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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 358}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   106  ~ \(\times\)  ~ 10
\item   705  ~ \(\times\)  ~ 10
\item   0,332  ~ \(\times\)  ~ 100
\item   84  ~ \(\times\)  ~ 100
\item   0,055  ~ \(\times\)  ~ 1 000
\item   65,6  ~ \(\times\)  ~ 10
\item   0,082  ~ \(\times\)  ~ 100
\item   63,9  ~ \(\times\)  ~ 10
\item   7,16  ~ \(\times\)  ~ 10
\item   0,19  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   48,93  ~ : ~ 10
\item   5,394  ~ : ~ 10
\item   1 118  ~ : ~ 100
\item   6,01  ~ : ~ 10
\item   244  ~ : ~ 100
\item   9 404  ~ : ~ 100
\item   323,2  ~ : ~ 1 000
\item   7,87  ~ : ~ 10
\item   1 989  ~ : ~ 10
\item   766,1  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   71,9  ~ \(\times\)  ~ ... ~ = ~ 719
\item   0,917  ~ \(\times\)  ~ ... ~ = ~ 9,17
\item   34  ~ \(\times\)  ~ ... ~ = ~ 34 000
\item   0,31  ~ \(\times\)  ~ ... ~ = ~ 310
\item   26  ~ \(\times\)  ~ ... ~ = ~ 26 000
\item   0,005  ~ \(\times\)  ~ ... ~ = ~ 0,5
\item   8,49  ~ \(\times\)  ~ ... ~ = ~ 8 490
\item   0,079  ~ \(\times\)  ~ ... ~ = ~ 7,9
\item   0,526  ~ \(\times\)  ~ ... ~ = ~ 526
\item   0,602  ~ \(\times\)  ~ ... ~ = ~ 6,02
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   397,4  ~ \(\times\)  ~ 0,01
\item   286  ~ \(\times\)  ~ 0,001
\item   49,6  ~ \(\times\)  ~ 0,01
\item   4 710  ~ \(\times\)  ~ 0,1
\item   7,391  ~ \(\times\)  ~ 0,001
\item   3,851  ~ \(\times\)  ~ 0,01
\item   493,8  ~ \(\times\)  ~ 0,001
\item   81,66  ~ \(\times\)  ~ 0,1
\item   1 369  ~ \(\times\)  ~ 0,01
\item   2 015  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,49  ~ \(\times\)  ~ ... ~ = ~  0,058 49
\item   2,85  ~ \(\times\)  ~ ... ~ = ~  0,028 5
\item   61,81  ~ \(\times\)  ~ ... ~ = ~  6,181
\item   3,477  ~ \(\times\)  ~ ... ~ = ~  0,034 77
\item   463,3  ~ \(\times\)  ~ ... ~ = ~  4,633
\item   303,2  ~ \(\times\)  ~ ... ~ = ~  30,32
\item   8,826  ~ \(\times\)  ~ ... ~ = ~  0,088 26
\item   9 427  ~ \(\times\)  ~ ... ~ = ~  94,27
\item   556,8  ~ \(\times\)  ~ ... ~ = ~  55,68
\item   454,3  ~ \(\times\)  ~ ... ~ = ~  4,543
\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~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   786,7 ~m~ = ...~cm
\item   2 344,8 ~mL~ = ...~L
\item   4 081,9 ~hL~ = ...~cL
\item   257,57 ~dag~ = ...~cg
\item   6 411,7 ~m~ = ...~dm
\item   1 470,2 ~cL~ = ...~mL
\item   2 381,1 ~kg~ = ...~hg
\item   699,16 ~daL~ = ...~dL
\item   864,61 ~cm~ = ...~m
\item   1 685,4 ~mg~ = ...~dag
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{6100}{100}\) = \(\dfrac{610}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{13}{100}\) = \(\dfrac{130}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   106  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 060}
\item   705  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 050}
\item   0,332  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 33,2}
\item   84  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 400}
\item   0,055  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 55}
\item   65,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 656}
\item   0,082  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,2}
\item   63,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 639}
\item   7,16  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 71,6}
\item   0,19  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 19}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   48,93 ~ : ~ 10 ~ = ~{\color{red} 4,893}
\item   5,394 ~ : ~ 10 ~ = ~{\color{red} 0,539 4}
\item   1 118 ~ : ~ 100 ~ = ~{\color{red} 11,18}
\item   6,01 ~ : ~ 10 ~ = ~{\color{red} 0,601}
\item   244 ~ : ~ 100 ~ = ~{\color{red} 2,44}
\item   9 404 ~ : ~ 100 ~ = ~{\color{red} 94,04}
\item   323,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,323 2}
\item   7,87 ~ : ~ 10 ~ = ~{\color{red} 0,787}
\item   1 989 ~ : ~ 10 ~ = ~{\color{red} 198,9}
\item   766,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,766 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   71,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~719
\item   0,917 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,17
\item   34 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~34 000
\item   0,31 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~310
\item   26 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~26 000
\item   0,005 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,5
\item   8,49 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 490
\item   0,079 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,9
\item   0,526 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~526
\item   0,602 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,02
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   397,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,974
}\item   286 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,286
}\item   49,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,496
}\item   4 710 ~ \(\times\)  0,1 ~ = ~{\color{red} 471
}\item   7,391 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 391
}\item   3,851 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,038 51
}\item   493,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,493 8
}\item   81,66 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,166
}\item   1 369 ~ \(\times\)  0,01 ~ = ~{\color{red} 13,69
}\item   2 015 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,015
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   58,49 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,058 49
\item   2,85 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,028 5
\item   61,81 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,181
\item   3,477 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,034 77
\item   463,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,633
\item   303,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 30,32
\item   8,826 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,088 26
\item   9 427 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 94,27
\item   556,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 55,68
\item   454,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,543
\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~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   786,7 ~m~ = {\color{red}  78 670 }~cm
\item   2 344,8 ~mL~ = {\color{red}  2,344 8 }~L
\item   4 081,9 ~hL~ = {\color{red}  40 819 000 }~cL
\item   257,57 ~dag~ = {\color{red}  257 570 }~cg
\item   6 411,7 ~m~ = {\color{red}  64 117 }~dm
\item   1 470,2 ~cL~ = {\color{red}  14 702 }~mL
\item   2 381,1 ~kg~ = {\color{red}  23 811 }~hg
\item   699,16 ~daL~ = {\color{red}  69 916 }~dL
\item   864,61 ~cm~ = {\color{red}  8,646 1 }~m
\item   1 685,4 ~mg~ = {\color{red}  0,168 54 }~dag
\end{itemize}
\end{multicols}
\end{document}
