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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 237}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{18}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,528  ~ \(\times\)  ~ 1 000
\item   738  ~ \(\times\)  ~ 100
\item   631  ~ \(\times\)  ~ 1 000
\item   6,3  ~ \(\times\)  ~ 100
\item   5,17  ~ \(\times\)  ~ 10
\item   0,978  ~ \(\times\)  ~ 100
\item   0,954  ~ \(\times\)  ~ 10
\item   0,001  ~ \(\times\)  ~ 1 000
\item   5,51  ~ \(\times\)  ~ 100
\item   1,58  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,263  ~ : ~ 100
\item   402,8  ~ : ~ 100
\item   6,195  ~ : ~ 100
\item   1,817  ~ : ~ 100
\item   221,1  ~ : ~ 100
\item   268,6  ~ : ~ 10
\item   222,6  ~ : ~ 100
\item   138,7  ~ : ~ 1 000
\item   6,14  ~ : ~ 1 000
\item   939  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,68  ~ \(\times\)  ~ ... ~ = ~ 2 680
\item   6,4  ~ \(\times\)  ~ ... ~ = ~ 6 400
\item   0,525  ~ \(\times\)  ~ ... ~ = ~ 525
\item   10,6  ~ \(\times\)  ~ ... ~ = ~ 10 600
\item   0,054  ~ \(\times\)  ~ ... ~ = ~ 54
\item   0,036  ~ \(\times\)  ~ ... ~ = ~ 0,36
\item   5,91  ~ \(\times\)  ~ ... ~ = ~ 591
\item   0,221  ~ \(\times\)  ~ ... ~ = ~ 2,21
\item   0,046  ~ \(\times\)  ~ ... ~ = ~ 46
\item   0,07  ~ \(\times\)  ~ ... ~ = ~ 7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   921,7  ~ \(\times\)  ~ 0,001
\item   1 360  ~ \(\times\)  ~ 0,1
\item   5 324  ~ \(\times\)  ~ 0,01
\item   5 528  ~ \(\times\)  ~ 0,1
\item   380,2  ~ \(\times\)  ~ 0,1
\item   94,75  ~ \(\times\)  ~ 0,1
\item   3,649  ~ \(\times\)  ~ 0,001
\item   9 434  ~ \(\times\)  ~ 0,001
\item   3 943  ~ \(\times\)  ~ 0,1
\item   3 929  ~ \(\times\)  ~ 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   9,194  ~ \(\times\)  ~ ... ~ = ~  0,919 4
\item   8 605  ~ \(\times\)  ~ ... ~ = ~  860,5
\item   7,573  ~ \(\times\)  ~ ... ~ = ~  0,757 3
\item   730,3  ~ \(\times\)  ~ ... ~ = ~  0,730 3
\item   798,4  ~ \(\times\)  ~ ... ~ = ~  0,798 4
\item   946  ~ \(\times\)  ~ ... ~ = ~  9,46
\item   6,97  ~ \(\times\)  ~ ... ~ = ~  0,697
\item   978,5  ~ \(\times\)  ~ ... ~ = ~  9,785
\item   38,57  ~ \(\times\)  ~ ... ~ = ~  0,038 57
\item   77,95  ~ \(\times\)  ~ ... ~ = ~  7,795
\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 ~hm~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~km
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 136,7 ~km~ = ...~cm
\item   512 ~m~ = ...~cm
\item   4 619,7 ~daL~ = ...~cL
\item   289,77 ~daL~ = ...~mL
\item   8 780,9 ~mL~ = ...~L
\item   534,49 ~hL~ = ...~cL
\item   484,29 ~dg~ = ...~dag
\item   500,62 ~g~ = ...~dg
\item   2 905,2 ~km~ = ...~dam
\item   6 836,4 ~dm~ = ...~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   8 = \(\dfrac{80}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{4100}{100}\) = \(\dfrac{410}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{18}{10}\) = \(\dfrac{180}{100}\)
\item   \(\dfrac{33}{100}\) = \(\dfrac{330}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,528  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 528}
\item   738  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 73 800}
\item   631  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 631 000}
\item   6,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 630}
\item   5,17  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 51,7}
\item   0,978  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 97,8}
\item   0,954  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,54}
\item   0,001  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1}
\item   5,51  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 551}
\item   1,58  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 15,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,263 ~ : ~ 100 ~ = ~{\color{red} 0,072 63}
\item   402,8 ~ : ~ 100 ~ = ~{\color{red} 4,028}
\item   6,195 ~ : ~ 100 ~ = ~{\color{red} 0,061 95}
\item   1,817 ~ : ~ 100 ~ = ~{\color{red} 0,018 17}
\item   221,1 ~ : ~ 100 ~ = ~{\color{red} 2,211}
\item   268,6 ~ : ~ 10 ~ = ~{\color{red} 26,86}
\item   222,6 ~ : ~ 100 ~ = ~{\color{red} 2,226}
\item   138,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,138 7}
\item   6,14 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 14}
\item   939 ~ : ~ 10 ~ = ~{\color{red} 93,9}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,68 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 680
\item   6,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~6 400
\item   0,525 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~525
\item   10,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~10 600
\item   0,054 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~54
\item   0,036 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,36
\item   5,91 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~591
\item   0,221 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,21
\item   0,046 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~46
\item   0,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   921,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,921 7
}\item   1 360 ~ \(\times\)  0,1 ~ = ~{\color{red} 136
}\item   5 324 ~ \(\times\)  0,01 ~ = ~{\color{red} 53,24
}\item   5 528 ~ \(\times\)  0,1 ~ = ~{\color{red} 552,8
}\item   380,2 ~ \(\times\)  0,1 ~ = ~{\color{red} 38,02
}\item   94,75 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,475
}\item   3,649 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 649
}\item   9 434 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,434
}\item   3 943 ~ \(\times\)  0,1 ~ = ~{\color{red} 394,3
}\item   3 929 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,929
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,194 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,919 4
\item   8 605 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 860,5
\item   7,573 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,757 3
\item   730,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,730 3
\item   798,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,798 4
\item   946 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,46
\item   6,97 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,697
\item   978,5 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 9,785
\item   38,57 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,038 57
\item   77,95 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,795
\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 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 136,7 ~km~ = {\color{red}  913 670 000 }~cm
\item   512 ~m~ = {\color{red}  51 200 }~cm
\item   4 619,7 ~daL~ = {\color{red}  4 619 700 }~cL
\item   289,77 ~daL~ = {\color{red}  2 897 700 }~mL
\item   8 780,9 ~mL~ = {\color{red}  8,780 9 }~L
\item   534,49 ~hL~ = {\color{red}  5 344 900 }~cL
\item   484,29 ~dg~ = {\color{red}  4,842 9 }~dag
\item   500,62 ~g~ = {\color{red}  5 006,2 }~dg
\item   2 905,2 ~km~ = {\color{red}  290 520 }~dam
\item   6 836,4 ~dm~ = {\color{red}  0,683 64 }~km
\end{itemize}
\end{multicols}
\end{document}
