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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 198}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{17}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,52  ~ \(\times\)  ~ 10
\item   45,1  ~ \(\times\)  ~ 100
\item   854  ~ \(\times\)  ~ 1 000
\item   0,051  ~ \(\times\)  ~ 1 000
\item   0,078  ~ \(\times\)  ~ 100
\item   2,68  ~ \(\times\)  ~ 10
\item   0,064  ~ \(\times\)  ~ 10
\item   961  ~ \(\times\)  ~ 1 000
\item   70,5  ~ \(\times\)  ~ 100
\item   56,6  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,267  ~ : ~ 10
\item   19,47  ~ : ~ 100
\item   6,049  ~ : ~ 100
\item   88,2  ~ : ~ 100
\item   3 381  ~ : ~ 10
\item   691  ~ : ~ 1 000
\item   6,221  ~ : ~ 1 000
\item   2,623  ~ : ~ 100
\item   751,8  ~ : ~ 100
\item   6 317  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,1  ~ \(\times\)  ~ ... ~ = ~ 90 100
\item   0,016  ~ \(\times\)  ~ ... ~ = ~ 0,16
\item   528  ~ \(\times\)  ~ ... ~ = ~ 52 800
\item   55,4  ~ \(\times\)  ~ ... ~ = ~ 5 540
\item   28,9  ~ \(\times\)  ~ ... ~ = ~ 289
\item   60,2  ~ \(\times\)  ~ ... ~ = ~ 60 200
\item   11,8  ~ \(\times\)  ~ ... ~ = ~ 11 800
\item   590  ~ \(\times\)  ~ ... ~ = ~ 5 900
\item   0,082  ~ \(\times\)  ~ ... ~ = ~ 82
\item   422  ~ \(\times\)  ~ ... ~ = ~ 42 200
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,27  ~ \(\times\)  ~ 0,01
\item   2,042  ~ \(\times\)  ~ 0,1
\item   5,572  ~ \(\times\)  ~ 0,1
\item   6 111  ~ \(\times\)  ~ 0,001
\item   22,56  ~ \(\times\)  ~ 0,01
\item   3,498  ~ \(\times\)  ~ 0,01
\item   48,77  ~ \(\times\)  ~ 0,01
\item   6 236  ~ \(\times\)  ~ 0,1
\item   85,97  ~ \(\times\)  ~ 0,1
\item   574,8  ~ \(\times\)  ~ 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   37,17  ~ \(\times\)  ~ ... ~ = ~  0,037 17
\item   22,08  ~ \(\times\)  ~ ... ~ = ~  0,022 08
\item   67,53  ~ \(\times\)  ~ ... ~ = ~  0,675 3
\item   2,573  ~ \(\times\)  ~ ... ~ = ~  0,002 573
\item   93,96  ~ \(\times\)  ~ ... ~ = ~  0,939 6
\item   3,37  ~ \(\times\)  ~ ... ~ = ~  0,033 7
\item   357  ~ \(\times\)  ~ ... ~ = ~  0,357
\item   4,307  ~ \(\times\)  ~ ... ~ = ~  0,043 07
\item   5 289  ~ \(\times\)  ~ ... ~ = ~  528,9
\item   239,9  ~ \(\times\)  ~ ... ~ = ~  23,99
\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 ~cm~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 007,6 ~mm~ = ...~hm
\item   1 266,9 ~hg~ = ...~kg
\item   231,33 ~cg~ = ...~kg
\item   5 185,2 ~kL~ = ...~hL
\item   7 963,1 ~cg~ = ...~g
\item   695,45 ~dL~ = ...~mL
\item   9 457,9 ~g~ = ...~cg
\item   963,57 ~kL~ = ...~daL
\item   125,87 ~cL~ = ...~daL
\item   378,3 ~L~ = ...~daL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{230}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{690}{100}\)
\item   \(\dfrac{17}{100}\) = \(\dfrac{170}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,52  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 55,2}
\item   45,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 510}
\item   854  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 854 000}
\item   0,051  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 51}
\item   0,078  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,8}
\item   2,68  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 26,8}
\item   0,064  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,64}
\item   961  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 961 000}
\item   70,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 050}
\item   56,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 56 600}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,267 ~ : ~ 10 ~ = ~{\color{red} 0,726 7}
\item   19,47 ~ : ~ 100 ~ = ~{\color{red} 0,194 7}
\item   6,049 ~ : ~ 100 ~ = ~{\color{red} 0,060 49}
\item   88,2 ~ : ~ 100 ~ = ~{\color{red} 0,882}
\item   3 381 ~ : ~ 10 ~ = ~{\color{red} 338,1}
\item   691 ~ : ~ 1 000 ~ = ~{\color{red} 0,691}
\item   6,221 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 221}
\item   2,623 ~ : ~ 100 ~ = ~{\color{red} 0,026 23}
\item   751,8 ~ : ~ 100 ~ = ~{\color{red} 7,518}
\item   6 317 ~ : ~ 100 ~ = ~{\color{red} 63,17}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   90,1 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~90 100
\item   0,016 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,16
\item   528 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~52 800
\item   55,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 540
\item   28,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~289
\item   60,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~60 200
\item   11,8 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~11 800
\item   590 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 900
\item   0,082 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~82
\item   422 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~42 200
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,27 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,112 7
}\item   2,042 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,204 2
}\item   5,572 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,557 2
}\item   6 111 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,111
}\item   22,56 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,225 6
}\item   3,498 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,034 98
}\item   48,77 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,487 7
}\item   6 236 ~ \(\times\)  0,1 ~ = ~{\color{red} 623,6
}\item   85,97 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,597
}\item   574,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 57,48
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   37,17 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,037 17
\item   22,08 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,022 08
\item   67,53 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,675 3
\item   2,573 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 573
\item   93,96 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,939 6
\item   3,37 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,033 7
\item   357 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,357
\item   4,307 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,043 07
\item   5 289 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 528,9
\item   239,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 23,99
\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 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 007,6 ~mm~ = {\color{red}  0,030 076 }~hm
\item   1 266,9 ~hg~ = {\color{red}  126,69 }~kg
\item   231,33 ~cg~ = {\color{red}  0,002 313 3 }~kg
\item   5 185,2 ~kL~ = {\color{red}  51 852 }~hL
\item   7 963,1 ~cg~ = {\color{red}  79,631 }~g
\item   695,45 ~dL~ = {\color{red}  69 545 }~mL
\item   9 457,9 ~g~ = {\color{red}  945 790 }~cg
\item   963,57 ~kL~ = {\color{red}  96 357 }~daL
\item   125,87 ~cL~ = {\color{red}  0,125 87 }~daL
\item   378,3 ~L~ = {\color{red}  37,83 }~daL
\end{itemize}
\end{multicols}
\end{document}
