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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 23}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{65}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{59}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,51  ~ \(\times\)  ~ 10
\item   75,2  ~ \(\times\)  ~ 100
\item   464  ~ \(\times\)  ~ 10
\item   0,644  ~ \(\times\)  ~ 10
\item   117  ~ \(\times\)  ~ 1 000
\item   0,519  ~ \(\times\)  ~ 10
\item   0,533  ~ \(\times\)  ~ 100
\item   798  ~ \(\times\)  ~ 10
\item   810  ~ \(\times\)  ~ 1 000
\item   38,6  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,4  ~ : ~ 1 000
\item   61,41  ~ : ~ 1 000
\item   5 251  ~ : ~ 100
\item   3,011  ~ : ~ 1 000
\item   743,2  ~ : ~ 10
\item   30,26  ~ : ~ 1 000
\item   862,1  ~ : ~ 1 000
\item   1 973  ~ : ~ 10
\item   7 082  ~ : ~ 1 000
\item   46,15  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   347  ~ \(\times\)  ~ ... ~ = ~ 34 700
\item   9,3  ~ \(\times\)  ~ ... ~ = ~ 9 300
\item   0,321  ~ \(\times\)  ~ ... ~ = ~ 321
\item   2,32  ~ \(\times\)  ~ ... ~ = ~ 23,2
\item   0,012  ~ \(\times\)  ~ ... ~ = ~ 0,12
\item   0,733  ~ \(\times\)  ~ ... ~ = ~ 7,33
\item   0,035  ~ \(\times\)  ~ ... ~ = ~ 0,35
\item   0,095  ~ \(\times\)  ~ ... ~ = ~ 0,95
\item   0,977  ~ \(\times\)  ~ ... ~ = ~ 9,77
\item   469  ~ \(\times\)  ~ ... ~ = ~ 4 690
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,92  ~ \(\times\)  ~ 0,1
\item   276,4  ~ \(\times\)  ~ 0,001
\item   30,9  ~ \(\times\)  ~ 0,001
\item   1,032  ~ \(\times\)  ~ 0,001
\item   16,21  ~ \(\times\)  ~ 0,1
\item   6,277  ~ \(\times\)  ~ 0,1
\item   707  ~ \(\times\)  ~ 0,01
\item   773,5  ~ \(\times\)  ~ 0,01
\item   494,4  ~ \(\times\)  ~ 0,1
\item   179,6  ~ \(\times\)  ~ 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   900,8  ~ \(\times\)  ~ ... ~ = ~  9,008
\item   1,739  ~ \(\times\)  ~ ... ~ = ~  0,173 9
\item   0,293  ~ \(\times\)  ~ ... ~ = ~  0,002 93
\item   689,1  ~ \(\times\)  ~ ... ~ = ~  0,689 1
\item   6 861  ~ \(\times\)  ~ ... ~ = ~  6,861
\item   40,07  ~ \(\times\)  ~ ... ~ = ~  0,400 7
\item   68,12  ~ \(\times\)  ~ ... ~ = ~  0,068 12
\item   9 111  ~ \(\times\)  ~ ... ~ = ~  91,11
\item   1 877  ~ \(\times\)  ~ ... ~ = ~  1,877
\item   23,81  ~ \(\times\)  ~ ... ~ = ~  0,023 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 ~cm~ = ...~dam
\item   1 ~m~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~dm
\item   1 ~hm~ = ...~cm
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 952,3 ~dg~ = ...~cg
\item   9 299,2 ~dg~ = ...~mg
\item   951,87 ~cm~ = ...~dam
\item   810,17 ~mg~ = ...~cg
\item   2 818,9 ~mL~ = ...~hL
\item   661,57 ~kg~ = ...~hg
\item   8 520 ~dg~ = ...~hg
\item   633,8 ~dam~ = ...~dm
\item   881,91 ~dm~ = ...~cm
\item   1 711,3 ~daL~ = ...~hL
\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   3 = \(\dfrac{300}{100}\)
\item   \(\dfrac{1300}{100}\) = \(\dfrac{130}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{65}{10}\) = \(\dfrac{650}{100}\)
\item   \(\dfrac{59}{100}\) = \(\dfrac{590}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,51  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 55,1}
\item   75,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 520}
\item   464  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 640}
\item   0,644  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,44}
\item   117  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 117 000}
\item   0,519  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,19}
\item   0,533  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 53,3}
\item   798  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 980}
\item   810  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 810 000}
\item   38,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 38 600}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,036 4}
\item   61,41 ~ : ~ 1 000 ~ = ~{\color{red} 0,061 41}
\item   5 251 ~ : ~ 100 ~ = ~{\color{red} 52,51}
\item   3,011 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 011}
\item   743,2 ~ : ~ 10 ~ = ~{\color{red} 74,32}
\item   30,26 ~ : ~ 1 000 ~ = ~{\color{red} 0,030 26}
\item   862,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,862 1}
\item   1 973 ~ : ~ 10 ~ = ~{\color{red} 197,3}
\item   7 082 ~ : ~ 1 000 ~ = ~{\color{red} 7,082}
\item   46,15 ~ : ~ 1 000 ~ = ~{\color{red} 0,046 15}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   347 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~34 700
\item   9,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 300
\item   0,321 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~321
\item   2,32 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~23,2
\item   0,012 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,12
\item   0,733 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,33
\item   0,035 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,35
\item   0,095 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,95
\item   0,977 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,77
\item   469 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 690
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,92 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,692
}\item   276,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,276 4
}\item   30,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,030 9
}\item   1,032 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 032
}\item   16,21 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,621
}\item   6,277 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,627 7
}\item   707 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,07
}\item   773,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 7,735
}\item   494,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 49,44
}\item   179,6 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,179 6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   900,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,008
\item   1,739 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,173 9
\item   0,293 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,002 93
\item   689,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,689 1
\item   6 861 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,861
\item   40,07 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,400 7
\item   68,12 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,068 12
\item   9 111 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 91,11
\item   1 877 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,877
\item   23,81 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,023 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 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 952,3 ~dg~ = {\color{red}  49 523 }~cg
\item   9 299,2 ~dg~ = {\color{red}  929 920 }~mg
\item   951,87 ~cm~ = {\color{red}  0,951 87 }~dam
\item   810,17 ~mg~ = {\color{red}  81,017 }~cg
\item   2 818,9 ~mL~ = {\color{red}  0,028 189 }~hL
\item   661,57 ~kg~ = {\color{red}  6 615,7 }~hg
\item   8 520 ~dg~ = {\color{red}  8,52 }~hg
\item   633,8 ~dam~ = {\color{red}  63 380 }~dm
\item   881,91 ~dm~ = {\color{red}  8 819,1 }~cm
\item   1 711,3 ~daL~ = {\color{red}  171,13 }~hL
\end{itemize}
\end{multicols}
\end{document}
