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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 15}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{31}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26  ~ \(\times\)  ~ 1 000
\item   1,59  ~ \(\times\)  ~ 10
\item   1,28  ~ \(\times\)  ~ 100
\item   7,34  ~ \(\times\)  ~ 100
\item   4,1  ~ \(\times\)  ~ 100
\item   24,3  ~ \(\times\)  ~ 100
\item   8,25  ~ \(\times\)  ~ 10
\item   0,032  ~ \(\times\)  ~ 100
\item   0,025  ~ \(\times\)  ~ 100
\item   0,869  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,394  ~ : ~ 1 000
\item   5,998  ~ : ~ 1 000
\item   5,264  ~ : ~ 100
\item   1,179  ~ : ~ 10
\item   330,7  ~ : ~ 1 000
\item   2 922  ~ : ~ 100
\item   8,784  ~ : ~ 10
\item   1 737  ~ : ~ 100
\item   877  ~ : ~ 100
\item   91,93  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\item   0,019  ~ \(\times\)  ~ ... ~ = ~ 19
\item   371  ~ \(\times\)  ~ ... ~ = ~ 3 710
\item   3,26  ~ \(\times\)  ~ ... ~ = ~ 32,6
\item   8,53  ~ \(\times\)  ~ ... ~ = ~ 853
\item   0,935  ~ \(\times\)  ~ ... ~ = ~ 93,5
\item   0,9  ~ \(\times\)  ~ ... ~ = ~ 9
\item   7,84  ~ \(\times\)  ~ ... ~ = ~ 784
\item   154  ~ \(\times\)  ~ ... ~ = ~ 154 000
\item   0,513  ~ \(\times\)  ~ ... ~ = ~ 51,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,53  ~ \(\times\)  ~ 0,001
\item   16,13  ~ \(\times\)  ~ 0,1
\item   0,778  ~ \(\times\)  ~ 0,1
\item   427,9  ~ \(\times\)  ~ 0,01
\item   9,358  ~ \(\times\)  ~ 0,01
\item   806  ~ \(\times\)  ~ 0,01
\item   1,439  ~ \(\times\)  ~ 0,1
\item   9,822  ~ \(\times\)  ~ 0,001
\item   4 289  ~ \(\times\)  ~ 0,001
\item   247  ~ \(\times\)  ~ 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   6,323  ~ \(\times\)  ~ ... ~ = ~  0,063 23
\item   10,17  ~ \(\times\)  ~ ... ~ = ~  0,010 17
\item   74,02  ~ \(\times\)  ~ ... ~ = ~  0,074 02
\item   0,607  ~ \(\times\)  ~ ... ~ = ~  0,006 07
\item   3,47  ~ \(\times\)  ~ ... ~ = ~  0,003 47
\item   6 465  ~ \(\times\)  ~ ... ~ = ~  646,5
\item   421,3  ~ \(\times\)  ~ ... ~ = ~  4,213
\item   84,99  ~ \(\times\)  ~ ... ~ = ~  0,849 9
\item   40,95  ~ \(\times\)  ~ ... ~ = ~  0,409 5
\item   5 322  ~ \(\times\)  ~ ... ~ = ~  5,322
\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~ = ...~m
\item   1 ~cm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 248,9 ~dL~ = ...~mL
\item   632,2 ~daL~ = ...~cL
\item   4 474,5 ~m~ = ...~cm
\item   4 441,2 ~km~ = ...~hm
\item   9 744,2 ~mg~ = ...~cg
\item   6 580,5 ~mm~ = ...~dam
\item   5 481,6 ~mL~ = ...~kL
\item   805,89 ~kg~ = ...~dg
\item   8 947,6 ~dm~ = ...~mm
\item   219,99 ~cL~ = ...~mL
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{7700}{100}\) = \(\dfrac{770}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{31}{10}\) = \(\dfrac{310}{100}\)
\item   \(\dfrac{41}{100}\) = \(\dfrac{410}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   26  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 26 000}
\item   1,59  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 15,9}
\item   1,28  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 128}
\item   7,34  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 734}
\item   4,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 410}
\item   24,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 430}
\item   8,25  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 82,5}
\item   0,032  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,2}
\item   0,025  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,5}
\item   0,869  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 86,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,394 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 394}
\item   5,998 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 998}
\item   5,264 ~ : ~ 100 ~ = ~{\color{red} 0,052 64}
\item   1,179 ~ : ~ 10 ~ = ~{\color{red} 0,117 9}
\item   330,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,330 7}
\item   2 922 ~ : ~ 100 ~ = ~{\color{red} 29,22}
\item   8,784 ~ : ~ 10 ~ = ~{\color{red} 0,878 4}
\item   1 737 ~ : ~ 100 ~ = ~{\color{red} 17,37}
\item   877 ~ : ~ 100 ~ = ~{\color{red} 8,77}
\item   91,93 ~ : ~ 100 ~ = ~{\color{red} 0,919 3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\item   0,019 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~19
\item   371 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3 710
\item   3,26 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~32,6
\item   8,53 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~853
\item   0,935 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~93,5
\item   0,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9
\item   7,84 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~784
\item   154 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~154 000
\item   0,513 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~51,3
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,53 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 53
}\item   16,13 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,613
}\item   0,778 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,077 8
}\item   427,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 4,279
}\item   9,358 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,093 58
}\item   806 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,06
}\item   1,439 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,143 9
}\item   9,822 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 822
}\item   4 289 ~ \(\times\)  0,001 ~ = ~{\color{red} 4,289
}\item   247 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,47
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,323 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,063 23
\item   10,17 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,010 17
\item   74,02 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,074 02
\item   0,607 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,006 07
\item   3,47 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 47
\item   6 465 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 646,5
\item   421,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,213
\item   84,99 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,849 9
\item   40,95 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,409 5
\item   5 322 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,322
\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}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 248,9 ~dL~ = {\color{red}  424 890 }~mL
\item   632,2 ~daL~ = {\color{red}  632 200 }~cL
\item   4 474,5 ~m~ = {\color{red}  447 450 }~cm
\item   4 441,2 ~km~ = {\color{red}  44 412 }~hm
\item   9 744,2 ~mg~ = {\color{red}  974,42 }~cg
\item   6 580,5 ~mm~ = {\color{red}  0,658 05 }~dam
\item   5 481,6 ~mL~ = {\color{red}  0,005 481 6 }~kL
\item   805,89 ~kg~ = {\color{red}  8 058 900 }~dg
\item   8 947,6 ~dm~ = {\color{red}  894 760 }~mm
\item   219,99 ~cL~ = {\color{red}  2 199,9 }~mL
\end{itemize}
\end{multicols}
\end{document}
