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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 181}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{50}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,8  ~ \(\times\)  ~ 10
\item   0,469  ~ \(\times\)  ~ 1 000
\item   86,4  ~ \(\times\)  ~ 10
\item   240  ~ \(\times\)  ~ 10
\item   9,81  ~ \(\times\)  ~ 100
\item   2,96  ~ \(\times\)  ~ 100
\item   0,095  ~ \(\times\)  ~ 100
\item   0,38  ~ \(\times\)  ~ 1 000
\item   9,51  ~ \(\times\)  ~ 10
\item   814  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,133  ~ : ~ 10
\item   726,4  ~ : ~ 10
\item   2,154  ~ : ~ 1 000
\item   2 472  ~ : ~ 1 000
\item   3 686  ~ : ~ 100
\item   9,578  ~ : ~ 10
\item   42,03  ~ : ~ 1 000
\item   6,407  ~ : ~ 100
\item   53,35  ~ : ~ 1 000
\item   300,6  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,606  ~ \(\times\)  ~ ... ~ = ~ 60,6
\item   0,04  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   0,69  ~ \(\times\)  ~ ... ~ = ~ 690
\item   0,093  ~ \(\times\)  ~ ... ~ = ~ 9,3
\item   0,195  ~ \(\times\)  ~ ... ~ = ~ 19,5
\item   2,2  ~ \(\times\)  ~ ... ~ = ~ 22
\item   9,2  ~ \(\times\)  ~ ... ~ = ~ 9 200
\item   6,54  ~ \(\times\)  ~ ... ~ = ~ 65,4
\item   67,9  ~ \(\times\)  ~ ... ~ = ~ 67 900
\item   606  ~ \(\times\)  ~ ... ~ = ~ 6 060
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,73  ~ \(\times\)  ~ 0,01
\item   26,66  ~ \(\times\)  ~ 0,001
\item   268  ~ \(\times\)  ~ 0,001
\item   4,419  ~ \(\times\)  ~ 0,1
\item   9 370  ~ \(\times\)  ~ 0,001
\item   777,7  ~ \(\times\)  ~ 0,01
\item   1 091  ~ \(\times\)  ~ 0,001
\item   91,24  ~ \(\times\)  ~ 0,01
\item   4,41  ~ \(\times\)  ~ 0,01
\item   298  ~ \(\times\)  ~ 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   3,255  ~ \(\times\)  ~ ... ~ = ~  0,032 55
\item   642,3  ~ \(\times\)  ~ ... ~ = ~  64,23
\item   8,61  ~ \(\times\)  ~ ... ~ = ~  0,861
\item   767  ~ \(\times\)  ~ ... ~ = ~  76,7
\item   469,4  ~ \(\times\)  ~ ... ~ = ~  46,94
\item   80,87  ~ \(\times\)  ~ ... ~ = ~  8,087
\item   57,77  ~ \(\times\)  ~ ... ~ = ~  5,777
\item   9 778  ~ \(\times\)  ~ ... ~ = ~  977,8
\item   542,9  ~ \(\times\)  ~ ... ~ = ~  5,429
\item   692,4  ~ \(\times\)  ~ ... ~ = ~  0,692 4
\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 ~dm~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   896,96 ~cg~ = ...~hg
\item   676,33 ~dag~ = ...~dg
\item   2 815,1 ~mL~ = ...~L
\item   142,12 ~cL~ = ...~mL
\item   384,72 ~mg~ = ...~kg
\item   191,98 ~kg~ = ...~dg
\item   2 689,3 ~dm~ = ...~hm
\item   400,43 ~cm~ = ...~dm
\item   876,4 ~cL~ = ...~dL
\item   374,41 ~mL~ = ...~dL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{5300}{100}\) = \(\dfrac{530}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{50}{100}\) = \(\dfrac{500}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 78}
\item   0,469  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 469}
\item   86,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 864}
\item   240  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 400}
\item   9,81  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 981}
\item   2,96  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 296}
\item   0,095  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,5}
\item   0,38  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 380}
\item   9,51  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 95,1}
\item   814  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 81 400}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,133 ~ : ~ 10 ~ = ~{\color{red} 0,913 3}
\item   726,4 ~ : ~ 10 ~ = ~{\color{red} 72,64}
\item   2,154 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 154}
\item   2 472 ~ : ~ 1 000 ~ = ~{\color{red} 2,472}
\item   3 686 ~ : ~ 100 ~ = ~{\color{red} 36,86}
\item   9,578 ~ : ~ 10 ~ = ~{\color{red} 0,957 8}
\item   42,03 ~ : ~ 1 000 ~ = ~{\color{red} 0,042 03}
\item   6,407 ~ : ~ 100 ~ = ~{\color{red} 0,064 07}
\item   53,35 ~ : ~ 1 000 ~ = ~{\color{red} 0,053 35}
\item   300,6 ~ : ~ 10 ~ = ~{\color{red} 30,06}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,606 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~60,6
\item   0,04 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,4
\item   0,69 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~690
\item   0,093 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9,3
\item   0,195 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~19,5
\item   2,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~22
\item   9,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 200
\item   6,54 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~65,4
\item   67,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~67 900
\item   606 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 060
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,73 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,077 3
}\item   26,66 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,026 66
}\item   268 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,268
}\item   4,419 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,441 9
}\item   9 370 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,37
}\item   777,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,777
}\item   1 091 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,091
}\item   91,24 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,912 4
}\item   4,41 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,044 1
}\item   298 ~ \(\times\)  0,1 ~ = ~{\color{red} 29,8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,255 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,032 55
\item   642,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 64,23
\item   8,61 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,861
\item   767 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 76,7
\item   469,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 46,94
\item   80,87 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 8,087
\item   57,77 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,777
\item   9 778 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 977,8
\item   542,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,429
\item   692,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,692 4
\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 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   896,96 ~cg~ = {\color{red}  0,089 696 }~hg
\item   676,33 ~dag~ = {\color{red}  67 633 }~dg
\item   2 815,1 ~mL~ = {\color{red}  2,815 1 }~L
\item   142,12 ~cL~ = {\color{red}  1 421,2 }~mL
\item   384,72 ~mg~ = {\color{red}  0,000 384 72 }~kg
\item   191,98 ~kg~ = {\color{red}  1 919 800 }~dg
\item   2 689,3 ~dm~ = {\color{red}  2,689 3 }~hm
\item   400,43 ~cm~ = {\color{red}  40,043 }~dm
\item   876,4 ~cL~ = {\color{red}  87,64 }~dL
\item   374,41 ~mL~ = {\color{red}  3,744 1 }~dL
\end{itemize}
\end{multicols}
\end{document}
