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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 215}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{21}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   690  ~ \(\times\)  ~ 1 000
\item   3,94  ~ \(\times\)  ~ 1 000
\item   40  ~ \(\times\)  ~ 1 000
\item   75,2  ~ \(\times\)  ~ 100
\item   659  ~ \(\times\)  ~ 1 000
\item   0,822  ~ \(\times\)  ~ 100
\item   54,2  ~ \(\times\)  ~ 1 000
\item   0,046  ~ \(\times\)  ~ 1 000
\item   42,9  ~ \(\times\)  ~ 100
\item   1,44  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,35  ~ : ~ 10
\item   106,1  ~ : ~ 10
\item   36,95  ~ : ~ 10
\item   88,3  ~ : ~ 100
\item   41,72  ~ : ~ 10
\item   724,8  ~ : ~ 1 000
\item   6 048  ~ : ~ 10
\item   98,37  ~ : ~ 1 000
\item   96,09  ~ : ~ 1 000
\item   2 642  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,801  ~ \(\times\)  ~ ... ~ = ~ 80,1
\item   5,34  ~ \(\times\)  ~ ... ~ = ~ 534
\item   1,73  ~ \(\times\)  ~ ... ~ = ~ 17,3
\item   307  ~ \(\times\)  ~ ... ~ = ~ 30 700
\item   0,038  ~ \(\times\)  ~ ... ~ = ~ 38
\item   8,45  ~ \(\times\)  ~ ... ~ = ~ 84,5
\item   6,5  ~ \(\times\)  ~ ... ~ = ~ 65
\item   0,064  ~ \(\times\)  ~ ... ~ = ~ 0,64
\item   255  ~ \(\times\)  ~ ... ~ = ~ 25 500
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 0,58
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   659,2  ~ \(\times\)  ~ 0,001
\item   1,48  ~ \(\times\)  ~ 0,001
\item   5 468  ~ \(\times\)  ~ 0,1
\item   258,9  ~ \(\times\)  ~ 0,1
\item   210,9  ~ \(\times\)  ~ 0,001
\item   3,295  ~ \(\times\)  ~ 0,01
\item   282,3  ~ \(\times\)  ~ 0,001
\item   8,43  ~ \(\times\)  ~ 0,01
\item   855,9  ~ \(\times\)  ~ 0,01
\item   19,7  ~ \(\times\)  ~ 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   1,734  ~ \(\times\)  ~ ... ~ = ~  0,001 734
\item   348,2  ~ \(\times\)  ~ ... ~ = ~  0,348 2
\item   3,61  ~ \(\times\)  ~ ... ~ = ~  0,036 1
\item   11,95  ~ \(\times\)  ~ ... ~ = ~  0,119 5
\item   620,6  ~ \(\times\)  ~ ... ~ = ~  6,206
\item   106,3  ~ \(\times\)  ~ ... ~ = ~  1,063
\item   3 474  ~ \(\times\)  ~ ... ~ = ~  3,474
\item   63,2  ~ \(\times\)  ~ ... ~ = ~  0,063 2
\item   23,92  ~ \(\times\)  ~ ... ~ = ~  2,392
\item   2,711  ~ \(\times\)  ~ ... ~ = ~  0,271 1
\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~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~m~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   295,54 ~dg~ = ...~hg
\item   878,49 ~mm~ = ...~dam
\item   274,17 ~km~ = ...~m
\item   6 261,3 ~dL~ = ...~kL
\item   8 027,8 ~hL~ = ...~dL
\item   221,41 ~dm~ = ...~dam
\item   9 915,9 ~km~ = ...~dm
\item   501,72 ~kL~ = ...~daL
\item   5 862,9 ~g~ = ...~dag
\item   155,13 ~dag~ = ...~dg
\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   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{2300}{100}\) = \(\dfrac{230}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{41}{10}\) = \(\dfrac{410}{100}\)
\item   \(\dfrac{21}{100}\) = \(\dfrac{210}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   690  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 690 000}
\item   3,94  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 940}
\item   40  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 40 000}
\item   75,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 520}
\item   659  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 659 000}
\item   0,822  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 82,2}
\item   54,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 54 200}
\item   0,046  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 46}
\item   42,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 290}
\item   1,44  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 440}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,35 ~ : ~ 10 ~ = ~{\color{red} 7,935}
\item   106,1 ~ : ~ 10 ~ = ~{\color{red} 10,61}
\item   36,95 ~ : ~ 10 ~ = ~{\color{red} 3,695}
\item   88,3 ~ : ~ 100 ~ = ~{\color{red} 0,883}
\item   41,72 ~ : ~ 10 ~ = ~{\color{red} 4,172}
\item   724,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,724 8}
\item   6 048 ~ : ~ 10 ~ = ~{\color{red} 604,8}
\item   98,37 ~ : ~ 1 000 ~ = ~{\color{red} 0,098 37}
\item   96,09 ~ : ~ 1 000 ~ = ~{\color{red} 0,096 09}
\item   2 642 ~ : ~ 10 ~ = ~{\color{red} 264,2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,801 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~80,1
\item   5,34 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~534
\item   1,73 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~17,3
\item   307 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~30 700
\item   0,038 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~38
\item   8,45 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~84,5
\item   6,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~65
\item   0,064 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,64
\item   255 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~25 500
\item   0,058 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,58
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   659,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,659 2
}\item   1,48 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 48
}\item   5 468 ~ \(\times\)  0,1 ~ = ~{\color{red} 546,8
}\item   258,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 25,89
}\item   210,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,210 9
}\item   3,295 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,032 95
}\item   282,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,282 3
}\item   8,43 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,084 3
}\item   855,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 8,559
}\item   19,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,197
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,734 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 734
\item   348,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,348 2
\item   3,61 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,036 1
\item   11,95 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,119 5
\item   620,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,206
\item   106,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,063
\item   3 474 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,474
\item   63,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,063 2
\item   23,92 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,392
\item   2,711 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,271 1
\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~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   295,54 ~dg~ = {\color{red}  0,295 54 }~hg
\item   878,49 ~mm~ = {\color{red}  0,087 849 }~dam
\item   274,17 ~km~ = {\color{red}  274 170 }~m
\item   6 261,3 ~dL~ = {\color{red}  0,626 13 }~kL
\item   8 027,8 ~hL~ = {\color{red}  8 027 800 }~dL
\item   221,41 ~dm~ = {\color{red}  2,214 1 }~dam
\item   9 915,9 ~km~ = {\color{red}  99 159 000 }~dm
\item   501,72 ~kL~ = {\color{red}  50 172 }~daL
\item   5 862,9 ~g~ = {\color{red}  586,29 }~dag
\item   155,13 ~dag~ = {\color{red}  15 513 }~dg
\end{itemize}
\end{multicols}
\end{document}
