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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 331}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{93}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,049  ~ \(\times\)  ~ 1 000
\item   0,035  ~ \(\times\)  ~ 1 000
\item   0,896  ~ \(\times\)  ~ 1 000
\item   0,846  ~ \(\times\)  ~ 1 000
\item   0,091  ~ \(\times\)  ~ 100
\item   0,05  ~ \(\times\)  ~ 1 000
\item   0,03  ~ \(\times\)  ~ 1 000
\item   6,21  ~ \(\times\)  ~ 100
\item   56,3  ~ \(\times\)  ~ 1 000
\item   1,56  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   986,1  ~ : ~ 10
\item   96,49  ~ : ~ 1 000
\item   4 634  ~ : ~ 10
\item   7 389  ~ : ~ 1 000
\item   2,347  ~ : ~ 1 000
\item   897,6  ~ : ~ 10
\item   5,162  ~ : ~ 10
\item   5 605  ~ : ~ 1 000
\item   69,6  ~ : ~ 1 000
\item   52,62  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,4  ~ \(\times\)  ~ ... ~ = ~ 114
\item   0,08  ~ \(\times\)  ~ ... ~ = ~ 0,8
\item   1,58  ~ \(\times\)  ~ ... ~ = ~ 15,8
\item   78,6  ~ \(\times\)  ~ ... ~ = ~ 786
\item   72,3  ~ \(\times\)  ~ ... ~ = ~ 723
\item   786  ~ \(\times\)  ~ ... ~ = ~ 78 600
\item   8,3  ~ \(\times\)  ~ ... ~ = ~ 83
\item   54,5  ~ \(\times\)  ~ ... ~ = ~ 54 500
\item   52,5  ~ \(\times\)  ~ ... ~ = ~ 525
\item   0,043  ~ \(\times\)  ~ ... ~ = ~ 43
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 199  ~ \(\times\)  ~ 0,01
\item   924,5  ~ \(\times\)  ~ 0,01
\item   0,75  ~ \(\times\)  ~ 0,001
\item   8 373  ~ \(\times\)  ~ 0,001
\item   2 473  ~ \(\times\)  ~ 0,001
\item   0,695  ~ \(\times\)  ~ 0,01
\item   8 582  ~ \(\times\)  ~ 0,001
\item   49,33  ~ \(\times\)  ~ 0,01
\item   98,21  ~ \(\times\)  ~ 0,01
\item   6,365  ~ \(\times\)  ~ 0,01
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,549  ~ \(\times\)  ~ ... ~ = ~  0,001 549
\item   71,96  ~ \(\times\)  ~ ... ~ = ~  0,071 96
\item   7,281  ~ \(\times\)  ~ ... ~ = ~  0,072 81
\item   234,3  ~ \(\times\)  ~ ... ~ = ~  0,234 3
\item   2,85  ~ \(\times\)  ~ ... ~ = ~  0,028 5
\item   585,7  ~ \(\times\)  ~ ... ~ = ~  5,857
\item   5,513  ~ \(\times\)  ~ ... ~ = ~  0,551 3
\item   9 415  ~ \(\times\)  ~ ... ~ = ~  94,15
\item   639,4  ~ \(\times\)  ~ ... ~ = ~  0,639 4
\item   0,568  ~ \(\times\)  ~ ... ~ = ~  0,056 8
\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~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~dm~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 500,3 ~dag~ = ...~cg
\item   3 030 ~hm~ = ...~dm
\item   472,09 ~L~ = ...~hL
\item   950,8 ~daL~ = ...~mL
\item   4 655 ~dam~ = ...~km
\item   3 830,3 ~cL~ = ...~mL
\item   852,96 ~dag~ = ...~hg
\item   1 941,1 ~dam~ = ...~cm
\item   777,43 ~cg~ = ...~hg
\item   776,59 ~cL~ = ...~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   6 = \(\dfrac{60}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{93}{10}\) = \(\dfrac{930}{100}\)
\item   \(\dfrac{71}{100}\) = \(\dfrac{710}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,049  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 49}
\item   0,035  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 35}
\item   0,896  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 896}
\item   0,846  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 846}
\item   0,091  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,1}
\item   0,05  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 50}
\item   0,03  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 30}
\item   6,21  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 621}
\item   56,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 56 300}
\item   1,56  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 560}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   986,1 ~ : ~ 10 ~ = ~{\color{red} 98,61}
\item   96,49 ~ : ~ 1 000 ~ = ~{\color{red} 0,096 49}
\item   4 634 ~ : ~ 10 ~ = ~{\color{red} 463,4}
\item   7 389 ~ : ~ 1 000 ~ = ~{\color{red} 7,389}
\item   2,347 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 347}
\item   897,6 ~ : ~ 10 ~ = ~{\color{red} 89,76}
\item   5,162 ~ : ~ 10 ~ = ~{\color{red} 0,516 2}
\item   5 605 ~ : ~ 1 000 ~ = ~{\color{red} 5,605}
\item   69,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,069 6}
\item   52,62 ~ : ~ 100 ~ = ~{\color{red} 0,526 2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   11,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~114
\item   0,08 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,8
\item   1,58 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~15,8
\item   78,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~786
\item   72,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~723
\item   786 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~78 600
\item   8,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~83
\item   54,5 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~54 500
\item   52,5 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~525
\item   0,043 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~43
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 199 ~ \(\times\)  0,01 ~ = ~{\color{red} 21,99
}\item   924,5 ~ \(\times\)  0,01 ~ = ~{\color{red} 9,245
}\item   0,75 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,000 75
}\item   8 373 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,373
}\item   2 473 ~ \(\times\)  0,001 ~ = ~{\color{red} 2,473
}\item   0,695 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,006 95
}\item   8 582 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,582
}\item   49,33 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,493 3
}\item   98,21 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,982 1
}\item   6,365 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,063 65
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,549 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 549
\item   71,96 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,071 96
\item   7,281 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,072 81
\item   234,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,234 3
\item   2,85 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,028 5
\item   585,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,857
\item   5,513 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,551 3
\item   9 415 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 94,15
\item   639,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,639 4
\item   0,568 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,056 8
\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~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 500,3 ~dag~ = {\color{red}  8 500 300 }~cg
\item   3 030 ~hm~ = {\color{red}  3 030 000 }~dm
\item   472,09 ~L~ = {\color{red}  4,720 9 }~hL
\item   950,8 ~daL~ = {\color{red}  9 508 000 }~mL
\item   4 655 ~dam~ = {\color{red}  46,55 }~km
\item   3 830,3 ~cL~ = {\color{red}  38 303 }~mL
\item   852,96 ~dag~ = {\color{red}  85,296 }~hg
\item   1 941,1 ~dam~ = {\color{red}  1 941 100 }~cm
\item   777,43 ~cg~ = {\color{red}  0,077 743 }~hg
\item   776,59 ~cL~ = {\color{red}  0,776 59 }~daL
\end{itemize}
\end{multicols}
\end{document}
