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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 174}

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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   1 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{1400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   23,9  ~ \(\times\)  ~ 10
\item   9,26  ~ \(\times\)  ~ 100
\item   6,79  ~ \(\times\)  ~ 1 000
\item   590  ~ \(\times\)  ~ 1 000
\item   3,39  ~ \(\times\)  ~ 1 000
\item   7,88  ~ \(\times\)  ~ 1 000
\item   475  ~ \(\times\)  ~ 1 000
\item   806  ~ \(\times\)  ~ 1 000
\item   570  ~ \(\times\)  ~ 100
\item   0,463  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,08  ~ : ~ 100
\item   7 664  ~ : ~ 100
\item   708  ~ : ~ 10
\item   297  ~ : ~ 100
\item   3,059  ~ : ~ 100
\item   70,9  ~ : ~ 100
\item   0,891  ~ : ~ 10
\item   3 974  ~ : ~ 1 000
\item   834,7  ~ : ~ 100
\item   24,02  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,094  ~ \(\times\)  ~ ... ~ = ~ 94
\item   0,647  ~ \(\times\)  ~ ... ~ = ~ 647
\item   96,4  ~ \(\times\)  ~ ... ~ = ~ 964
\item   94,9  ~ \(\times\)  ~ ... ~ = ~ 94 900
\item   157  ~ \(\times\)  ~ ... ~ = ~ 15 700
\item   7,71  ~ \(\times\)  ~ ... ~ = ~ 771
\item   10,9  ~ \(\times\)  ~ ... ~ = ~ 1 090
\item   0,071  ~ \(\times\)  ~ ... ~ = ~ 71
\item   455  ~ \(\times\)  ~ ... ~ = ~ 4 550
\item   0,204  ~ \(\times\)  ~ ... ~ = ~ 204
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,38  ~ \(\times\)  ~ 0,001
\item   5 678  ~ \(\times\)  ~ 0,01
\item   8 433  ~ \(\times\)  ~ 0,001
\item   4 760  ~ \(\times\)  ~ 0,1
\item   10,18  ~ \(\times\)  ~ 0,001
\item   0,401  ~ \(\times\)  ~ 0,001
\item   3,174  ~ \(\times\)  ~ 0,1
\item   6,541  ~ \(\times\)  ~ 0,01
\item   3 891  ~ \(\times\)  ~ 0,01
\item   91,46  ~ \(\times\)  ~ 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   8,21  ~ \(\times\)  ~ ... ~ = ~  0,821
\item   66,74  ~ \(\times\)  ~ ... ~ = ~  0,667 4
\item   7,184  ~ \(\times\)  ~ ... ~ = ~  0,718 4
\item   2 833  ~ \(\times\)  ~ ... ~ = ~  283,3
\item   602  ~ \(\times\)  ~ ... ~ = ~  60,2
\item   21,29  ~ \(\times\)  ~ ... ~ = ~  0,021 29
\item   349,2  ~ \(\times\)  ~ ... ~ = ~  34,92
\item   366,1  ~ \(\times\)  ~ ... ~ = ~  3,661
\item   97,47  ~ \(\times\)  ~ ... ~ = ~  9,747
\item   5 870  ~ \(\times\)  ~ ... ~ = ~  587
\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 ~cm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 139,2 ~mg~ = ...~kg
\item   182,9 ~kL~ = ...~hL
\item   9 927,8 ~mL~ = ...~kL
\item   4 709,6 ~kg~ = ...~mg
\item   2 726,3 ~hg~ = ...~cg
\item   349,19 ~dg~ = ...~cg
\item   5 079,4 ~g~ = ...~hg
\item   2 961,5 ~g~ = ...~cg
\item   1 598,7 ~dL~ = ...~daL
\item   330,86 ~L~ = ...~daL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 = \(\dfrac{10}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{1400}{100}\) = \(\dfrac{140}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{57}{10}\) = \(\dfrac{570}{100}\)
\item   \(\dfrac{19}{100}\) = \(\dfrac{190}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   23,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 239}
\item   9,26  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 926}
\item   6,79  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 6 790}
\item   590  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 590 000}
\item   3,39  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 3 390}
\item   7,88  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7 880}
\item   475  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 475 000}
\item   806  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 806 000}
\item   570  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 57 000}
\item   0,463  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 46,3}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,08 ~ : ~ 100 ~ = ~{\color{red} 0,110 8}
\item   7 664 ~ : ~ 100 ~ = ~{\color{red} 76,64}
\item   708 ~ : ~ 10 ~ = ~{\color{red} 70,8}
\item   297 ~ : ~ 100 ~ = ~{\color{red} 2,97}
\item   3,059 ~ : ~ 100 ~ = ~{\color{red} 0,030 59}
\item   70,9 ~ : ~ 100 ~ = ~{\color{red} 0,709}
\item   0,891 ~ : ~ 10 ~ = ~{\color{red} 0,089 1}
\item   3 974 ~ : ~ 1 000 ~ = ~{\color{red} 3,974}
\item   834,7 ~ : ~ 100 ~ = ~{\color{red} 8,347}
\item   24,02 ~ : ~ 1 000 ~ = ~{\color{red} 0,024 02}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,094 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~94
\item   0,647 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~647
\item   96,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~964
\item   94,9 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~94 900
\item   157 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~15 700
\item   7,71 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~771
\item   10,9 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 090
\item   0,071 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~71
\item   455 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 550
\item   0,204 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~204
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,38 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,051 38
}\item   5 678 ~ \(\times\)  0,01 ~ = ~{\color{red} 56,78
}\item   8 433 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,433
}\item   4 760 ~ \(\times\)  0,1 ~ = ~{\color{red} 476
}\item   10,18 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,010 18
}\item   0,401 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 401
}\item   3,174 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,317 4
}\item   6,541 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,065 41
}\item   3 891 ~ \(\times\)  0,01 ~ = ~{\color{red} 38,91
}\item   91,46 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,146
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,21 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,821
\item   66,74 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,667 4
\item   7,184 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,718 4
\item   2 833 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 283,3
\item   602 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 60,2
\item   21,29 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,021 29
\item   349,2 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 34,92
\item   366,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,661
\item   97,47 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,747
\item   5 870 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 587
\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 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 139,2 ~mg~ = {\color{red}  0,003 139 2 }~kg
\item   182,9 ~kL~ = {\color{red}  1 829 }~hL
\item   9 927,8 ~mL~ = {\color{red}  0,009 927 8 }~kL
\item   4 709,6 ~kg~ = {\color{red}  4 709 600 000 }~mg
\item   2 726,3 ~hg~ = {\color{red}  27 263 000 }~cg
\item   349,19 ~dg~ = {\color{red}  3 491,9 }~cg
\item   5 079,4 ~g~ = {\color{red}  50,794 }~hg
\item   2 961,5 ~g~ = {\color{red}  296 150 }~cg
\item   1 598,7 ~dL~ = {\color{red}  15,987 }~daL
\item   330,86 ~L~ = {\color{red}  33,086 }~daL
\end{itemize}
\end{multicols}
\end{document}
