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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 289}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{11}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{14}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,394  ~ \(\times\)  ~ 10
\item   0,436  ~ \(\times\)  ~ 10
\item   511  ~ \(\times\)  ~ 1 000
\item   0,84  ~ \(\times\)  ~ 10
\item   753  ~ \(\times\)  ~ 10
\item   41  ~ \(\times\)  ~ 10
\item   73,1  ~ \(\times\)  ~ 1 000
\item   617  ~ \(\times\)  ~ 1 000
\item   461  ~ \(\times\)  ~ 10
\item   0,026  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   648,6  ~ : ~ 1 000
\item   944  ~ : ~ 100
\item   70,79  ~ : ~ 100
\item   73,3  ~ : ~ 100
\item   134,8  ~ : ~ 10
\item   2,131  ~ : ~ 10
\item   435,5  ~ : ~ 1 000
\item   16,99  ~ : ~ 1 000
\item   7 840  ~ : ~ 100
\item   0,343  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   568  ~ \(\times\)  ~ ... ~ = ~ 56 800
\item   356  ~ \(\times\)  ~ ... ~ = ~ 356 000
\item   0,94  ~ \(\times\)  ~ ... ~ = ~ 94
\item   157  ~ \(\times\)  ~ ... ~ = ~ 1 570
\item   7,1  ~ \(\times\)  ~ ... ~ = ~ 71
\item   0,847  ~ \(\times\)  ~ ... ~ = ~ 8,47
\item   16,6  ~ \(\times\)  ~ ... ~ = ~ 1 660
\item   4,42  ~ \(\times\)  ~ ... ~ = ~ 44,2
\item   88  ~ \(\times\)  ~ ... ~ = ~ 8 800
\item   35,4  ~ \(\times\)  ~ ... ~ = ~ 354
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   25,2  ~ \(\times\)  ~ 0,1
\item   7 036  ~ \(\times\)  ~ 0,001
\item   8 124  ~ \(\times\)  ~ 0,001
\item   70,66  ~ \(\times\)  ~ 0,01
\item   65,66  ~ \(\times\)  ~ 0,01
\item   7 412  ~ \(\times\)  ~ 0,01
\item   1 695  ~ \(\times\)  ~ 0,001
\item   2,666  ~ \(\times\)  ~ 0,1
\item   82,36  ~ \(\times\)  ~ 0,01
\item   8,906  ~ \(\times\)  ~ 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   235  ~ \(\times\)  ~ ... ~ = ~  0,235
\item   7,71  ~ \(\times\)  ~ ... ~ = ~  0,007 71
\item   3,31  ~ \(\times\)  ~ ... ~ = ~  0,003 31
\item   8,447  ~ \(\times\)  ~ ... ~ = ~  0,008 447
\item   5 090  ~ \(\times\)  ~ ... ~ = ~  509
\item   229,9  ~ \(\times\)  ~ ... ~ = ~  2,299
\item   1,52  ~ \(\times\)  ~ ... ~ = ~  0,001 52
\item   87,22  ~ \(\times\)  ~ ... ~ = ~  0,087 22
\item   7 711  ~ \(\times\)  ~ ... ~ = ~  771,1
\item   6,558  ~ \(\times\)  ~ ... ~ = ~  0,655 8
\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 ~m~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   160,95 ~daL~ = ...~L
\item   596,18 ~g~ = ...~kg
\item   9 694,9 ~hL~ = ...~mL
\item   993,21 ~mL~ = ...~L
\item   9 561 ~dm~ = ...~hm
\item   9 380,3 ~kg~ = ...~hg
\item   283,01 ~hg~ = ...~kg
\item   7 111,2 ~mL~ = ...~cL
\item   638,9 ~hm~ = ...~mm
\item   4 378,6 ~dag~ = ...~hg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{2100}{100}\) = \(\dfrac{210}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{11}{10}\) = \(\dfrac{110}{100}\)
\item   \(\dfrac{14}{100}\) = \(\dfrac{140}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,394  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,94}
\item   0,436  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,36}
\item   511  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 511 000}
\item   0,84  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,4}
\item   753  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 530}
\item   41  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 410}
\item   73,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 73 100}
\item   617  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 617 000}
\item   461  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 610}
\item   0,026  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,26}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   648,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,648 6}
\item   944 ~ : ~ 100 ~ = ~{\color{red} 9,44}
\item   70,79 ~ : ~ 100 ~ = ~{\color{red} 0,707 9}
\item   73,3 ~ : ~ 100 ~ = ~{\color{red} 0,733}
\item   134,8 ~ : ~ 10 ~ = ~{\color{red} 13,48}
\item   2,131 ~ : ~ 10 ~ = ~{\color{red} 0,213 1}
\item   435,5 ~ : ~ 1 000 ~ = ~{\color{red} 0,435 5}
\item   16,99 ~ : ~ 1 000 ~ = ~{\color{red} 0,016 99}
\item   7 840 ~ : ~ 100 ~ = ~{\color{red} 78,4}
\item   0,343 ~ : ~ 100 ~ = ~{\color{red} 0,003 43}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   568 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~56 800
\item   356 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~356 000
\item   0,94 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~94
\item   157 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1 570
\item   7,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~71
\item   0,847 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,47
\item   16,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 660
\item   4,42 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~44,2
\item   88 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 800
\item   35,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~354
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   25,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,52
}\item   7 036 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,036
}\item   8 124 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,124
}\item   70,66 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,706 6
}\item   65,66 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,656 6
}\item   7 412 ~ \(\times\)  0,01 ~ = ~{\color{red} 74,12
}\item   1 695 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,695
}\item   2,666 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,266 6
}\item   82,36 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,823 6
}\item   8,906 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,890 6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   235 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,235
\item   7,71 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 71
\item   3,31 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 31
\item   8,447 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 447
\item   5 090 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 509
\item   229,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,299
\item   1,52 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 52
\item   87,22 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,087 22
\item   7 711 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 771,1
\item   6,558 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,655 8
\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 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   160,95 ~daL~ = {\color{red}  1 609,5 }~L
\item   596,18 ~g~ = {\color{red}  0,596 18 }~kg
\item   9 694,9 ~hL~ = {\color{red}  969 490 000 }~mL
\item   993,21 ~mL~ = {\color{red}  0,993 21 }~L
\item   9 561 ~dm~ = {\color{red}  9,561 }~hm
\item   9 380,3 ~kg~ = {\color{red}  93 803 }~hg
\item   283,01 ~hg~ = {\color{red}  28,301 }~kg
\item   7 111,2 ~mL~ = {\color{red}  711,12 }~cL
\item   638,9 ~hm~ = {\color{red}  63 890 000 }~mm
\item   4 378,6 ~dag~ = {\color{red}  437,86 }~hg
\end{itemize}
\end{multicols}
\end{document}
