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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 178}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{54}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   29,9  ~ \(\times\)  ~ 10
\item   0,978  ~ \(\times\)  ~ 10
\item   57,5  ~ \(\times\)  ~ 100
\item   50,1  ~ \(\times\)  ~ 10
\item   0,054  ~ \(\times\)  ~ 100
\item   487  ~ \(\times\)  ~ 10
\item   68,2  ~ \(\times\)  ~ 1 000
\item   832  ~ \(\times\)  ~ 100
\item   0,289  ~ \(\times\)  ~ 1 000
\item   89  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,629  ~ : ~ 1 000
\item   42,63  ~ : ~ 10
\item   50,3  ~ : ~ 10
\item   1,805  ~ : ~ 1 000
\item   89,62  ~ : ~ 1 000
\item   229,8  ~ : ~ 1 000
\item   5 860  ~ : ~ 100
\item   3,169  ~ : ~ 10
\item   9,236  ~ : ~ 1 000
\item   463,2  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,288  ~ \(\times\)  ~ ... ~ = ~ 2,88
\item   9,59  ~ \(\times\)  ~ ... ~ = ~ 9 590
\item   0,062  ~ \(\times\)  ~ ... ~ = ~ 62
\item   0,03  ~ \(\times\)  ~ ... ~ = ~ 30
\item   0,398  ~ \(\times\)  ~ ... ~ = ~ 398
\item   7,01  ~ \(\times\)  ~ ... ~ = ~ 701
\item   759  ~ \(\times\)  ~ ... ~ = ~ 75 900
\item   7,85  ~ \(\times\)  ~ ... ~ = ~ 785
\item   0,958  ~ \(\times\)  ~ ... ~ = ~ 958
\item   28,7  ~ \(\times\)  ~ ... ~ = ~ 28 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 653  ~ \(\times\)  ~ 0,001
\item   23,8  ~ \(\times\)  ~ 0,1
\item   78,49  ~ \(\times\)  ~ 0,1
\item   14,09  ~ \(\times\)  ~ 0,001
\item   721  ~ \(\times\)  ~ 0,1
\item   4,135  ~ \(\times\)  ~ 0,001
\item   18  ~ \(\times\)  ~ 0,1
\item   625,3  ~ \(\times\)  ~ 0,001
\item   2 862  ~ \(\times\)  ~ 0,1
\item   158  ~ \(\times\)  ~ 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   4,594  ~ \(\times\)  ~ ... ~ = ~  0,459 4
\item   798,6  ~ \(\times\)  ~ ... ~ = ~  79,86
\item   585,9  ~ \(\times\)  ~ ... ~ = ~  0,585 9
\item   0,825  ~ \(\times\)  ~ ... ~ = ~  0,008 25
\item   944,9  ~ \(\times\)  ~ ... ~ = ~  94,49
\item   5 519  ~ \(\times\)  ~ ... ~ = ~  5,519
\item   8 722  ~ \(\times\)  ~ ... ~ = ~  87,22
\item   299,2  ~ \(\times\)  ~ ... ~ = ~  2,992
\item   38,65  ~ \(\times\)  ~ ... ~ = ~  0,038 65
\item   3,317  ~ \(\times\)  ~ ... ~ = ~  0,033 17
\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 ~hm~ = ...~m
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   472,78 ~cg~ = ...~g
\item   297,22 ~dL~ = ...~cL
\item   556,46 ~dm~ = ...~hm
\item   3 561,9 ~dm~ = ...~m
\item   8 356,1 ~mg~ = ...~cg
\item   346,35 ~cg~ = ...~dg
\item   8 233,6 ~dam~ = ...~m
\item   234,8 ~hg~ = ...~cg
\item   474,29 ~daL~ = ...~L
\item   916,34 ~L~ = ...~kL
\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   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{9300}{100}\) = \(\dfrac{930}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{54}{10}\) = \(\dfrac{540}{100}\)
\item   \(\dfrac{72}{100}\) = \(\dfrac{720}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   29,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 299}
\item   0,978  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,78}
\item   57,5  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 750}
\item   50,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 501}
\item   0,054  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,4}
\item   487  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 870}
\item   68,2  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 68 200}
\item   832  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 83 200}
\item   0,289  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 289}
\item   89  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 89 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,629 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 629}
\item   42,63 ~ : ~ 10 ~ = ~{\color{red} 4,263}
\item   50,3 ~ : ~ 10 ~ = ~{\color{red} 5,03}
\item   1,805 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 805}
\item   89,62 ~ : ~ 1 000 ~ = ~{\color{red} 0,089 62}
\item   229,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,229 8}
\item   5 860 ~ : ~ 100 ~ = ~{\color{red} 58,6}
\item   3,169 ~ : ~ 10 ~ = ~{\color{red} 0,316 9}
\item   9,236 ~ : ~ 1 000 ~ = ~{\color{red} 0,009 236}
\item   463,2 ~ : ~ 100 ~ = ~{\color{red} 4,632}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,288 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,88
\item   9,59 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~9 590
\item   0,062 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~62
\item   0,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~30
\item   0,398 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~398
\item   7,01 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~701
\item   759 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~75 900
\item   7,85 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~785
\item   0,958 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~958
\item   28,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~28 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 653 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,653
}\item   23,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,38
}\item   78,49 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,849
}\item   14,09 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,014 09
}\item   721 ~ \(\times\)  0,1 ~ = ~{\color{red} 72,1
}\item   4,135 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 135
}\item   18 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,8
}\item   625,3 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,625 3
}\item   2 862 ~ \(\times\)  0,1 ~ = ~{\color{red} 286,2
}\item   158 ~ \(\times\)  0,1 ~ = ~{\color{red} 15,8
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,594 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,459 4
\item   798,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 79,86
\item   585,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,585 9
\item   0,825 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,008 25
\item   944,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 94,49
\item   5 519 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,519
\item   8 722 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 87,22
\item   299,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,992
\item   38,65 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,038 65
\item   3,317 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,033 17
\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 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\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   472,78 ~cg~ = {\color{red}  4,727 8 }~g
\item   297,22 ~dL~ = {\color{red}  2 972,2 }~cL
\item   556,46 ~dm~ = {\color{red}  0,556 46 }~hm
\item   3 561,9 ~dm~ = {\color{red}  356,19 }~m
\item   8 356,1 ~mg~ = {\color{red}  835,61 }~cg
\item   346,35 ~cg~ = {\color{red}  34,635 }~dg
\item   8 233,6 ~dam~ = {\color{red}  82 336 }~m
\item   234,8 ~hg~ = {\color{red}  2 348 000 }~cg
\item   474,29 ~daL~ = {\color{red}  4 742,9 }~L
\item   916,34 ~L~ = {\color{red}  0,916 34 }~kL
\end{itemize}
\end{multicols}
\end{document}
