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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 40}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68,9  ~ \(\times\)  ~ 10
\item   7,89  ~ \(\times\)  ~ 100
\item   0,909  ~ \(\times\)  ~ 10
\item   54,9  ~ \(\times\)  ~ 10
\item   66,5  ~ \(\times\)  ~ 1 000
\item   0,733  ~ \(\times\)  ~ 10
\item   0,019  ~ \(\times\)  ~ 100
\item   1,25  ~ \(\times\)  ~ 100
\item   0,016  ~ \(\times\)  ~ 1 000
\item   0,086  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 775  ~ : ~ 100
\item   560,4  ~ : ~ 1 000
\item   26,21  ~ : ~ 10
\item   86,27  ~ : ~ 1 000
\item   4,875  ~ : ~ 10
\item   970,3  ~ : ~ 100
\item   7 202  ~ : ~ 10
\item   966,4  ~ : ~ 1 000
\item   9 690  ~ : ~ 10
\item   77,53  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,4  ~ \(\times\)  ~ ... ~ = ~ 2 040
\item   473  ~ \(\times\)  ~ ... ~ = ~ 47 300
\item   6,62  ~ \(\times\)  ~ ... ~ = ~ 6 620
\item   0,96  ~ \(\times\)  ~ ... ~ = ~ 96
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 88
\item   81,8  ~ \(\times\)  ~ ... ~ = ~ 818
\item   4,7  ~ \(\times\)  ~ ... ~ = ~ 4 700
\item   40,3  ~ \(\times\)  ~ ... ~ = ~ 40 300
\item   466  ~ \(\times\)  ~ ... ~ = ~ 466 000
\item   43,4  ~ \(\times\)  ~ ... ~ = ~ 43 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,417  ~ \(\times\)  ~ 0,01
\item   861,1  ~ \(\times\)  ~ 0,1
\item   731,4  ~ \(\times\)  ~ 0,1
\item   27,15  ~ \(\times\)  ~ 0,01
\item   160,4  ~ \(\times\)  ~ 0,01
\item   277,5  ~ \(\times\)  ~ 0,1
\item   406,4  ~ \(\times\)  ~ 0,1
\item   839,4  ~ \(\times\)  ~ 0,1
\item   6,968  ~ \(\times\)  ~ 0,01
\item   51,94  ~ \(\times\)  ~ 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   4 172  ~ \(\times\)  ~ ... ~ = ~  4,172
\item   6 644  ~ \(\times\)  ~ ... ~ = ~  664,4
\item   27,63  ~ \(\times\)  ~ ... ~ = ~  2,763
\item   50,69  ~ \(\times\)  ~ ... ~ = ~  0,506 9
\item   70,85  ~ \(\times\)  ~ ... ~ = ~  0,070 85
\item   6,91  ~ \(\times\)  ~ ... ~ = ~  0,006 91
\item   78,81  ~ \(\times\)  ~ ... ~ = ~  0,078 81
\item   8 955  ~ \(\times\)  ~ ... ~ = ~  8,955
\item   3 613  ~ \(\times\)  ~ ... ~ = ~  3,613
\item   60,88  ~ \(\times\)  ~ ... ~ = ~  0,060 88
\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 ~km~ = ...~cm
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~dam~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   674,81 ~mL~ = ...~L
\item   2 878,5 ~kL~ = ...~hL
\item   2 001,6 ~g~ = ...~hg
\item   762,23 ~cg~ = ...~mg
\item   8 919,5 ~dag~ = ...~dg
\item   322,64 ~cm~ = ...~m
\item   542,54 ~kg~ = ...~cg
\item   626,25 ~hg~ = ...~dag
\item   3 977,6 ~dam~ = ...~hm
\item   342,82 ~km~ = ...~hm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{96}{10}\) = \(\dfrac{960}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{920}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   68,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 689}
\item   7,89  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 789}
\item   0,909  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,09}
\item   54,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 549}
\item   66,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 66 500}
\item   0,733  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,33}
\item   0,019  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,9}
\item   1,25  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 125}
\item   0,016  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 16}
\item   0,086  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,86}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 775 ~ : ~ 100 ~ = ~{\color{red} 67,75}
\item   560,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,560 4}
\item   26,21 ~ : ~ 10 ~ = ~{\color{red} 2,621}
\item   86,27 ~ : ~ 1 000 ~ = ~{\color{red} 0,086 27}
\item   4,875 ~ : ~ 10 ~ = ~{\color{red} 0,487 5}
\item   970,3 ~ : ~ 100 ~ = ~{\color{red} 9,703}
\item   7 202 ~ : ~ 10 ~ = ~{\color{red} 720,2}
\item   966,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,966 4}
\item   9 690 ~ : ~ 10 ~ = ~{\color{red} 969}
\item   77,53 ~ : ~ 10 ~ = ~{\color{red} 7,753}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   20,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2 040
\item   473 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~47 300
\item   6,62 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 620
\item   0,96 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96
\item   0,088 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~88
\item   81,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~818
\item   4,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 700
\item   40,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~40 300
\item   466 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~466 000
\item   43,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43 400
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,417 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,004 17
}\item   861,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 86,11
}\item   731,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 73,14
}\item   27,15 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,271 5
}\item   160,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,604
}\item   277,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 27,75
}\item   406,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 40,64
}\item   839,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 83,94
}\item   6,968 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,069 68
}\item   51,94 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,051 94
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 172 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,172
\item   6 644 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 664,4
\item   27,63 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,763
\item   50,69 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,506 9
\item   70,85 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,070 85
\item   6,91 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 91
\item   78,81 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,078 81
\item   8 955 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 8,955
\item   3 613 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,613
\item   60,88 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,060 88
\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 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   674,81 ~mL~ = {\color{red}  0,674 81 }~L
\item   2 878,5 ~kL~ = {\color{red}  28 785 }~hL
\item   2 001,6 ~g~ = {\color{red}  20,016 }~hg
\item   762,23 ~cg~ = {\color{red}  7 622,3 }~mg
\item   8 919,5 ~dag~ = {\color{red}  891 950 }~dg
\item   322,64 ~cm~ = {\color{red}  3,226 4 }~m
\item   542,54 ~kg~ = {\color{red}  54 254 000 }~cg
\item   626,25 ~hg~ = {\color{red}  6 262,5 }~dag
\item   3 977,6 ~dam~ = {\color{red}  397,76 }~hm
\item   342,82 ~km~ = {\color{red}  3 428,2 }~hm
\end{itemize}
\end{multicols}
\end{document}
