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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 77}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{25}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,308  ~ \(\times\)  ~ 1 000
\item   63,5  ~ \(\times\)  ~ 10
\item   0,058  ~ \(\times\)  ~ 10
\item   8,8  ~ \(\times\)  ~ 10
\item   0,864  ~ \(\times\)  ~ 10
\item   82  ~ \(\times\)  ~ 1 000
\item   0,864  ~ \(\times\)  ~ 10
\item   3,48  ~ \(\times\)  ~ 10
\item   0,01  ~ \(\times\)  ~ 100
\item   0,555  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   379,7  ~ : ~ 10
\item   142,7  ~ : ~ 1 000
\item   9,277  ~ : ~ 1 000
\item   8 927  ~ : ~ 10
\item   35,75  ~ : ~ 10
\item   1,656  ~ : ~ 10
\item   8 915  ~ : ~ 100
\item   7 387  ~ : ~ 100
\item   8 779  ~ : ~ 100
\item   964,4  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,595  ~ \(\times\)  ~ ... ~ = ~ 59,5
\item   76,4  ~ \(\times\)  ~ ... ~ = ~ 7 640
\item   22  ~ \(\times\)  ~ ... ~ = ~ 220
\item   516  ~ \(\times\)  ~ ... ~ = ~ 516 000
\item   0,375  ~ \(\times\)  ~ ... ~ = ~ 3,75
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 27
\item   0,713  ~ \(\times\)  ~ ... ~ = ~ 7,13
\item   0,675  ~ \(\times\)  ~ ... ~ = ~ 675
\item   679  ~ \(\times\)  ~ ... ~ = ~ 6 790
\item   0,031  ~ \(\times\)  ~ ... ~ = ~ 0,31
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,382  ~ \(\times\)  ~ 0,01
\item   6 908  ~ \(\times\)  ~ 0,1
\item   798,8  ~ \(\times\)  ~ 0,1
\item   23,5  ~ \(\times\)  ~ 0,1
\item   7 740  ~ \(\times\)  ~ 0,01
\item   7 898  ~ \(\times\)  ~ 0,1
\item   40,22  ~ \(\times\)  ~ 0,1
\item   150,9  ~ \(\times\)  ~ 0,1
\item   2 544  ~ \(\times\)  ~ 0,1
\item   3,924  ~ \(\times\)  ~ 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   6,938  ~ \(\times\)  ~ ... ~ = ~  0,006 938
\item   4 488  ~ \(\times\)  ~ ... ~ = ~  44,88
\item   69  ~ \(\times\)  ~ ... ~ = ~  0,069
\item   46,27  ~ \(\times\)  ~ ... ~ = ~  0,462 7
\item   3 199  ~ \(\times\)  ~ ... ~ = ~  3,199
\item   8 071  ~ \(\times\)  ~ ... ~ = ~  807,1
\item   40,9  ~ \(\times\)  ~ ... ~ = ~  4,09
\item   1 574  ~ \(\times\)  ~ ... ~ = ~  1,574
\item   3 443  ~ \(\times\)  ~ ... ~ = ~  34,43
\item   2 810  ~ \(\times\)  ~ ... ~ = ~  2,81
\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~ = ...~hm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 823,9 ~kg~ = ...~g
\item   757,04 ~m~ = ...~hm
\item   474,67 ~mm~ = ...~dam
\item   8 798,7 ~kg~ = ...~mg
\item   378,48 ~dg~ = ...~kg
\item   911,94 ~dm~ = ...~cm
\item   592,58 ~cL~ = ...~hL
\item   3 026,7 ~dam~ = ...~cm
\item   8 226,4 ~g~ = ...~dag
\item   688,24 ~km~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{3600}{100}\) = \(\dfrac{360}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{35}{10}\) = \(\dfrac{350}{100}\)
\item   \(\dfrac{25}{100}\) = \(\dfrac{250}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,308  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 308}
\item   63,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 635}
\item   0,058  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,58}
\item   8,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 88}
\item   0,864  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,64}
\item   82  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 82 000}
\item   0,864  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,64}
\item   3,48  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 34,8}
\item   0,01  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1}
\item   0,555  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,55}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   379,7 ~ : ~ 10 ~ = ~{\color{red} 37,97}
\item   142,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,142 7}
\item   9,277 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 277}
\item   8 927 ~ : ~ 10 ~ = ~{\color{red} 892,7}
\item   35,75 ~ : ~ 10 ~ = ~{\color{red} 3,575}
\item   1,656 ~ : ~ 10 ~ = ~{\color{red} 0,165 6}
\item   8 915 ~ : ~ 100 ~ = ~{\color{red} 89,15}
\item   7 387 ~ : ~ 100 ~ = ~{\color{red} 73,87}
\item   8 779 ~ : ~ 100 ~ = ~{\color{red} 87,79}
\item   964,4 ~ : ~ 10 ~ = ~{\color{red} 96,44}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,595 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~59,5
\item   76,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 640
\item   22 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~220
\item   516 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~516 000
\item   0,375 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,75
\item   0,027 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27
\item   0,713 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,13
\item   0,675 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~675
\item   679 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 790
\item   0,031 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,31
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,382 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,003 82
}\item   6 908 ~ \(\times\)  0,1 ~ = ~{\color{red} 690,8
}\item   798,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 79,88
}\item   23,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,35
}\item   7 740 ~ \(\times\)  0,01 ~ = ~{\color{red} 77,4
}\item   7 898 ~ \(\times\)  0,1 ~ = ~{\color{red} 789,8
}\item   40,22 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,022
}\item   150,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 15,09
}\item   2 544 ~ \(\times\)  0,1 ~ = ~{\color{red} 254,4
}\item   3,924 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 924
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,938 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 938
\item   4 488 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 44,88
\item   69 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,069
\item   46,27 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,462 7
\item   3 199 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,199
\item   8 071 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 807,1
\item   40,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,09
\item   1 574 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,574
\item   3 443 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 34,43
\item   2 810 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,81
\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}  10 ~ }hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 823,9 ~kg~ = {\color{red}  5 823 900 }~g
\item   757,04 ~m~ = {\color{red}  7,570 4 }~hm
\item   474,67 ~mm~ = {\color{red}  0,047 467 }~dam
\item   8 798,7 ~kg~ = {\color{red}  8 798 700 000 }~mg
\item   378,48 ~dg~ = {\color{red}  0,037 848 }~kg
\item   911,94 ~dm~ = {\color{red}  9 119,4 }~cm
\item   592,58 ~cL~ = {\color{red}  0,059 258 }~hL
\item   3 026,7 ~dam~ = {\color{red}  3 026 700 }~cm
\item   8 226,4 ~g~ = {\color{red}  822,64 }~dag
\item   688,24 ~km~ = {\color{red}  6 882 400 }~dm
\end{itemize}
\end{multicols}
\end{document}
