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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 53}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,76  ~ \(\times\)  ~ 1 000
\item   40  ~ \(\times\)  ~ 10
\item   36,1  ~ \(\times\)  ~ 100
\item   911  ~ \(\times\)  ~ 10
\item   0,57  ~ \(\times\)  ~ 10
\item   46  ~ \(\times\)  ~ 10
\item   13,8  ~ \(\times\)  ~ 100
\item   5,28  ~ \(\times\)  ~ 1 000
\item   0,685  ~ \(\times\)  ~ 10
\item   3,49  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,583  ~ : ~ 100
\item   730  ~ : ~ 1 000
\item   2 644  ~ : ~ 100
\item   796,5  ~ : ~ 100
\item   980,3  ~ : ~ 10
\item   1 401  ~ : ~ 1 000
\item   1 665  ~ : ~ 100
\item   65,95  ~ : ~ 100
\item   3 949  ~ : ~ 100
\item   693,2  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,021  ~ \(\times\)  ~ ... ~ = ~ 2,1
\item   6,65  ~ \(\times\)  ~ ... ~ = ~ 6 650
\item   0,204  ~ \(\times\)  ~ ... ~ = ~ 2,04
\item   0,544  ~ \(\times\)  ~ ... ~ = ~ 54,4
\item   0,186  ~ \(\times\)  ~ ... ~ = ~ 1,86
\item   6,26  ~ \(\times\)  ~ ... ~ = ~ 62,6
\item   0,766  ~ \(\times\)  ~ ... ~ = ~ 7,66
\item   0,408  ~ \(\times\)  ~ ... ~ = ~ 4,08
\item   31,2  ~ \(\times\)  ~ ... ~ = ~ 31 200
\item   41,8  ~ \(\times\)  ~ ... ~ = ~ 4 180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   39,95  ~ \(\times\)  ~ 0,1
\item   3,236  ~ \(\times\)  ~ 0,01
\item   708,1  ~ \(\times\)  ~ 0,1
\item   36,59  ~ \(\times\)  ~ 0,1
\item   30,6  ~ \(\times\)  ~ 0,01
\item   5,374  ~ \(\times\)  ~ 0,1
\item   28,9  ~ \(\times\)  ~ 0,001
\item   1,432  ~ \(\times\)  ~ 0,01
\item   436,5  ~ \(\times\)  ~ 0,001
\item   4,316  ~ \(\times\)  ~ 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   557,4  ~ \(\times\)  ~ ... ~ = ~  55,74
\item   91,74  ~ \(\times\)  ~ ... ~ = ~  9,174
\item   1,119  ~ \(\times\)  ~ ... ~ = ~  0,011 19
\item   0,433  ~ \(\times\)  ~ ... ~ = ~  0,000 433
\item   7,673  ~ \(\times\)  ~ ... ~ = ~  0,767 3
\item   664,9  ~ \(\times\)  ~ ... ~ = ~  0,664 9
\item   6 126  ~ \(\times\)  ~ ... ~ = ~  612,6
\item   4,404  ~ \(\times\)  ~ ... ~ = ~  0,004 404
\item   5,14  ~ \(\times\)  ~ ... ~ = ~  0,514
\item   56,19  ~ \(\times\)  ~ ... ~ = ~  5,619
\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~ = ...~cm
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~cm
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 039,2 ~dam~ = ...~km
\item   4 010,2 ~dag~ = ...~g
\item   325,52 ~dL~ = ...~daL
\item   692,55 ~mg~ = ...~dag
\item   139,18 ~g~ = ...~mg
\item   5 381,3 ~dam~ = ...~mm
\item   6 406,3 ~cL~ = ...~dL
\item   705,87 ~km~ = ...~cm
\item   198,29 ~cg~ = ...~dag
\item   560,54 ~kL~ = ...~dL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{7500}{100}\) = \(\dfrac{750}{10}\)
\item   \(\dfrac{8}{10}\) = \(\dfrac{800}{1\,000}\)
\item   \(\dfrac{77}{10}\) = \(\dfrac{770}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{570}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,76  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 760}
\item   40  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 400}
\item   36,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 610}
\item   911  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9 110}
\item   0,57  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,7}
\item   46  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 460}
\item   13,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 380}
\item   5,28  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 280}
\item   0,685  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,85}
\item   3,49  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 34,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,583 ~ : ~ 100 ~ = ~{\color{red} 0,015 83}
\item   730 ~ : ~ 1 000 ~ = ~{\color{red} 0,73}
\item   2 644 ~ : ~ 100 ~ = ~{\color{red} 26,44}
\item   796,5 ~ : ~ 100 ~ = ~{\color{red} 7,965}
\item   980,3 ~ : ~ 10 ~ = ~{\color{red} 98,03}
\item   1 401 ~ : ~ 1 000 ~ = ~{\color{red} 1,401}
\item   1 665 ~ : ~ 100 ~ = ~{\color{red} 16,65}
\item   65,95 ~ : ~ 100 ~ = ~{\color{red} 0,659 5}
\item   3 949 ~ : ~ 100 ~ = ~{\color{red} 39,49}
\item   693,2 ~ : ~ 10 ~ = ~{\color{red} 69,32}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,021 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~2,1
\item   6,65 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 650
\item   0,204 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,04
\item   0,544 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~54,4
\item   0,186 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,86
\item   6,26 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~62,6
\item   0,766 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~7,66
\item   0,408 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,08
\item   31,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~31 200
\item   41,8 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   39,95 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,995
}\item   3,236 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,032 36
}\item   708,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 70,81
}\item   36,59 ~ \(\times\)  0,1 ~ = ~{\color{red} 3,659
}\item   30,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,306
}\item   5,374 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,537 4
}\item   28,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,028 9
}\item   1,432 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,014 32
}\item   436,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,436 5
}\item   4,316 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 316
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   557,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 55,74
\item   91,74 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,174
\item   1,119 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,011 19
\item   0,433 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,000 433
\item   7,673 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,767 3
\item   664,9 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,664 9
\item   6 126 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 612,6
\item   4,404 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 404
\item   5,14 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,514
\item   56,19 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,619
\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~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 039,2 ~dam~ = {\color{red}  80,392 }~km
\item   4 010,2 ~dag~ = {\color{red}  40 102 }~g
\item   325,52 ~dL~ = {\color{red}  3,255 2 }~daL
\item   692,55 ~mg~ = {\color{red}  0,069 255 }~dag
\item   139,18 ~g~ = {\color{red}  139 180 }~mg
\item   5 381,3 ~dam~ = {\color{red}  53 813 000 }~mm
\item   6 406,3 ~cL~ = {\color{red}  640,63 }~dL
\item   705,87 ~km~ = {\color{red}  70 587 000 }~cm
\item   198,29 ~cg~ = {\color{red}  0,198 29 }~dag
\item   560,54 ~kL~ = {\color{red}  5 605 400 }~dL
\end{itemize}
\end{multicols}
\end{document}
