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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 245}

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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   3 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{68}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,084  ~ \(\times\)  ~ 1 000
\item   483  ~ \(\times\)  ~ 1 000
\item   2,28  ~ \(\times\)  ~ 10
\item   0,851  ~ \(\times\)  ~ 1 000
\item   6,71  ~ \(\times\)  ~ 100
\item   41,9  ~ \(\times\)  ~ 1 000
\item   0,48  ~ \(\times\)  ~ 1 000
\item   0,019  ~ \(\times\)  ~ 1 000
\item   8,82  ~ \(\times\)  ~ 10
\item   0,687  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,967  ~ : ~ 10
\item   9 813  ~ : ~ 10
\item   2 373  ~ : ~ 1 000
\item   997  ~ : ~ 1 000
\item   59,53  ~ : ~ 10
\item   6,262  ~ : ~ 1 000
\item   57,31  ~ : ~ 1 000
\item   3 950  ~ : ~ 100
\item   1,764  ~ : ~ 1 000
\item   909,5  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,039  ~ \(\times\)  ~ ... ~ = ~ 3,9
\item   4,01  ~ \(\times\)  ~ ... ~ = ~ 4 010
\item   0,437  ~ \(\times\)  ~ ... ~ = ~ 4,37
\item   0,085  ~ \(\times\)  ~ ... ~ = ~ 0,85
\item   2,76  ~ \(\times\)  ~ ... ~ = ~ 27,6
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 0,02
\item   3,22  ~ \(\times\)  ~ ... ~ = ~ 322
\item   0,843  ~ \(\times\)  ~ ... ~ = ~ 843
\item   81,6  ~ \(\times\)  ~ ... ~ = ~ 816
\item   648  ~ \(\times\)  ~ ... ~ = ~ 648 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,29  ~ \(\times\)  ~ 0,01
\item   9 626  ~ \(\times\)  ~ 0,01
\item   2 106  ~ \(\times\)  ~ 0,001
\item   34,87  ~ \(\times\)  ~ 0,001
\item   714,9  ~ \(\times\)  ~ 0,001
\item   7,1  ~ \(\times\)  ~ 0,1
\item   2,243  ~ \(\times\)  ~ 0,01
\item   949,1  ~ \(\times\)  ~ 0,01
\item   7,616  ~ \(\times\)  ~ 0,1
\item   42,64  ~ \(\times\)  ~ 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   178,1  ~ \(\times\)  ~ ... ~ = ~  17,81
\item   343,8  ~ \(\times\)  ~ ... ~ = ~  3,438
\item   337  ~ \(\times\)  ~ ... ~ = ~  0,337
\item   726  ~ \(\times\)  ~ ... ~ = ~  7,26
\item   5,59  ~ \(\times\)  ~ ... ~ = ~  0,005 59
\item   148,5  ~ \(\times\)  ~ ... ~ = ~  1,485
\item   7,148  ~ \(\times\)  ~ ... ~ = ~  0,714 8
\item   8,693  ~ \(\times\)  ~ ... ~ = ~  0,008 693
\item   21,38  ~ \(\times\)  ~ ... ~ = ~  0,021 38
\item   35,85  ~ \(\times\)  ~ ... ~ = ~  0,035 85
\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~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~m~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   370,87 ~hm~ = ...~km
\item   556,61 ~daL~ = ...~mL
\item   963,03 ~dm~ = ...~cm
\item   1 506,6 ~hL~ = ...~daL
\item   887,15 ~kL~ = ...~dL
\item   3 067,2 ~dag~ = ...~kg
\item   974,86 ~daL~ = ...~kL
\item   5 465,8 ~hL~ = ...~L
\item   2 131,2 ~dL~ = ...~cL
\item   937,18 ~cm~ = ...~dm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 = \(\dfrac{30}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{7100}{100}\) = \(\dfrac{710}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{68}{10}\) = \(\dfrac{680}{100}\)
\item   \(\dfrac{53}{100}\) = \(\dfrac{530}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,084  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84}
\item   483  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 483 000}
\item   2,28  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 22,8}
\item   0,851  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 851}
\item   6,71  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 671}
\item   41,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 41 900}
\item   0,48  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 480}
\item   0,019  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 19}
\item   8,82  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 88,2}
\item   0,687  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 687}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,967 ~ : ~ 10 ~ = ~{\color{red} 0,096 7}
\item   9 813 ~ : ~ 10 ~ = ~{\color{red} 981,3}
\item   2 373 ~ : ~ 1 000 ~ = ~{\color{red} 2,373}
\item   997 ~ : ~ 1 000 ~ = ~{\color{red} 0,997}
\item   59,53 ~ : ~ 10 ~ = ~{\color{red} 5,953}
\item   6,262 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 262}
\item   57,31 ~ : ~ 1 000 ~ = ~{\color{red} 0,057 31}
\item   3 950 ~ : ~ 100 ~ = ~{\color{red} 39,5}
\item   1,764 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 764}
\item   909,5 ~ : ~ 10 ~ = ~{\color{red} 90,95}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,039 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,9
\item   4,01 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 010
\item   0,437 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,37
\item   0,085 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,85
\item   2,76 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~27,6
\item   0,002 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,02
\item   3,22 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~322
\item   0,843 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~843
\item   81,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~816
\item   648 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~648 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,29 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,172 9
}\item   9 626 ~ \(\times\)  0,01 ~ = ~{\color{red} 96,26
}\item   2 106 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,106
}\item   34,87 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,034 87
}\item   714,9 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,714 9
}\item   7,1 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,71
}\item   2,243 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,022 43
}\item   949,1 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,491
}\item   7,616 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,761 6
}\item   42,64 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,264
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   178,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 17,81
\item   343,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 3,438
\item   337 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,337
\item   726 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,26
\item   5,59 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 59
\item   148,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,485
\item   7,148 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,714 8
\item   8,693 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 693
\item   21,38 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,021 38
\item   35,85 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,035 85
\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}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   370,87 ~hm~ = {\color{red}  37,087 }~km
\item   556,61 ~daL~ = {\color{red}  5 566 100 }~mL
\item   963,03 ~dm~ = {\color{red}  9 630,3 }~cm
\item   1 506,6 ~hL~ = {\color{red}  15 066 }~daL
\item   887,15 ~kL~ = {\color{red}  8 871 500 }~dL
\item   3 067,2 ~dag~ = {\color{red}  30,672 }~kg
\item   974,86 ~daL~ = {\color{red}  9,748 6 }~kL
\item   5 465,8 ~hL~ = {\color{red}  546 580 }~L
\item   2 131,2 ~dL~ = {\color{red}  21 312 }~cL
\item   937,18 ~cm~ = {\color{red}  93,718 }~dm
\end{itemize}
\end{multicols}
\end{document}
