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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 194}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{43}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{66}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,764  ~ \(\times\)  ~ 1 000
\item   0,449  ~ \(\times\)  ~ 100
\item   155  ~ \(\times\)  ~ 1 000
\item   0,181  ~ \(\times\)  ~ 10
\item   0,081  ~ \(\times\)  ~ 10
\item   569  ~ \(\times\)  ~ 1 000
\item   58,4  ~ \(\times\)  ~ 100
\item   4,88  ~ \(\times\)  ~ 10
\item   22,6  ~ \(\times\)  ~ 100
\item   0,74  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   734,9  ~ : ~ 100
\item   3 611  ~ : ~ 100
\item   7,02  ~ : ~ 100
\item   6,874  ~ : ~ 1 000
\item   928,6  ~ : ~ 100
\item   8,299  ~ : ~ 100
\item   5,854  ~ : ~ 1 000
\item   91,25  ~ : ~ 10
\item   53,81  ~ : ~ 100
\item   80,14  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,35  ~ \(\times\)  ~ ... ~ = ~ 1 350
\item   51,4  ~ \(\times\)  ~ ... ~ = ~ 5 140
\item   360  ~ \(\times\)  ~ ... ~ = ~ 360 000
\item   825  ~ \(\times\)  ~ ... ~ = ~ 8 250
\item   7,83  ~ \(\times\)  ~ ... ~ = ~ 78,3
\item   0,079  ~ \(\times\)  ~ ... ~ = ~ 0,79
\item   607  ~ \(\times\)  ~ ... ~ = ~ 60 700
\item   98,5  ~ \(\times\)  ~ ... ~ = ~ 98 500
\item   5,9  ~ \(\times\)  ~ ... ~ = ~ 590
\item   749  ~ \(\times\)  ~ ... ~ = ~ 7 490
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 584  ~ \(\times\)  ~ 0,001
\item   8 947  ~ \(\times\)  ~ 0,1
\item   6 035  ~ \(\times\)  ~ 0,1
\item   6 895  ~ \(\times\)  ~ 0,01
\item   751  ~ \(\times\)  ~ 0,01
\item   6,965  ~ \(\times\)  ~ 0,001
\item   8,325  ~ \(\times\)  ~ 0,01
\item   2 762  ~ \(\times\)  ~ 0,01
\item   12,21  ~ \(\times\)  ~ 0,001
\item   978,3  ~ \(\times\)  ~ 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   1,375  ~ \(\times\)  ~ ... ~ = ~  0,013 75
\item   11,12  ~ \(\times\)  ~ ... ~ = ~  0,011 12
\item   79,79  ~ \(\times\)  ~ ... ~ = ~  0,079 79
\item   877,5  ~ \(\times\)  ~ ... ~ = ~  8,775
\item   167,7  ~ \(\times\)  ~ ... ~ = ~  16,77
\item   652  ~ \(\times\)  ~ ... ~ = ~  0,652
\item   3,674  ~ \(\times\)  ~ ... ~ = ~  0,036 74
\item   119,6  ~ \(\times\)  ~ ... ~ = ~  11,96
\item   9,555  ~ \(\times\)  ~ ... ~ = ~  0,955 5
\item   258  ~ \(\times\)  ~ ... ~ = ~  25,8
\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~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~m
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 488,7 ~g~ = ...~dg
\item   150,86 ~hm~ = ...~m
\item   136,67 ~dL~ = ...~kL
\item   9 986,1 ~dm~ = ...~m
\item   964,15 ~L~ = ...~cL
\item   9 857,8 ~g~ = ...~kg
\item   464,53 ~dL~ = ...~mL
\item   6 136,2 ~dag~ = ...~g
\item   518,59 ~dm~ = ...~hm
\item   9 042,9 ~cg~ = ...~mg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{5600}{100}\) = \(\dfrac{560}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{43}{10}\) = \(\dfrac{430}{100}\)
\item   \(\dfrac{66}{100}\) = \(\dfrac{660}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,764  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 764}
\item   0,449  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 44,9}
\item   155  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 155 000}
\item   0,181  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,81}
\item   0,081  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,81}
\item   569  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 569 000}
\item   58,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 840}
\item   4,88  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 48,8}
\item   22,6  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2 260}
\item   0,74  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   734,9 ~ : ~ 100 ~ = ~{\color{red} 7,349}
\item   3 611 ~ : ~ 100 ~ = ~{\color{red} 36,11}
\item   7,02 ~ : ~ 100 ~ = ~{\color{red} 0,070 2}
\item   6,874 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 874}
\item   928,6 ~ : ~ 100 ~ = ~{\color{red} 9,286}
\item   8,299 ~ : ~ 100 ~ = ~{\color{red} 0,082 99}
\item   5,854 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 854}
\item   91,25 ~ : ~ 10 ~ = ~{\color{red} 9,125}
\item   53,81 ~ : ~ 100 ~ = ~{\color{red} 0,538 1}
\item   80,14 ~ : ~ 1 000 ~ = ~{\color{red} 0,080 14}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,35 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 350
\item   51,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~5 140
\item   360 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~360 000
\item   825 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 250
\item   7,83 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~78,3
\item   0,079 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,79
\item   607 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~60 700
\item   98,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~98 500
\item   5,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~590
\item   749 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7 490
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 584 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,584
}\item   8 947 ~ \(\times\)  0,1 ~ = ~{\color{red} 894,7
}\item   6 035 ~ \(\times\)  0,1 ~ = ~{\color{red} 603,5
}\item   6 895 ~ \(\times\)  0,01 ~ = ~{\color{red} 68,95
}\item   751 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,51
}\item   6,965 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,006 965
}\item   8,325 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,083 25
}\item   2 762 ~ \(\times\)  0,01 ~ = ~{\color{red} 27,62
}\item   12,21 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,012 21
}\item   978,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 97,83
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,375 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,013 75
\item   11,12 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,011 12
\item   79,79 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,079 79
\item   877,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,775
\item   167,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 16,77
\item   652 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,652
\item   3,674 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,036 74
\item   119,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 11,96
\item   9,555 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,955 5
\item   258 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 25,8
\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}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 488,7 ~g~ = {\color{red}  74 887 }~dg
\item   150,86 ~hm~ = {\color{red}  15 086 }~m
\item   136,67 ~dL~ = {\color{red}  0,013 667 }~kL
\item   9 986,1 ~dm~ = {\color{red}  998,61 }~m
\item   964,15 ~L~ = {\color{red}  96 415 }~cL
\item   9 857,8 ~g~ = {\color{red}  9,857 8 }~kg
\item   464,53 ~dL~ = {\color{red}  46 453 }~mL
\item   6 136,2 ~dag~ = {\color{red}  61 362 }~g
\item   518,59 ~dm~ = {\color{red}  0,518 59 }~hm
\item   9 042,9 ~cg~ = {\color{red}  90 429 }~mg
\end{itemize}
\end{multicols}
\end{document}
