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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 126}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{71}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24,3  ~ \(\times\)  ~ 1 000
\item   0,145  ~ \(\times\)  ~ 10
\item   7,68  ~ \(\times\)  ~ 1 000
\item   1,53  ~ \(\times\)  ~ 10
\item   0,792  ~ \(\times\)  ~ 100
\item   0,043  ~ \(\times\)  ~ 100
\item   8,28  ~ \(\times\)  ~ 100
\item   0,051  ~ \(\times\)  ~ 10
\item   819  ~ \(\times\)  ~ 100
\item   18,8  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,637  ~ : ~ 100
\item   4,107  ~ : ~ 10
\item   4,195  ~ : ~ 10
\item   45,8  ~ : ~ 1 000
\item   329,6  ~ : ~ 100
\item   2,14  ~ : ~ 1 000
\item   158,8  ~ : ~ 100
\item   94,77  ~ : ~ 100
\item   6,835  ~ : ~ 1 000
\item   86,4  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,46  ~ \(\times\)  ~ ... ~ = ~ 460
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 32
\item   74,6  ~ \(\times\)  ~ ... ~ = ~ 7 460
\item   73,6  ~ \(\times\)  ~ ... ~ = ~ 736
\item   809  ~ \(\times\)  ~ ... ~ = ~ 809 000
\item   612  ~ \(\times\)  ~ ... ~ = ~ 61 200
\item   4,13  ~ \(\times\)  ~ ... ~ = ~ 41,3
\item   537  ~ \(\times\)  ~ ... ~ = ~ 53 700
\item   88,7  ~ \(\times\)  ~ ... ~ = ~ 887
\item   8,44  ~ \(\times\)  ~ ... ~ = ~ 844
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   358,5  ~ \(\times\)  ~ 0,001
\item   6,986  ~ \(\times\)  ~ 0,01
\item   948,8  ~ \(\times\)  ~ 0,01
\item   8 145  ~ \(\times\)  ~ 0,01
\item   90,29  ~ \(\times\)  ~ 0,001
\item   89,1  ~ \(\times\)  ~ 0,01
\item   9 452  ~ \(\times\)  ~ 0,001
\item   321,2  ~ \(\times\)  ~ 0,001
\item   8,576  ~ \(\times\)  ~ 0,001
\item   57,53  ~ \(\times\)  ~ 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   6 429  ~ \(\times\)  ~ ... ~ = ~  64,29
\item   46,6  ~ \(\times\)  ~ ... ~ = ~  0,046 6
\item   652  ~ \(\times\)  ~ ... ~ = ~  65,2
\item   28,26  ~ \(\times\)  ~ ... ~ = ~  0,282 6
\item   1,95  ~ \(\times\)  ~ ... ~ = ~  0,195
\item   52,8  ~ \(\times\)  ~ ... ~ = ~  0,528
\item   317  ~ \(\times\)  ~ ... ~ = ~  31,7
\item   330,5  ~ \(\times\)  ~ ... ~ = ~  33,05
\item   6,546  ~ \(\times\)  ~ ... ~ = ~  0,065 46
\item   3,354  ~ \(\times\)  ~ ... ~ = ~  0,033 54
\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 ~dam~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   213,93 ~km~ = ...~dam
\item   509,01 ~m~ = ...~dm
\item   393,93 ~mg~ = ...~cg
\item   8 735,3 ~dg~ = ...~mg
\item   7 670,7 ~hg~ = ...~cg
\item   8 060 ~mL~ = ...~hL
\item   818,82 ~cm~ = ...~m
\item   877,68 ~mm~ = ...~dm
\item   526,26 ~cg~ = ...~dag
\item   7 427,5 ~g~ = ...~kg
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{71}{10}\) = \(\dfrac{710}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 24 300}
\item   0,145  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,45}
\item   7,68  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 680}
\item   1,53  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 15,3}
\item   0,792  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 79,2}
\item   0,043  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,3}
\item   8,28  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 828}
\item   0,051  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,51}
\item   819  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 81 900}
\item   18,8  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 18 800}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,637 ~ : ~ 100 ~ = ~{\color{red} 0,036 37}
\item   4,107 ~ : ~ 10 ~ = ~{\color{red} 0,410 7}
\item   4,195 ~ : ~ 10 ~ = ~{\color{red} 0,419 5}
\item   45,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,045 8}
\item   329,6 ~ : ~ 100 ~ = ~{\color{red} 3,296}
\item   2,14 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 14}
\item   158,8 ~ : ~ 100 ~ = ~{\color{red} 1,588}
\item   94,77 ~ : ~ 100 ~ = ~{\color{red} 0,947 7}
\item   6,835 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 835}
\item   86,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,086 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,46 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~460
\item   0,032 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~32
\item   74,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 460
\item   73,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~736
\item   809 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~809 000
\item   612 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~61 200
\item   4,13 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~41,3
\item   537 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~53 700
\item   88,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~887
\item   8,44 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~844
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   358,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,358 5
}\item   6,986 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,069 86
}\item   948,8 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,488
}\item   8 145 ~ \(\times\)  0,01 ~ = ~{\color{red} 81,45
}\item   90,29 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,090 29
}\item   89,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,891
}\item   9 452 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,452
}\item   321,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,321 2
}\item   8,576 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 576
}\item   57,53 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,057 53
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 429 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 64,29
\item   46,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,046 6
\item   652 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 65,2
\item   28,26 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,282 6
\item   1,95 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,195
\item   52,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,528
\item   317 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 31,7
\item   330,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 33,05
\item   6,546 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,065 46
\item   3,354 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,033 54
\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 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   213,93 ~km~ = {\color{red}  21 393 }~dam
\item   509,01 ~m~ = {\color{red}  5 090,1 }~dm
\item   393,93 ~mg~ = {\color{red}  39,393 }~cg
\item   8 735,3 ~dg~ = {\color{red}  873 530 }~mg
\item   7 670,7 ~hg~ = {\color{red}  76 707 000 }~cg
\item   8 060 ~mL~ = {\color{red}  0,080 6 }~hL
\item   818,82 ~cm~ = {\color{red}  8,188 2 }~m
\item   877,68 ~mm~ = {\color{red}  8,776 8 }~dm
\item   526,26 ~cg~ = {\color{red}  0,526 26 }~dag
\item   7 427,5 ~g~ = {\color{red}  7,427 5 }~kg
\end{itemize}
\end{multicols}
\end{document}
