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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 90}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{56}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,833  ~ \(\times\)  ~ 1 000
\item   9,18  ~ \(\times\)  ~ 100
\item   5,09  ~ \(\times\)  ~ 100
\item   0,009  ~ \(\times\)  ~ 1 000
\item   156  ~ \(\times\)  ~ 1 000
\item   0,659  ~ \(\times\)  ~ 100
\item   479  ~ \(\times\)  ~ 10
\item   0,057  ~ \(\times\)  ~ 10
\item   64  ~ \(\times\)  ~ 10
\item   0,013  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 587  ~ : ~ 10
\item   7 049  ~ : ~ 10
\item   162  ~ : ~ 10
\item   2 730  ~ : ~ 1 000
\item   7 230  ~ : ~ 100
\item   53,66  ~ : ~ 1 000
\item   460,7  ~ : ~ 1 000
\item   61,99  ~ : ~ 100
\item   5,334  ~ : ~ 100
\item   8 862  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,036  ~ \(\times\)  ~ ... ~ = ~ 36
\item   0,519  ~ \(\times\)  ~ ... ~ = ~ 519
\item   75,2  ~ \(\times\)  ~ ... ~ = ~ 75 200
\item   27,5  ~ \(\times\)  ~ ... ~ = ~ 2 750
\item   0,007  ~ \(\times\)  ~ ... ~ = ~ 0,7
\item   49,8  ~ \(\times\)  ~ ... ~ = ~ 498
\item   57,9  ~ \(\times\)  ~ ... ~ = ~ 57 900
\item   58,1  ~ \(\times\)  ~ ... ~ = ~ 581
\item   5,8  ~ \(\times\)  ~ ... ~ = ~ 5 800
\item   70,3  ~ \(\times\)  ~ ... ~ = ~ 70 300
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   30,21  ~ \(\times\)  ~ 0,01
\item   4,55  ~ \(\times\)  ~ 0,1
\item   5 928  ~ \(\times\)  ~ 0,01
\item   8 280  ~ \(\times\)  ~ 0,01
\item   2,09  ~ \(\times\)  ~ 0,001
\item   659,7  ~ \(\times\)  ~ 0,1
\item   2,64  ~ \(\times\)  ~ 0,001
\item   8 398  ~ \(\times\)  ~ 0,01
\item   5,247  ~ \(\times\)  ~ 0,1
\item   14,19  ~ \(\times\)  ~ 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   7 125  ~ \(\times\)  ~ ... ~ = ~  7,125
\item   3 297  ~ \(\times\)  ~ ... ~ = ~  329,7
\item   9 051  ~ \(\times\)  ~ ... ~ = ~  905,1
\item   6,086  ~ \(\times\)  ~ ... ~ = ~  0,006 086
\item   2,856  ~ \(\times\)  ~ ... ~ = ~  0,028 56
\item   3 508  ~ \(\times\)  ~ ... ~ = ~  35,08
\item   2,794  ~ \(\times\)  ~ ... ~ = ~  0,027 94
\item   1,1  ~ \(\times\)  ~ ... ~ = ~  0,001 1
\item   641,2  ~ \(\times\)  ~ ... ~ = ~  0,641 2
\item   14,86  ~ \(\times\)  ~ ... ~ = ~  0,148 6
\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~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~hm
\item   1 ~dm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 261,2 ~hL~ = ...~L
\item   321,68 ~dm~ = ...~dam
\item   591,08 ~L~ = ...~cL
\item   2 335,8 ~hm~ = ...~m
\item   217,59 ~daL~ = ...~kL
\item   911,33 ~mm~ = ...~cm
\item   3 996 ~m~ = ...~mm
\item   337,09 ~cL~ = ...~mL
\item   468,89 ~mg~ = ...~g
\item   4 104,6 ~mm~ = ...~km
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{7200}{100}\) = \(\dfrac{720}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{92}{10}\) = \(\dfrac{920}{100}\)
\item   \(\dfrac{56}{100}\) = \(\dfrac{560}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,833  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 833}
\item   9,18  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 918}
\item   5,09  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 509}
\item   0,009  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9}
\item   156  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 156 000}
\item   0,659  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 65,9}
\item   479  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 790}
\item   0,057  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,57}
\item   64  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 640}
\item   0,013  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 587 ~ : ~ 10 ~ = ~{\color{red} 358,7}
\item   7 049 ~ : ~ 10 ~ = ~{\color{red} 704,9}
\item   162 ~ : ~ 10 ~ = ~{\color{red} 16,2}
\item   2 730 ~ : ~ 1 000 ~ = ~{\color{red} 2,73}
\item   7 230 ~ : ~ 100 ~ = ~{\color{red} 72,3}
\item   53,66 ~ : ~ 1 000 ~ = ~{\color{red} 0,053 66}
\item   460,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,460 7}
\item   61,99 ~ : ~ 100 ~ = ~{\color{red} 0,619 9}
\item   5,334 ~ : ~ 100 ~ = ~{\color{red} 0,053 34}
\item   8 862 ~ : ~ 100 ~ = ~{\color{red} 88,62}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,036 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~36
\item   0,519 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~519
\item   75,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~75 200
\item   27,5 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 750
\item   0,007 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,7
\item   49,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~498
\item   57,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~57 900
\item   58,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~581
\item   5,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~5 800
\item   70,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~70 300
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   30,21 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,302 1
}\item   4,55 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,455
}\item   5 928 ~ \(\times\)  0,01 ~ = ~{\color{red} 59,28
}\item   8 280 ~ \(\times\)  0,01 ~ = ~{\color{red} 82,8
}\item   2,09 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 09
}\item   659,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 65,97
}\item   2,64 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 64
}\item   8 398 ~ \(\times\)  0,01 ~ = ~{\color{red} 83,98
}\item   5,247 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,524 7
}\item   14,19 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,014 19
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 125 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,125
\item   3 297 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 329,7
\item   9 051 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 905,1
\item   6,086 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 086
\item   2,856 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,028 56
\item   3 508 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 35,08
\item   2,794 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,027 94
\item   1,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 1
\item   641,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,641 2
\item   14,86 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,148 6
\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~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 261,2 ~hL~ = {\color{red}  826 120 }~L
\item   321,68 ~dm~ = {\color{red}  3,216 8 }~dam
\item   591,08 ~L~ = {\color{red}  59 108 }~cL
\item   2 335,8 ~hm~ = {\color{red}  233 580 }~m
\item   217,59 ~daL~ = {\color{red}  2,175 9 }~kL
\item   911,33 ~mm~ = {\color{red}  91,133 }~cm
\item   3 996 ~m~ = {\color{red}  3 996 000 }~mm
\item   337,09 ~cL~ = {\color{red}  3 370,9 }~mL
\item   468,89 ~mg~ = {\color{red}  0,468 89 }~g
\item   4 104,6 ~mm~ = {\color{red}  0,004 104 6 }~km
\end{itemize}
\end{multicols}
\end{document}
