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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 110}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   564  ~ \(\times\)  ~ 1 000
\item   0,044  ~ \(\times\)  ~ 100
\item   772  ~ \(\times\)  ~ 10
\item   0,084  ~ \(\times\)  ~ 10
\item   0,163  ~ \(\times\)  ~ 1 000
\item   0,002  ~ \(\times\)  ~ 100
\item   0,098  ~ \(\times\)  ~ 1 000
\item   2,45  ~ \(\times\)  ~ 100
\item   3,8  ~ \(\times\)  ~ 1 000
\item   0,119  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   76,03  ~ : ~ 1 000
\item   218,2  ~ : ~ 100
\item   6,83  ~ : ~ 10
\item   3,001  ~ : ~ 10
\item   1,477  ~ : ~ 100
\item   549,8  ~ : ~ 10
\item   511,2  ~ : ~ 10
\item   458  ~ : ~ 10
\item   98,76  ~ : ~ 1 000
\item   2 406  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42  ~ \(\times\)  ~ ... ~ = ~ 420
\item   0,051  ~ \(\times\)  ~ ... ~ = ~ 5,1
\item   0,034  ~ \(\times\)  ~ ... ~ = ~ 34
\item   386  ~ \(\times\)  ~ ... ~ = ~ 38 600
\item   0,974  ~ \(\times\)  ~ ... ~ = ~ 97,4
\item   544  ~ \(\times\)  ~ ... ~ = ~ 54 400
\item   446  ~ \(\times\)  ~ ... ~ = ~ 4 460
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 97
\item   18,2  ~ \(\times\)  ~ ... ~ = ~ 18 200
\item   122  ~ \(\times\)  ~ ... ~ = ~ 1 220
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   224,8  ~ \(\times\)  ~ 0,001
\item   2 540  ~ \(\times\)  ~ 0,001
\item   92,05  ~ \(\times\)  ~ 0,1
\item   8 565  ~ \(\times\)  ~ 0,1
\item   8 359  ~ \(\times\)  ~ 0,1
\item   83,4  ~ \(\times\)  ~ 0,001
\item   278  ~ \(\times\)  ~ 0,01
\item   2 338  ~ \(\times\)  ~ 0,1
\item   5 562  ~ \(\times\)  ~ 0,001
\item   1 799  ~ \(\times\)  ~ 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   12,58  ~ \(\times\)  ~ ... ~ = ~  1,258
\item   7,628  ~ \(\times\)  ~ ... ~ = ~  0,076 28
\item   89,3  ~ \(\times\)  ~ ... ~ = ~  0,089 3
\item   745,5  ~ \(\times\)  ~ ... ~ = ~  7,455
\item   289,8  ~ \(\times\)  ~ ... ~ = ~  0,289 8
\item   8,074  ~ \(\times\)  ~ ... ~ = ~  0,080 74
\item   347,9  ~ \(\times\)  ~ ... ~ = ~  3,479
\item   855,6  ~ \(\times\)  ~ ... ~ = ~  8,556
\item   3 076  ~ \(\times\)  ~ ... ~ = ~  307,6
\item   298,9  ~ \(\times\)  ~ ... ~ = ~  29,89
\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~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~dam~ = ...~hm
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~dam~ = ...~km
\item   1 ~m~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 784,5 ~cm~ = ...~km
\item   245,93 ~daL~ = ...~dL
\item   736,47 ~dg~ = ...~kg
\item   129,17 ~daL~ = ...~kL
\item   243,56 ~km~ = ...~hm
\item   2 249,4 ~hL~ = ...~L
\item   3 125,7 ~dam~ = ...~km
\item   583,75 ~mL~ = ...~daL
\item   4 514,6 ~hL~ = ...~mL
\item   2 966,3 ~kL~ = ...~hL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 = \(\dfrac{70}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{6300}{100}\) = \(\dfrac{630}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{46}{10}\) = \(\dfrac{460}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{920}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   564  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 564 000}
\item   0,044  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,4}
\item   772  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 720}
\item   0,084  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,84}
\item   0,163  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 163}
\item   0,002  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,2}
\item   0,098  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 98}
\item   2,45  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 245}
\item   3,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 800}
\item   0,119  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 119}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   76,03 ~ : ~ 1 000 ~ = ~{\color{red} 0,076 03}
\item   218,2 ~ : ~ 100 ~ = ~{\color{red} 2,182}
\item   6,83 ~ : ~ 10 ~ = ~{\color{red} 0,683}
\item   3,001 ~ : ~ 10 ~ = ~{\color{red} 0,300 1}
\item   1,477 ~ : ~ 100 ~ = ~{\color{red} 0,014 77}
\item   549,8 ~ : ~ 10 ~ = ~{\color{red} 54,98}
\item   511,2 ~ : ~ 10 ~ = ~{\color{red} 51,12}
\item   458 ~ : ~ 10 ~ = ~{\color{red} 45,8}
\item   98,76 ~ : ~ 1 000 ~ = ~{\color{red} 0,098 76}
\item   2 406 ~ : ~ 100 ~ = ~{\color{red} 24,06}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   42 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~420
\item   0,051 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5,1
\item   0,034 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~34
\item   386 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~38 600
\item   0,974 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~97,4
\item   544 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~54 400
\item   446 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 460
\item   0,097 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~97
\item   18,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~18 200
\item   122 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 220
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   224,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,224 8
}\item   2 540 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,54
}\item   92,05 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,205
}\item   8 565 ~ \(\times\)  0,1 ~ = ~{\color{red} 856,5
}\item   8 359 ~ \(\times\)  0,1 ~ = ~{\color{red} 835,9
}\item   83,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,083 4
}\item   278 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,78
}\item   2 338 ~ \(\times\)  0,1 ~ = ~{\color{red} 233,8
}\item   5 562 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,562
}\item   1 799 ~ \(\times\)  0,01 ~ = ~{\color{red} 17,99
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   12,58 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,258
\item   7,628 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,076 28
\item   89,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,089 3
\item   745,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,455
\item   289,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,289 8
\item   8,074 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,080 74
\item   347,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,479
\item   855,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,556
\item   3 076 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 307,6
\item   298,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 29,89
\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~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 784,5 ~cm~ = {\color{red}  0,087 845 }~km
\item   245,93 ~daL~ = {\color{red}  24 593 }~dL
\item   736,47 ~dg~ = {\color{red}  0,073 647 }~kg
\item   129,17 ~daL~ = {\color{red}  1,291 7 }~kL
\item   243,56 ~km~ = {\color{red}  2 435,6 }~hm
\item   2 249,4 ~hL~ = {\color{red}  224 940 }~L
\item   3 125,7 ~dam~ = {\color{red}  31,257 }~km
\item   583,75 ~mL~ = {\color{red}  0,058 375 }~daL
\item   4 514,6 ~hL~ = {\color{red}  451 460 000 }~mL
\item   2 966,3 ~kL~ = {\color{red}  29 663 }~hL
\end{itemize}
\end{multicols}
\end{document}
