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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 154}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{67}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,014  ~ \(\times\)  ~ 100
\item   0,814  ~ \(\times\)  ~ 100
\item   0,097  ~ \(\times\)  ~ 1 000
\item   0,058  ~ \(\times\)  ~ 1 000
\item   834  ~ \(\times\)  ~ 100
\item   0,077  ~ \(\times\)  ~ 100
\item   0,74  ~ \(\times\)  ~ 100
\item   0,094  ~ \(\times\)  ~ 10
\item   2,78  ~ \(\times\)  ~ 10
\item   784  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 031  ~ : ~ 1 000
\item   9,279  ~ : ~ 10
\item   7,17  ~ : ~ 10
\item   2 856  ~ : ~ 1 000
\item   5 405  ~ : ~ 100
\item   7 502  ~ : ~ 1 000
\item   3,408  ~ : ~ 1 000
\item   5 089  ~ : ~ 1 000
\item   3,82  ~ : ~ 1 000
\item   403,1  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,509  ~ \(\times\)  ~ ... ~ = ~ 509
\item   23,6  ~ \(\times\)  ~ ... ~ = ~ 23 600
\item   38,5  ~ \(\times\)  ~ ... ~ = ~ 385
\item   0,024  ~ \(\times\)  ~ ... ~ = ~ 2,4
\item   5,1  ~ \(\times\)  ~ ... ~ = ~ 51
\item   238  ~ \(\times\)  ~ ... ~ = ~ 23 800
\item   9  ~ \(\times\)  ~ ... ~ = ~ 90
\item   11,2  ~ \(\times\)  ~ ... ~ = ~ 1 120
\item   0,022  ~ \(\times\)  ~ ... ~ = ~ 2,2
\item   5,64  ~ \(\times\)  ~ ... ~ = ~ 56,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 744  ~ \(\times\)  ~ 0,1
\item   2 238  ~ \(\times\)  ~ 0,001
\item   42,93  ~ \(\times\)  ~ 0,001
\item   8,686  ~ \(\times\)  ~ 0,01
\item   2 149  ~ \(\times\)  ~ 0,1
\item   2,825  ~ \(\times\)  ~ 0,1
\item   48,03  ~ \(\times\)  ~ 0,001
\item   16,15  ~ \(\times\)  ~ 0,01
\item   0,456  ~ \(\times\)  ~ 0,001
\item   9,315  ~ \(\times\)  ~ 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   833,2  ~ \(\times\)  ~ ... ~ = ~  8,332
\item   98,8  ~ \(\times\)  ~ ... ~ = ~  9,88
\item   3,254  ~ \(\times\)  ~ ... ~ = ~  0,325 4
\item   1 518  ~ \(\times\)  ~ ... ~ = ~  1,518
\item   2 537  ~ \(\times\)  ~ ... ~ = ~  253,7
\item   3,819  ~ \(\times\)  ~ ... ~ = ~  0,003 819
\item   30,13  ~ \(\times\)  ~ ... ~ = ~  3,013
\item   2 231  ~ \(\times\)  ~ ... ~ = ~  2,231
\item   4,06  ~ \(\times\)  ~ ... ~ = ~  0,004 06
\item   11,52  ~ \(\times\)  ~ ... ~ = ~  0,115 2
\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~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~km~ = ...~dam
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 184,7 ~kL~ = ...~cL
\item   343,1 ~g~ = ...~cg
\item   3 216 ~hL~ = ...~cL
\item   3 321,9 ~hg~ = ...~dg
\item   695,78 ~mm~ = ...~km
\item   603,53 ~mm~ = ...~hm
\item   6 354,6 ~daL~ = ...~L
\item   1 741,6 ~dag~ = ...~cg
\item   631,85 ~hL~ = ...~dL
\item   284,51 ~daL~ = ...~mL
\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   8 = \(\dfrac{800}{100}\)
\item   \(\dfrac{7300}{100}\) = \(\dfrac{730}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{67}{10}\) = \(\dfrac{670}{100}\)
\item   \(\dfrac{76}{100}\) = \(\dfrac{760}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,014  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,4}
\item   0,814  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 81,4}
\item   0,097  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 97}
\item   0,058  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 58}
\item   834  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 83 400}
\item   0,077  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,7}
\item   0,74  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 74}
\item   0,094  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,94}
\item   2,78  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 27,8}
\item   784  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 78 400}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 031 ~ : ~ 1 000 ~ = ~{\color{red} 5,031}
\item   9,279 ~ : ~ 10 ~ = ~{\color{red} 0,927 9}
\item   7,17 ~ : ~ 10 ~ = ~{\color{red} 0,717}
\item   2 856 ~ : ~ 1 000 ~ = ~{\color{red} 2,856}
\item   5 405 ~ : ~ 100 ~ = ~{\color{red} 54,05}
\item   7 502 ~ : ~ 1 000 ~ = ~{\color{red} 7,502}
\item   3,408 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 408}
\item   5 089 ~ : ~ 1 000 ~ = ~{\color{red} 5,089}
\item   3,82 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 82}
\item   403,1 ~ : ~ 10 ~ = ~{\color{red} 40,31}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,509 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~509
\item   23,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~23 600
\item   38,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~385
\item   0,024 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,4
\item   5,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~51
\item   238 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~23 800
\item   9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~90
\item   11,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 120
\item   0,022 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,2
\item   5,64 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~56,4
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 744 ~ \(\times\)  0,1 ~ = ~{\color{red} 274,4
}\item   2 238 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,238
}\item   42,93 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,042 93
}\item   8,686 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,086 86
}\item   2 149 ~ \(\times\)  0,1 ~ = ~{\color{red} 214,9
}\item   2,825 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,282 5
}\item   48,03 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,048 03
}\item   16,15 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,161 5
}\item   0,456 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 456
}\item   9,315 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,093 15
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   833,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,332
\item   98,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,88
\item   3,254 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,325 4
\item   1 518 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,518
\item   2 537 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 253,7
\item   3,819 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 819
\item   30,13 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,013
\item   2 231 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,231
\item   4,06 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 06
\item   11,52 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,115 2
\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~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 184,7 ~kL~ = {\color{red}  918 470 000 }~cL
\item   343,1 ~g~ = {\color{red}  34 310 }~cg
\item   3 216 ~hL~ = {\color{red}  32 160 000 }~cL
\item   3 321,9 ~hg~ = {\color{red}  3 321 900 }~dg
\item   695,78 ~mm~ = {\color{red}  0,000 695 78 }~km
\item   603,53 ~mm~ = {\color{red}  0,006 035 3 }~hm
\item   6 354,6 ~daL~ = {\color{red}  63 546 }~L
\item   1 741,6 ~dag~ = {\color{red}  1 741 600 }~cg
\item   631,85 ~hL~ = {\color{red}  631 850 }~dL
\item   284,51 ~daL~ = {\color{red}  2 845 100 }~mL
\end{itemize}
\end{multicols}
\end{document}
