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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 351}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{48}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,476  ~ \(\times\)  ~ 10
\item   0,419  ~ \(\times\)  ~ 10
\item   2,89  ~ \(\times\)  ~ 1 000
\item   6,57  ~ \(\times\)  ~ 100
\item   0,089  ~ \(\times\)  ~ 100
\item   889  ~ \(\times\)  ~ 1 000
\item   0,41  ~ \(\times\)  ~ 100
\item   70,7  ~ \(\times\)  ~ 10
\item   0,052  ~ \(\times\)  ~ 100
\item   15,3  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 246  ~ : ~ 1 000
\item   3,539  ~ : ~ 100
\item   946,1  ~ : ~ 100
\item   832,7  ~ : ~ 10
\item   342,4  ~ : ~ 1 000
\item   2 632  ~ : ~ 10
\item   918,8  ~ : ~ 100
\item   77,32  ~ : ~ 100
\item   92,5  ~ : ~ 100
\item   44,28  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,264  ~ \(\times\)  ~ ... ~ = ~ 264
\item   31,3  ~ \(\times\)  ~ ... ~ = ~ 313
\item   93,3  ~ \(\times\)  ~ ... ~ = ~ 93 300
\item   52,9  ~ \(\times\)  ~ ... ~ = ~ 52 900
\item   829  ~ \(\times\)  ~ ... ~ = ~ 82 900
\item   30,8  ~ \(\times\)  ~ ... ~ = ~ 3 080
\item   8,13  ~ \(\times\)  ~ ... ~ = ~ 8 130
\item   9,02  ~ \(\times\)  ~ ... ~ = ~ 90,2
\item   0,011  ~ \(\times\)  ~ ... ~ = ~ 0,11
\item   64,3  ~ \(\times\)  ~ ... ~ = ~ 643
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,465  ~ \(\times\)  ~ 0,001
\item   7 530  ~ \(\times\)  ~ 0,1
\item   956  ~ \(\times\)  ~ 0,01
\item   3 823  ~ \(\times\)  ~ 0,01
\item   3 374  ~ \(\times\)  ~ 0,001
\item   9,253  ~ \(\times\)  ~ 0,001
\item   4,735  ~ \(\times\)  ~ 0,001
\item   309,2  ~ \(\times\)  ~ 0,1
\item   6,353  ~ \(\times\)  ~ 0,01
\item   30,38  ~ \(\times\)  ~ 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   4,2  ~ \(\times\)  ~ ... ~ = ~  0,042
\item   1,493  ~ \(\times\)  ~ ... ~ = ~  0,001 493
\item   733,7  ~ \(\times\)  ~ ... ~ = ~  73,37
\item   13,2  ~ \(\times\)  ~ ... ~ = ~  0,013 2
\item   115,5  ~ \(\times\)  ~ ... ~ = ~  1,155
\item   570,8  ~ \(\times\)  ~ ... ~ = ~  57,08
\item   50,19  ~ \(\times\)  ~ ... ~ = ~  5,019
\item   28,54  ~ \(\times\)  ~ ... ~ = ~  2,854
\item   354  ~ \(\times\)  ~ ... ~ = ~  3,54
\item   64,18  ~ \(\times\)  ~ ... ~ = ~  6,418
\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 ~dm~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~hm
\item   1 ~hm~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~dam~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 418,2 ~mm~ = ...~m
\item   808,73 ~dg~ = ...~g
\item   184,21 ~m~ = ...~mm
\item   990,84 ~mL~ = ...~L
\item   9 679,3 ~cL~ = ...~kL
\item   698,86 ~daL~ = ...~mL
\item   4 733,9 ~hg~ = ...~dg
\item   5 978,2 ~dam~ = ...~km
\item   827,23 ~mL~ = ...~daL
\item   834,74 ~mm~ = ...~km
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{4500}{100}\) = \(\dfrac{450}{10}\)
\item   \(\dfrac{6}{10}\) = \(\dfrac{600}{1\,000}\)
\item   \(\dfrac{48}{10}\) = \(\dfrac{480}{100}\)
\item   \(\dfrac{90}{100}\) = \(\dfrac{900}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,476  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,76}
\item   0,419  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,19}
\item   2,89  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 890}
\item   6,57  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 657}
\item   0,089  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8,9}
\item   889  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 889 000}
\item   0,41  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 41}
\item   70,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 707}
\item   0,052  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5,2}
\item   15,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 530}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 246 ~ : ~ 1 000 ~ = ~{\color{red} 7,246}
\item   3,539 ~ : ~ 100 ~ = ~{\color{red} 0,035 39}
\item   946,1 ~ : ~ 100 ~ = ~{\color{red} 9,461}
\item   832,7 ~ : ~ 10 ~ = ~{\color{red} 83,27}
\item   342,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,342 4}
\item   2 632 ~ : ~ 10 ~ = ~{\color{red} 263,2}
\item   918,8 ~ : ~ 100 ~ = ~{\color{red} 9,188}
\item   77,32 ~ : ~ 100 ~ = ~{\color{red} 0,773 2}
\item   92,5 ~ : ~ 100 ~ = ~{\color{red} 0,925}
\item   44,28 ~ : ~ 1 000 ~ = ~{\color{red} 0,044 28}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,264 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~264
\item   31,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~313
\item   93,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~93 300
\item   52,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~52 900
\item   829 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~82 900
\item   30,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 080
\item   8,13 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 130
\item   9,02 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~90,2
\item   0,011 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,11
\item   64,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~643
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5,465 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,005 465
}\item   7 530 ~ \(\times\)  0,1 ~ = ~{\color{red} 753
}\item   956 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,56
}\item   3 823 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,23
}\item   3 374 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,374
}\item   9,253 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 253
}\item   4,735 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 735
}\item   309,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 30,92
}\item   6,353 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,063 53
}\item   30,38 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,038
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,042
\item   1,493 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 493
\item   733,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 73,37
\item   13,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,013 2
\item   115,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,155
\item   570,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 57,08
\item   50,19 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,019
\item   28,54 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,854
\item   354 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,54
\item   64,18 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,418
\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 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 418,2 ~mm~ = {\color{red}  3,418 2 }~m
\item   808,73 ~dg~ = {\color{red}  80,873 }~g
\item   184,21 ~m~ = {\color{red}  184 210 }~mm
\item   990,84 ~mL~ = {\color{red}  0,990 84 }~L
\item   9 679,3 ~cL~ = {\color{red}  0,096 793 }~kL
\item   698,86 ~daL~ = {\color{red}  6 988 600 }~mL
\item   4 733,9 ~hg~ = {\color{red}  4 733 900 }~dg
\item   5 978,2 ~dam~ = {\color{red}  59,782 }~km
\item   827,23 ~mL~ = {\color{red}  0,082 723 }~daL
\item   834,74 ~mm~ = {\color{red}  0,000 834 74 }~km
\end{itemize}
\end{multicols}
\end{document}
