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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 60}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{8400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{44}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,836  ~ \(\times\)  ~ 100
\item   9,15  ~ \(\times\)  ~ 10
\item   820  ~ \(\times\)  ~ 1 000
\item   88,7  ~ \(\times\)  ~ 10
\item   408  ~ \(\times\)  ~ 10
\item   663  ~ \(\times\)  ~ 100
\item   81,8  ~ \(\times\)  ~ 10
\item   0,032  ~ \(\times\)  ~ 1 000
\item   82,3  ~ \(\times\)  ~ 1 000
\item   0,062  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   892  ~ : ~ 100
\item   2 551  ~ : ~ 1 000
\item   36,88  ~ : ~ 10
\item   90,6  ~ : ~ 10
\item   374,6  ~ : ~ 1 000
\item   429,9  ~ : ~ 1 000
\item   3 308  ~ : ~ 1 000
\item   5,317  ~ : ~ 100
\item   6 268  ~ : ~ 1 000
\item   1 676  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   580  ~ \(\times\)  ~ ... ~ = ~ 5 800
\item   0,188  ~ \(\times\)  ~ ... ~ = ~ 188
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 33
\item   0,407  ~ \(\times\)  ~ ... ~ = ~ 407
\item   71,9  ~ \(\times\)  ~ ... ~ = ~ 7 190
\item   7,42  ~ \(\times\)  ~ ... ~ = ~ 742
\item   973  ~ \(\times\)  ~ ... ~ = ~ 973 000
\item   0,072  ~ \(\times\)  ~ ... ~ = ~ 7,2
\item   0,033  ~ \(\times\)  ~ ... ~ = ~ 3,3
\item   55  ~ \(\times\)  ~ ... ~ = ~ 550
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,783  ~ \(\times\)  ~ 0,001
\item   1,556  ~ \(\times\)  ~ 0,1
\item   8,427  ~ \(\times\)  ~ 0,1
\item   7 089  ~ \(\times\)  ~ 0,1
\item   959,1  ~ \(\times\)  ~ 0,1
\item   31,47  ~ \(\times\)  ~ 0,001
\item   6,992  ~ \(\times\)  ~ 0,1
\item   3 871  ~ \(\times\)  ~ 0,01
\item   559,4  ~ \(\times\)  ~ 0,1
\item   55,08  ~ \(\times\)  ~ 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   5 658  ~ \(\times\)  ~ ... ~ = ~  565,8
\item   48,43  ~ \(\times\)  ~ ... ~ = ~  4,843
\item   914,1  ~ \(\times\)  ~ ... ~ = ~  0,914 1
\item   57,66  ~ \(\times\)  ~ ... ~ = ~  5,766
\item   2,694  ~ \(\times\)  ~ ... ~ = ~  0,026 94
\item   34,57  ~ \(\times\)  ~ ... ~ = ~  0,034 57
\item   3 204  ~ \(\times\)  ~ ... ~ = ~  320,4
\item   249,5  ~ \(\times\)  ~ ... ~ = ~  24,95
\item   0,404  ~ \(\times\)  ~ ... ~ = ~  0,000 404
\item   178,7  ~ \(\times\)  ~ ... ~ = ~  0,178 7
\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~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~cm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 977,4 ~hL~ = ...~dL
\item   951,14 ~m~ = ...~dm
\item   988,94 ~dm~ = ...~hm
\item   295,78 ~cm~ = ...~hm
\item   535,74 ~hL~ = ...~mL
\item   164,81 ~kL~ = ...~cL
\item   338,61 ~kg~ = ...~dg
\item   574,06 ~daL~ = ...~dL
\item   314,02 ~dag~ = ...~cg
\item   884,6 ~kg~ = ...~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   5 = \(\dfrac{50}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{8400}{100}\) = \(\dfrac{840}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{44}{10}\) = \(\dfrac{440}{100}\)
\item   \(\dfrac{40}{100}\) = \(\dfrac{400}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,836  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 83,6}
\item   9,15  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 91,5}
\item   820  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 820 000}
\item   88,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 887}
\item   408  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 080}
\item   663  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66 300}
\item   81,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 818}
\item   0,032  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 32}
\item   82,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 82 300}
\item   0,062  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 62}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   892 ~ : ~ 100 ~ = ~{\color{red} 8,92}
\item   2 551 ~ : ~ 1 000 ~ = ~{\color{red} 2,551}
\item   36,88 ~ : ~ 10 ~ = ~{\color{red} 3,688}
\item   90,6 ~ : ~ 10 ~ = ~{\color{red} 9,06}
\item   374,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,374 6}
\item   429,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,429 9}
\item   3 308 ~ : ~ 1 000 ~ = ~{\color{red} 3,308}
\item   5,317 ~ : ~ 100 ~ = ~{\color{red} 0,053 17}
\item   6 268 ~ : ~ 1 000 ~ = ~{\color{red} 6,268}
\item   1 676 ~ : ~ 10 ~ = ~{\color{red} 167,6}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   580 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 800
\item   0,188 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~188
\item   0,033 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~33
\item   0,407 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~407
\item   71,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7 190
\item   7,42 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~742
\item   973 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~973 000
\item   0,072 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7,2
\item   0,033 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,3
\item   55 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~550
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3,783 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 783
}\item   1,556 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,155 6
}\item   8,427 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,842 7
}\item   7 089 ~ \(\times\)  0,1 ~ = ~{\color{red} 708,9
}\item   959,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 95,91
}\item   31,47 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,031 47
}\item   6,992 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,699 2
}\item   3 871 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,71
}\item   559,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 55,94
}\item   55,08 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,550 8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 658 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 565,8
\item   48,43 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,843
\item   914,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,914 1
\item   57,66 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,766
\item   2,694 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,026 94
\item   34,57 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,034 57
\item   3 204 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 320,4
\item   249,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 24,95
\item   0,404 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 404
\item   178,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,178 7
\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~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 977,4 ~hL~ = {\color{red}  7 977 400 }~dL
\item   951,14 ~m~ = {\color{red}  9 511,4 }~dm
\item   988,94 ~dm~ = {\color{red}  0,988 94 }~hm
\item   295,78 ~cm~ = {\color{red}  0,029 578 }~hm
\item   535,74 ~hL~ = {\color{red}  53 574 000 }~mL
\item   164,81 ~kL~ = {\color{red}  16 481 000 }~cL
\item   338,61 ~kg~ = {\color{red}  3 386 100 }~dg
\item   574,06 ~daL~ = {\color{red}  57 406 }~dL
\item   314,02 ~dag~ = {\color{red}  314 020 }~cg
\item   884,6 ~kg~ = {\color{red}  884 600 000 }~mg
\end{itemize}
\end{multicols}
\end{document}
