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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 283}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,404  ~ \(\times\)  ~ 10
\item   0,073  ~ \(\times\)  ~ 10
\item   59,5  ~ \(\times\)  ~ 10
\item   58,2  ~ \(\times\)  ~ 100
\item   0,946  ~ \(\times\)  ~ 100
\item   0,908  ~ \(\times\)  ~ 10
\item   0,033  ~ \(\times\)  ~ 100
\item   43,2  ~ \(\times\)  ~ 10
\item   0,039  ~ \(\times\)  ~ 10
\item   210  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 844  ~ : ~ 100
\item   318,6  ~ : ~ 1 000
\item   2,97  ~ : ~ 10
\item   8 806  ~ : ~ 100
\item   45,32  ~ : ~ 100
\item   181  ~ : ~ 1 000
\item   59,55  ~ : ~ 10
\item   282,4  ~ : ~ 100
\item   37,08  ~ : ~ 100
\item   217,1  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,43  ~ \(\times\)  ~ ... ~ = ~ 843
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,04
\item   69,9  ~ \(\times\)  ~ ... ~ = ~ 699
\item   57,7  ~ \(\times\)  ~ ... ~ = ~ 577
\item   56,7  ~ \(\times\)  ~ ... ~ = ~ 56 700
\item   0,752  ~ \(\times\)  ~ ... ~ = ~ 75,2
\item   0,922  ~ \(\times\)  ~ ... ~ = ~ 92,2
\item   580  ~ \(\times\)  ~ ... ~ = ~ 580 000
\item   194  ~ \(\times\)  ~ ... ~ = ~ 19 400
\item   3,61  ~ \(\times\)  ~ ... ~ = ~ 36,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,18  ~ \(\times\)  ~ 0,1
\item   8 511  ~ \(\times\)  ~ 0,01
\item   29,63  ~ \(\times\)  ~ 0,1
\item   47,7  ~ \(\times\)  ~ 0,001
\item   2,229  ~ \(\times\)  ~ 0,001
\item   7 960  ~ \(\times\)  ~ 0,1
\item   1,353  ~ \(\times\)  ~ 0,001
\item   2,058  ~ \(\times\)  ~ 0,01
\item   5 137  ~ \(\times\)  ~ 0,1
\item   7,076  ~ \(\times\)  ~ 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   2 588  ~ \(\times\)  ~ ... ~ = ~  2,588
\item   582,7  ~ \(\times\)  ~ ... ~ = ~  0,582 7
\item   3,036  ~ \(\times\)  ~ ... ~ = ~  0,003 036
\item   781,1  ~ \(\times\)  ~ ... ~ = ~  7,811
\item   8,484  ~ \(\times\)  ~ ... ~ = ~  0,848 4
\item   8 669  ~ \(\times\)  ~ ... ~ = ~  86,69
\item   1,622  ~ \(\times\)  ~ ... ~ = ~  0,001 622
\item   939,1  ~ \(\times\)  ~ ... ~ = ~  93,91
\item   48,21  ~ \(\times\)  ~ ... ~ = ~  0,048 21
\item   30,37  ~ \(\times\)  ~ ... ~ = ~  3,037
\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 ~m~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 271,6 ~g~ = ...~hg
\item   608,04 ~dag~ = ...~g
\item   8 507,4 ~dag~ = ...~dg
\item   712,46 ~mg~ = ...~dag
\item   380,12 ~km~ = ...~hm
\item   737,92 ~dag~ = ...~cg
\item   3 704,9 ~daL~ = ...~hL
\item   870,78 ~kL~ = ...~mL
\item   422,25 ~dag~ = ...~mg
\item   921,4 ~hg~ = ...~cg
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{7800}{100}\) = \(\dfrac{780}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{69}{10}\) = \(\dfrac{690}{100}\)
\item   \(\dfrac{91}{100}\) = \(\dfrac{910}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,404  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4,04}
\item   0,073  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,73}
\item   59,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 595}
\item   58,2  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 5 820}
\item   0,946  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 94,6}
\item   0,908  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9,08}
\item   0,033  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,3}
\item   43,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 432}
\item   0,039  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,39}
\item   210  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 21 000}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 844 ~ : ~ 100 ~ = ~{\color{red} 28,44}
\item   318,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,318 6}
\item   2,97 ~ : ~ 10 ~ = ~{\color{red} 0,297}
\item   8 806 ~ : ~ 100 ~ = ~{\color{red} 88,06}
\item   45,32 ~ : ~ 100 ~ = ~{\color{red} 0,453 2}
\item   181 ~ : ~ 1 000 ~ = ~{\color{red} 0,181}
\item   59,55 ~ : ~ 10 ~ = ~{\color{red} 5,955}
\item   282,4 ~ : ~ 100 ~ = ~{\color{red} 2,824}
\item   37,08 ~ : ~ 100 ~ = ~{\color{red} 0,370 8}
\item   217,1 ~ : ~ 1 000 ~ = ~{\color{red} 0,217 1}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,43 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~843
\item   0,004 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,04
\item   69,9 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~699
\item   57,7 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~577
\item   56,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~56 700
\item   0,752 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~75,2
\item   0,922 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~92,2
\item   580 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~580 000
\item   194 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~19 400
\item   3,61 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~36,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   15,18 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,518
}\item   8 511 ~ \(\times\)  0,01 ~ = ~{\color{red} 85,11
}\item   29,63 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,963
}\item   47,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,047 7
}\item   2,229 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 229
}\item   7 960 ~ \(\times\)  0,1 ~ = ~{\color{red} 796
}\item   1,353 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 353
}\item   2,058 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,020 58
}\item   5 137 ~ \(\times\)  0,1 ~ = ~{\color{red} 513,7
}\item   7,076 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,707 6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 588 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,588
\item   582,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,582 7
\item   3,036 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 036
\item   781,1 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,811
\item   8,484 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,848 4
\item   8 669 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 86,69
\item   1,622 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 622
\item   939,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 93,91
\item   48,21 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,048 21
\item   30,37 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,037
\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 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7 271,6 ~g~ = {\color{red}  72,716 }~hg
\item   608,04 ~dag~ = {\color{red}  6 080,4 }~g
\item   8 507,4 ~dag~ = {\color{red}  850 740 }~dg
\item   712,46 ~mg~ = {\color{red}  0,071 246 }~dag
\item   380,12 ~km~ = {\color{red}  3 801,2 }~hm
\item   737,92 ~dag~ = {\color{red}  737 920 }~cg
\item   3 704,9 ~daL~ = {\color{red}  370,49 }~hL
\item   870,78 ~kL~ = {\color{red}  870 780 000 }~mL
\item   422,25 ~dag~ = {\color{red}  4 222 500 }~mg
\item   921,4 ~hg~ = {\color{red}  9 214 000 }~cg
\end{itemize}
\end{multicols}
\end{document}
