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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 337}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{12}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   5,5  ~ \(\times\)  ~ 100
\item   0,856  ~ \(\times\)  ~ 10
\item   0,39  ~ \(\times\)  ~ 1 000
\item   3,3  ~ \(\times\)  ~ 100
\item   105  ~ \(\times\)  ~ 10
\item   0,016  ~ \(\times\)  ~ 10
\item   77,1  ~ \(\times\)  ~ 1 000
\item   0,038  ~ \(\times\)  ~ 1 000
\item   51,6  ~ \(\times\)  ~ 100
\item   46,8  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,055  ~ : ~ 100
\item   831,2  ~ : ~ 100
\item   822,2  ~ : ~ 1 000
\item   2,022  ~ : ~ 100
\item   146,9  ~ : ~ 1 000
\item   76,03  ~ : ~ 10
\item   23,56  ~ : ~ 1 000
\item   4 417  ~ : ~ 100
\item   563,5  ~ : ~ 10
\item   147,7  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,843  ~ \(\times\)  ~ ... ~ = ~ 843
\item   83,7  ~ \(\times\)  ~ ... ~ = ~ 837
\item   0,074  ~ \(\times\)  ~ ... ~ = ~ 7,4
\item   29  ~ \(\times\)  ~ ... ~ = ~ 29 000
\item   236  ~ \(\times\)  ~ ... ~ = ~ 23 600
\item   741  ~ \(\times\)  ~ ... ~ = ~ 741 000
\item   8,91  ~ \(\times\)  ~ ... ~ = ~ 891
\item   163  ~ \(\times\)  ~ ... ~ = ~ 163 000
\item   0,46  ~ \(\times\)  ~ ... ~ = ~ 46
\item   0,977  ~ \(\times\)  ~ ... ~ = ~ 9,77
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 169  ~ \(\times\)  ~ 0,01
\item   6,052  ~ \(\times\)  ~ 0,01
\item   464,4  ~ \(\times\)  ~ 0,001
\item   37,79  ~ \(\times\)  ~ 0,01
\item   8 089  ~ \(\times\)  ~ 0,1
\item   6,692  ~ \(\times\)  ~ 0,01
\item   3 038  ~ \(\times\)  ~ 0,1
\item   71,65  ~ \(\times\)  ~ 0,001
\item   9,055  ~ \(\times\)  ~ 0,001
\item   9 741  ~ \(\times\)  ~ 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   8 007  ~ \(\times\)  ~ ... ~ = ~  80,07
\item   430,4  ~ \(\times\)  ~ ... ~ = ~  4,304
\item   7 582  ~ \(\times\)  ~ ... ~ = ~  758,2
\item   4,574  ~ \(\times\)  ~ ... ~ = ~  0,045 74
\item   42,1  ~ \(\times\)  ~ ... ~ = ~  0,421
\item   5,229  ~ \(\times\)  ~ ... ~ = ~  0,005 229
\item   8 677  ~ \(\times\)  ~ ... ~ = ~  867,7
\item   24,28  ~ \(\times\)  ~ ... ~ = ~  0,024 28
\item   9 161  ~ \(\times\)  ~ ... ~ = ~  916,1
\item   1 755  ~ \(\times\)  ~ ... ~ = ~  17,55
\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~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~hm
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 365,3 ~L~ = ...~cL
\item   192,58 ~m~ = ...~mm
\item   9 136,3 ~dam~ = ...~dm
\item   872,31 ~hg~ = ...~kg
\item   8 070,7 ~mL~ = ...~daL
\item   317,74 ~km~ = ...~m
\item   2 956,5 ~km~ = ...~cm
\item   862,63 ~cm~ = ...~dam
\item   8 086,9 ~kL~ = ...~daL
\item   8 418,4 ~cm~ = ...~km
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{7700}{100}\) = \(\dfrac{770}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{12}{10}\) = \(\dfrac{120}{100}\)
\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   5,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 550}
\item   0,856  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,56}
\item   0,39  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 390}
\item   3,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 330}
\item   105  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 050}
\item   0,016  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,16}
\item   77,1  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 77 100}
\item   0,038  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 38}
\item   51,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 160}
\item   46,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4 680}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,055 ~ : ~ 100 ~ = ~{\color{red} 0,030 55}
\item   831,2 ~ : ~ 100 ~ = ~{\color{red} 8,312}
\item   822,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,822 2}
\item   2,022 ~ : ~ 100 ~ = ~{\color{red} 0,020 22}
\item   146,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,146 9}
\item   76,03 ~ : ~ 10 ~ = ~{\color{red} 7,603}
\item   23,56 ~ : ~ 1 000 ~ = ~{\color{red} 0,023 56}
\item   4 417 ~ : ~ 100 ~ = ~{\color{red} 44,17}
\item   563,5 ~ : ~ 10 ~ = ~{\color{red} 56,35}
\item   147,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,147 7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,843 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~843
\item   83,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~837
\item   0,074 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,4
\item   29 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~29 000
\item   236 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~23 600
\item   741 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~741 000
\item   8,91 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~891
\item   163 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~163 000
\item   0,46 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~46
\item   0,977 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,77
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 169 ~ \(\times\)  0,01 ~ = ~{\color{red} 31,69
}\item   6,052 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,060 52
}\item   464,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,464 4
}\item   37,79 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,377 9
}\item   8 089 ~ \(\times\)  0,1 ~ = ~{\color{red} 808,9
}\item   6,692 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,066 92
}\item   3 038 ~ \(\times\)  0,1 ~ = ~{\color{red} 303,8
}\item   71,65 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,071 65
}\item   9,055 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 055
}\item   9 741 ~ \(\times\)  0,1 ~ = ~{\color{red} 974,1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 007 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 80,07
\item   430,4 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 4,304
\item   7 582 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 758,2
\item   4,574 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,045 74
\item   42,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,421
\item   5,229 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 229
\item   8 677 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 867,7
\item   24,28 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,024 28
\item   9 161 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 916,1
\item   1 755 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 17,55
\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~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ 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   8 365,3 ~L~ = {\color{red}  836 530 }~cL
\item   192,58 ~m~ = {\color{red}  192 580 }~mm
\item   9 136,3 ~dam~ = {\color{red}  913 630 }~dm
\item   872,31 ~hg~ = {\color{red}  87,231 }~kg
\item   8 070,7 ~mL~ = {\color{red}  0,807 07 }~daL
\item   317,74 ~km~ = {\color{red}  317 740 }~m
\item   2 956,5 ~km~ = {\color{red}  295 650 000 }~cm
\item   862,63 ~cm~ = {\color{red}  0,862 63 }~dam
\item   8 086,9 ~kL~ = {\color{red}  808 690 }~daL
\item   8 418,4 ~cm~ = {\color{red}  0,084 184 }~km
\end{itemize}
\end{multicols}
\end{document}
