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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 305}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,074  ~ \(\times\)  ~ 10
\item   0,198  ~ \(\times\)  ~ 1 000
\item   32  ~ \(\times\)  ~ 1 000
\item   197  ~ \(\times\)  ~ 1 000
\item   0,708  ~ \(\times\)  ~ 1 000
\item   51,4  ~ \(\times\)  ~ 100
\item   75,7  ~ \(\times\)  ~ 100
\item   2,3  ~ \(\times\)  ~ 10
\item   0,059  ~ \(\times\)  ~ 10
\item   0,37  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,189  ~ : ~ 100
\item   2 654  ~ : ~ 1 000
\item   349,9  ~ : ~ 100
\item   82,03  ~ : ~ 10
\item   4 235  ~ : ~ 10
\item   2 430  ~ : ~ 1 000
\item   1,377  ~ : ~ 1 000
\item   348  ~ : ~ 100
\item   460,3  ~ : ~ 1 000
\item   9 861  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,3  ~ \(\times\)  ~ ... ~ = ~ 9 300
\item   6,63  ~ \(\times\)  ~ ... ~ = ~ 663
\item   0,176  ~ \(\times\)  ~ ... ~ = ~ 1,76
\item   8,8  ~ \(\times\)  ~ ... ~ = ~ 880
\item   4,73  ~ \(\times\)  ~ ... ~ = ~ 47,3
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,04
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 88
\item   2,95  ~ \(\times\)  ~ ... ~ = ~ 2 950
\item   89,7  ~ \(\times\)  ~ ... ~ = ~ 89 700
\item   0,189  ~ \(\times\)  ~ ... ~ = ~ 189
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   290,4  ~ \(\times\)  ~ 0,01
\item   104,5  ~ \(\times\)  ~ 0,1
\item   6 619  ~ \(\times\)  ~ 0,01
\item   3 974  ~ \(\times\)  ~ 0,1
\item   7,47  ~ \(\times\)  ~ 0,01
\item   3,775  ~ \(\times\)  ~ 0,01
\item   90,7  ~ \(\times\)  ~ 0,1
\item   13,32  ~ \(\times\)  ~ 0,1
\item   719,5  ~ \(\times\)  ~ 0,01
\item   906,1  ~ \(\times\)  ~ 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   19,59  ~ \(\times\)  ~ ... ~ = ~  1,959
\item   5,311  ~ \(\times\)  ~ ... ~ = ~  0,053 11
\item   5 757  ~ \(\times\)  ~ ... ~ = ~  5,757
\item   220  ~ \(\times\)  ~ ... ~ = ~  0,22
\item   141,3  ~ \(\times\)  ~ ... ~ = ~  14,13
\item   703,2  ~ \(\times\)  ~ ... ~ = ~  0,703 2
\item   0,562  ~ \(\times\)  ~ ... ~ = ~  0,000 562
\item   98,3  ~ \(\times\)  ~ ... ~ = ~  9,83
\item   3,418  ~ \(\times\)  ~ ... ~ = ~  0,034 18
\item   63,42  ~ \(\times\)  ~ ... ~ = ~  0,634 2
\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~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   162,7 ~mg~ = ...~hg
\item   9 550,9 ~cL~ = ...~daL
\item   7 741,6 ~mg~ = ...~g
\item   210,09 ~daL~ = ...~kL
\item   557,21 ~mL~ = ...~cL
\item   388,77 ~hg~ = ...~cg
\item   777,75 ~cm~ = ...~mm
\item   1 599,6 ~hm~ = ...~mm
\item   8 366,4 ~cg~ = ...~g
\item   4 538,4 ~g~ = ...~kg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{9100}{100}\) = \(\dfrac{910}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{770}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{330}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,074  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,74}
\item   0,198  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 198}
\item   32  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32 000}
\item   197  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 197 000}
\item   0,708  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 708}
\item   51,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 140}
\item   75,7  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 570}
\item   2,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 23}
\item   0,059  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,59}
\item   0,37  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 37}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,189 ~ : ~ 100 ~ = ~{\color{red} 0,041 89}
\item   2 654 ~ : ~ 1 000 ~ = ~{\color{red} 2,654}
\item   349,9 ~ : ~ 100 ~ = ~{\color{red} 3,499}
\item   82,03 ~ : ~ 10 ~ = ~{\color{red} 8,203}
\item   4 235 ~ : ~ 10 ~ = ~{\color{red} 423,5}
\item   2 430 ~ : ~ 1 000 ~ = ~{\color{red} 2,43}
\item   1,377 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 377}
\item   348 ~ : ~ 100 ~ = ~{\color{red} 3,48}
\item   460,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,460 3}
\item   9 861 ~ : ~ 1 000 ~ = ~{\color{red} 9,861}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 300
\item   6,63 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~663
\item   0,176 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,76
\item   8,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~880
\item   4,73 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~47,3
\item   0,004 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,04
\item   0,088 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~88
\item   2,95 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 950
\item   89,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~89 700
\item   0,189 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~189
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   290,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,904
}\item   104,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 10,45
}\item   6 619 ~ \(\times\)  0,01 ~ = ~{\color{red} 66,19
}\item   3 974 ~ \(\times\)  0,1 ~ = ~{\color{red} 397,4
}\item   7,47 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,074 7
}\item   3,775 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,037 75
}\item   90,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,07
}\item   13,32 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,332
}\item   719,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,195
}\item   906,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,061
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   19,59 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,959
\item   5,311 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,053 11
\item   5 757 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,757
\item   220 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,22
\item   141,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 14,13
\item   703,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,703 2
\item   0,562 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 562
\item   98,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,83
\item   3,418 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,034 18
\item   63,42 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,634 2
\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}  100 ~ }dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\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   162,7 ~mg~ = {\color{red}  0,001 627 }~hg
\item   9 550,9 ~cL~ = {\color{red}  9,550 9 }~daL
\item   7 741,6 ~mg~ = {\color{red}  7,741 6 }~g
\item   210,09 ~daL~ = {\color{red}  2,100 9 }~kL
\item   557,21 ~mL~ = {\color{red}  55,721 }~cL
\item   388,77 ~hg~ = {\color{red}  3 887 700 }~cg
\item   777,75 ~cm~ = {\color{red}  7 777,5 }~mm
\item   1 599,6 ~hm~ = {\color{red}  159 960 000 }~mm
\item   8 366,4 ~cg~ = {\color{red}  83,664 }~g
\item   4 538,4 ~g~ = {\color{red}  4,538 4 }~kg
\end{itemize}
\end{multicols}
\end{document}
