0,412  ~ \(\times\)  ~ 10
\item   0,099  ~ \(\times\)  ~ 1 000
\item   367  ~ \(\times\)  ~ 100
\item   8,16  ~ \(\times\)  ~ 10
\item   0,067  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,3  ~ : ~ 10
\item   4 232  ~ : ~ 10
\item   4 190  ~ : ~ 10
\item   2,62  ~ : ~ 100
\item   477,9  ~ : ~ 100
\item   7 262  ~ : ~ 100
\item   113,8  ~ : ~ 1 000
\item   1 320  ~ : ~ 100
\item   29,24  ~ : ~ 1 000
\item   869,5  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   402  ~ \(\times\)  ~ ... ~ = ~ 40 200
\item   0,008  ~ \(\times\)  ~ ... ~ = ~ 0,8
\item   791  ~ \(\times\)  ~ ... ~ = ~ 79 100
\item   0,537  ~ \(\times\)  ~ ... ~ = ~ 537
\item   681  ~ \(\times\)  ~ ... ~ = ~ 681 000
\item   3,18  ~ \(\times\)  ~ ... ~ = ~ 3 180
\item   0,919  ~ \(\times\)  ~ ... ~ = ~ 919
\item   0,071  ~ \(\times\)  ~ ... ~ = ~ 7,1
\item   915  ~ \(\times\)  ~ ... ~ = ~ 915 000
\item   33,7  ~ \(\times\)  ~ ... ~ = ~ 33 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 660  ~ \(\times\)  ~ 0,001
\item   4 670  ~ \(\times\)  ~ 0,01
\item   754,2  ~ \(\times\)  ~ 0,1
\item   89,49  ~ \(\times\)  ~ 0,01
\item   310,8  ~ \(\times\)  ~ 0,001
\item   867,2  ~ \(\times\)  ~ 0,01
\item   18,1  ~ \(\times\)  ~ 0,01
\item   82,55  ~ \(\times\)  ~ 0,01
\item   3,767  ~ \(\times\)  ~ 0,001
\item   441,2  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 765  ~ \(\times\)  ~ ... ~ = ~  37,65
\item   9 061  ~ \(\times\)  ~ ... ~ = ~  906,1
\item   207,7  ~ \(\times\)  ~ ... ~ = ~  0,207 7
\item   557,5  ~ \(\times\)  ~ ... ~ = ~  55,75
\item   3 522  ~ \(\times\)  ~ ... ~ = ~  35,22
\item   87,68  ~ \(\times\)  ~ ... ~ = ~  8,768
\item   69,54  ~ \(\times\)  ~ ... ~ = ~  0,695 4
\item   917  ~ \(\times\)  ~ ... ~ = ~  9,17
\item   70,2  ~ \(\times\)  ~ ... ~ = ~  0,702
\item   65,87  ~ \(\times\)  ~ ... ~ = ~  6,587
\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 ~dam~ = ...~cm
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 168 ~hm~ = ...~m
\item   694,19 ~mL~ = ...~dL
\item   852,77 ~dam~ = ...~m
\item   1 137,5 ~dL~ = ...~daL
\item   255,62 ~daL~ = ...~mL
\item   306,1 ~dag~ = ...~mg
\item   851,96 ~daL~ = ...~hL
\item   7 109,2 ~kL~ = ...~daL
\item   3 157,6 ~cg~ = ...~dg
\item   3 534 ~cL~ = ...~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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{30}{10}\) = \(\dfrac{300}{100}\)
\item   \(\dfrac{39}{100}\) = \(\dfrac{390}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 17 000}
\item   0,583  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 58,3}
\item   34,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 345}
\item   16,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 168}
\item   457  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 457 000}
\item   0,412  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,12}
\item   0,099  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 99}
\item   367  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 36 700}
\item   8,16  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 81,6}
\item   0,067  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,67}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,3 ~ : ~ 10 ~ = ~{\color{red} 0,83}
\item   4 232 ~ : ~ 10 ~ = ~{\color{red} 423,2}
\item   4 190 ~ : ~ 10 ~ = ~{\color{red} 419}
\item   2,62 ~ : ~ 100 ~ = ~{\color{red} 0,026 2}
\item   477,9 ~ : ~ 100 ~ = ~{\color{red} 4,779}
\item   7 262 ~ : ~ 100 ~ = ~{\color{red} 72,62}
\item   113,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,113 8}
\item   1 320 ~ : ~ 100 ~ = ~{\color{red} 13,2}
\item   29,24 ~ : ~ 1 000 ~ = ~{\color{red} 0,029 24}
\item   869,5 ~ : ~ 100 ~ = ~{\color{red} 8,695}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   402 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~40 200
\item   0,008 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,8
\item   791 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~79 100
\item   0,537 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~537
\item   681 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~681 000
\item   3,18 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~3 180
\item   0,919 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~919
\item   0,071 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,1
\item   915 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~915 000
\item   33,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 660 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,66
}\item   4 670 ~ \(\times\)  0,01 ~ = ~{\color{red} 46,7
}\item   754,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 75,42
}\item   89,49 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,894 9
}\item   310,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,310 8
}\item   867,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,672
}\item   18,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,181
}\item   82,55 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,825 5
}\item   3,767 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 767
}\item   441,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,412
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 765 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 37,65
\item   9 061 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 906,1
\item   207,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,207 7
\item   557,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 55,75
\item   3 522 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 35,22
\item   87,68 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,768
\item   69,54 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,695 4
\item   917 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,17
\item   70,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,702
\item   65,87 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,587
\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 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ 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   9 168 ~hm~ = {\color{red}  916 800 }~m
\item   694,19 ~mL~ = {\color{red}  6,941 9 }~dL
\item   852,77 ~dam~ = {\color{red}  8 527,7 }~m
\item   1 137,5 ~dL~ = {\color{red}  11,375 }~daL
\item   255,62 ~daL~ = {\color{red}  2 556 200 }~mL
\item   306,1 ~dag~ = {\color{red}  3 061 000 }~mg
\item   851,96 ~daL~ = {\color{red}  85,196 }~hL
\item   7 109,2 ~kL~ = {\color{red}  710 920 }~daL
\item   3 157,6 ~cg~ = {\color{red}  315,76 }~dg
\item   3 534 ~cL~ = {\color{red}  0,035 34 }~kL
\end{itemize}
\end{multicols}
\end{document}
