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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 158}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,786  ~ \(\times\)  ~ 1 000
\item   49  ~ \(\times\)  ~ 10
\item   0,001  ~ \(\times\)  ~ 100
\item   57  ~ \(\times\)  ~ 10
\item   0,089  ~ \(\times\)  ~ 1 000
\item   0,074  ~ \(\times\)  ~ 100
\item   4,2  ~ \(\times\)  ~ 1 000
\item   860  ~ \(\times\)  ~ 100
\item   68,2  ~ \(\times\)  ~ 10
\item   4,07  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   199,5  ~ : ~ 10
\item   2 395  ~ : ~ 1 000
\item   58,21  ~ : ~ 100
\item   56  ~ : ~ 10
\item   43,24  ~ : ~ 1 000
\item   508,8  ~ : ~ 1 000
\item   5,954  ~ : ~ 1 000
\item   0,927  ~ : ~ 10
\item   31,76  ~ : ~ 1 000
\item   918,1  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,089  ~ \(\times\)  ~ ... ~ = ~ 8,9
\item   0,71  ~ \(\times\)  ~ ... ~ = ~ 7,1
\item   843  ~ \(\times\)  ~ ... ~ = ~ 8 430
\item   33,3  ~ \(\times\)  ~ ... ~ = ~ 333
\item   2,77  ~ \(\times\)  ~ ... ~ = ~ 2 770
\item   0,64  ~ \(\times\)  ~ ... ~ = ~ 64
\item   0,079  ~ \(\times\)  ~ ... ~ = ~ 0,79
\item   69  ~ \(\times\)  ~ ... ~ = ~ 690
\item   798  ~ \(\times\)  ~ ... ~ = ~ 79 800
\item   0,098  ~ \(\times\)  ~ ... ~ = ~ 0,98
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   615,8  ~ \(\times\)  ~ 0,1
\item   494,8  ~ \(\times\)  ~ 0,001
\item   7,748  ~ \(\times\)  ~ 0,1
\item   6,405  ~ \(\times\)  ~ 0,01
\item   3,335  ~ \(\times\)  ~ 0,001
\item   6,14  ~ \(\times\)  ~ 0,01
\item   120,9  ~ \(\times\)  ~ 0,001
\item   39,15  ~ \(\times\)  ~ 0,001
\item   58,42  ~ \(\times\)  ~ 0,001
\item   4 633  ~ \(\times\)  ~ 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   5 879  ~ \(\times\)  ~ ... ~ = ~  58,79
\item   79,3  ~ \(\times\)  ~ ... ~ = ~  0,079 3
\item   1,149  ~ \(\times\)  ~ ... ~ = ~  0,011 49
\item   34,7  ~ \(\times\)  ~ ... ~ = ~  0,034 7
\item   7 159  ~ \(\times\)  ~ ... ~ = ~  7,159
\item   68,93  ~ \(\times\)  ~ ... ~ = ~  6,893
\item   3,7  ~ \(\times\)  ~ ... ~ = ~  0,003 7
\item   887,6  ~ \(\times\)  ~ ... ~ = ~  8,876
\item   8 490  ~ \(\times\)  ~ ... ~ = ~  849
\item   148,7  ~ \(\times\)  ~ ... ~ = ~  14,87
\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~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~m~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   293,61 ~daL~ = ...~mL
\item   242,44 ~daL~ = ...~hL
\item   960,9 ~cg~ = ...~g
\item   8 988,9 ~m~ = ...~cm
\item   4 892,9 ~dg~ = ...~g
\item   5 332,6 ~kg~ = ...~cg
\item   3 436,4 ~km~ = ...~dam
\item   9 452,4 ~hm~ = ...~km
\item   3 268,2 ~dag~ = ...~dg
\item   9 576,3 ~dag~ = ...~g
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{1800}{100}\) = \(\dfrac{180}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{83}{10}\) = \(\dfrac{830}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{530}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,786  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 786}
\item   49  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 490}
\item   0,001  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,1}
\item   57  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 570}
\item   0,089  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 89}
\item   0,074  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7,4}
\item   4,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 200}
\item   860  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 86 000}
\item   68,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 682}
\item   4,07  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 070}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   199,5 ~ : ~ 10 ~ = ~{\color{red} 19,95}
\item   2 395 ~ : ~ 1 000 ~ = ~{\color{red} 2,395}
\item   58,21 ~ : ~ 100 ~ = ~{\color{red} 0,582 1}
\item   56 ~ : ~ 10 ~ = ~{\color{red} 5,6}
\item   43,24 ~ : ~ 1 000 ~ = ~{\color{red} 0,043 24}
\item   508,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,508 8}
\item   5,954 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 954}
\item   0,927 ~ : ~ 10 ~ = ~{\color{red} 0,092 7}
\item   31,76 ~ : ~ 1 000 ~ = ~{\color{red} 0,031 76}
\item   918,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,918 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,089 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,9
\item   0,71 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,1
\item   843 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 430
\item   33,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~333
\item   2,77 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 770
\item   0,64 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~64
\item   0,079 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,79
\item   69 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~690
\item   798 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~79 800
\item   0,098 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,98
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   615,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 61,58
}\item   494,8 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,494 8
}\item   7,748 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,774 8
}\item   6,405 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,064 05
}\item   3,335 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 335
}\item   6,14 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,061 4
}\item   120,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,120 9
}\item   39,15 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,039 15
}\item   58,42 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,058 42
}\item   4 633 ~ \(\times\)  0,01 ~ = ~{\color{red} 46,33
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 879 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 58,79
\item   79,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,079 3
\item   1,149 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,011 49
\item   34,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,034 7
\item   7 159 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,159
\item   68,93 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,893
\item   3,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 7
\item   887,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,876
\item   8 490 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 849
\item   148,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 14,87
\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~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   293,61 ~daL~ = {\color{red}  2 936 100 }~mL
\item   242,44 ~daL~ = {\color{red}  24,244 }~hL
\item   960,9 ~cg~ = {\color{red}  9,609 }~g
\item   8 988,9 ~m~ = {\color{red}  898 890 }~cm
\item   4 892,9 ~dg~ = {\color{red}  489,29 }~g
\item   5 332,6 ~kg~ = {\color{red}  533 260 000 }~cg
\item   3 436,4 ~km~ = {\color{red}  343 640 }~dam
\item   9 452,4 ~hm~ = {\color{red}  945,24 }~km
\item   3 268,2 ~dag~ = {\color{red}  326 820 }~dg
\item   9 576,3 ~dag~ = {\color{red}  95 763 }~g
\end{itemize}
\end{multicols}
\end{document}
