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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 96}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{23}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,46  ~ \(\times\)  ~ 10
\item   724  ~ \(\times\)  ~ 10
\item   4,26  ~ \(\times\)  ~ 10
\item   2,7  ~ \(\times\)  ~ 100
\item   29,1  ~ \(\times\)  ~ 1 000
\item   836  ~ \(\times\)  ~ 1 000
\item   0,05  ~ \(\times\)  ~ 100
\item   4,64  ~ \(\times\)  ~ 10
\item   7,14  ~ \(\times\)  ~ 1 000
\item   0,094  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,4  ~ : ~ 10
\item   2,144  ~ : ~ 1 000
\item   35,86  ~ : ~ 10
\item   2 294  ~ : ~ 1 000
\item   50,59  ~ : ~ 100
\item   3,279  ~ : ~ 100
\item   9 846  ~ : ~ 100
\item   84,17  ~ : ~ 1 000
\item   9,779  ~ : ~ 100
\item   162,6  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,86  ~ \(\times\)  ~ ... ~ = ~ 48,6
\item   0,005  ~ \(\times\)  ~ ... ~ = ~ 0,5
\item   14,1  ~ \(\times\)  ~ ... ~ = ~ 14 100
\item   1,85  ~ \(\times\)  ~ ... ~ = ~ 185
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 0,27
\item   181  ~ \(\times\)  ~ ... ~ = ~ 1 810
\item   0,85  ~ \(\times\)  ~ ... ~ = ~ 85
\item   681  ~ \(\times\)  ~ ... ~ = ~ 6 810
\item   831  ~ \(\times\)  ~ ... ~ = ~ 83 100
\item   187  ~ \(\times\)  ~ ... ~ = ~ 187 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   451  ~ \(\times\)  ~ 0,1
\item   3 026  ~ \(\times\)  ~ 0,1
\item   34,58  ~ \(\times\)  ~ 0,01
\item   16  ~ \(\times\)  ~ 0,01
\item   149,3  ~ \(\times\)  ~ 0,001
\item   967,9  ~ \(\times\)  ~ 0,01
\item   512,5  ~ \(\times\)  ~ 0,01
\item   2 345  ~ \(\times\)  ~ 0,1
\item   8,314  ~ \(\times\)  ~ 0,01
\item   693,8  ~ \(\times\)  ~ 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   3 277  ~ \(\times\)  ~ ... ~ = ~  32,77
\item   7 042  ~ \(\times\)  ~ ... ~ = ~  70,42
\item   9,254  ~ \(\times\)  ~ ... ~ = ~  0,009 254
\item   208  ~ \(\times\)  ~ ... ~ = ~  0,208
\item   150,5  ~ \(\times\)  ~ ... ~ = ~  0,150 5
\item   3,995  ~ \(\times\)  ~ ... ~ = ~  0,003 995
\item   446,1  ~ \(\times\)  ~ ... ~ = ~  4,461
\item   8,76  ~ \(\times\)  ~ ... ~ = ~  0,876
\item   31,86  ~ \(\times\)  ~ ... ~ = ~  0,318 6
\item   6,693  ~ \(\times\)  ~ ... ~ = ~  0,066 93
\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~ = ...~cm
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 819,7 ~daL~ = ...~cL
\item   5 383,7 ~hL~ = ...~kL
\item   9 911,7 ~mL~ = ...~L
\item   963,11 ~g~ = ...~dg
\item   284,17 ~km~ = ...~dam
\item   565,34 ~km~ = ...~cm
\item   4 303,5 ~mg~ = ...~dg
\item   769,31 ~dam~ = ...~hm
\item   7 896 ~cm~ = ...~mm
\item   733,78 ~g~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{9700}{100}\) = \(\dfrac{970}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{37}{10}\) = \(\dfrac{370}{100}\)
\item   \(\dfrac{23}{100}\) = \(\dfrac{230}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,46  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 84,6}
\item   724  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 240}
\item   4,26  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 42,6}
\item   2,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 270}
\item   29,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 29 100}
\item   836  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 836 000}
\item   0,05  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5}
\item   4,64  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 46,4}
\item   7,14  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 140}
\item   0,094  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,4 ~ : ~ 10 ~ = ~{\color{red} 5,64}
\item   2,144 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 144}
\item   35,86 ~ : ~ 10 ~ = ~{\color{red} 3,586}
\item   2 294 ~ : ~ 1 000 ~ = ~{\color{red} 2,294}
\item   50,59 ~ : ~ 100 ~ = ~{\color{red} 0,505 9}
\item   3,279 ~ : ~ 100 ~ = ~{\color{red} 0,032 79}
\item   9 846 ~ : ~ 100 ~ = ~{\color{red} 98,46}
\item   84,17 ~ : ~ 1 000 ~ = ~{\color{red} 0,084 17}
\item   9,779 ~ : ~ 100 ~ = ~{\color{red} 0,097 79}
\item   162,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,162 6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,86 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~48,6
\item   0,005 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,5
\item   14,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~14 100
\item   1,85 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~185
\item   0,027 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,27
\item   181 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 810
\item   0,85 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~85
\item   681 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 810
\item   831 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~83 100
\item   187 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~187 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   451 ~ \(\times\)  0,1 ~ = ~{\color{red} 45,1
}\item   3 026 ~ \(\times\)  0,1 ~ = ~{\color{red} 302,6
}\item   34,58 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,345 8
}\item   16 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,16
}\item   149,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,149 3
}\item   967,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,679
}\item   512,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,125
}\item   2 345 ~ \(\times\)  0,1 ~ = ~{\color{red} 234,5
}\item   8,314 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,083 14
}\item   693,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 69,38
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 277 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 32,77
\item   7 042 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 70,42
\item   9,254 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,009 254
\item   208 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,208
\item   150,5 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,150 5
\item   3,995 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 995
\item   446,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,461
\item   8,76 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,876
\item   31,86 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,318 6
\item   6,693 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,066 93
\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~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 819,7 ~daL~ = {\color{red}  9 819 700 }~cL
\item   5 383,7 ~hL~ = {\color{red}  538,37 }~kL
\item   9 911,7 ~mL~ = {\color{red}  9,911 7 }~L
\item   963,11 ~g~ = {\color{red}  9 631,1 }~dg
\item   284,17 ~km~ = {\color{red}  28 417 }~dam
\item   565,34 ~km~ = {\color{red}  56 534 000 }~cm
\item   4 303,5 ~mg~ = {\color{red}  43,035 }~dg
\item   769,31 ~dam~ = {\color{red}  76,931 }~hm
\item   7 896 ~cm~ = {\color{red}  78 960 }~mm
\item   733,78 ~g~ = {\color{red}  733 780 }~mg
\end{itemize}
\end{multicols}
\end{document}
