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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 197}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{2700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,02  ~ \(\times\)  ~ 10
\item   0,005  ~ \(\times\)  ~ 100
\item   475  ~ \(\times\)  ~ 10
\item   0,099  ~ \(\times\)  ~ 100
\item   83,4  ~ \(\times\)  ~ 1 000
\item   64,8  ~ \(\times\)  ~ 10
\item   0,608  ~ \(\times\)  ~ 100
\item   0,051  ~ \(\times\)  ~ 1 000
\item   0,032  ~ \(\times\)  ~ 100
\item   314  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   691,8  ~ : ~ 100
\item   82,25  ~ : ~ 10
\item   48,37  ~ : ~ 100
\item   5,73  ~ : ~ 1 000
\item   16,31  ~ : ~ 100
\item   47,43  ~ : ~ 100
\item   52,18  ~ : ~ 100
\item   97,52  ~ : ~ 10
\item   28,87  ~ : ~ 1 000
\item   605  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,883  ~ \(\times\)  ~ ... ~ = ~ 8,83
\item   0,347  ~ \(\times\)  ~ ... ~ = ~ 3,47
\item   0,044  ~ \(\times\)  ~ ... ~ = ~ 44
\item   0,774  ~ \(\times\)  ~ ... ~ = ~ 774
\item   0,902  ~ \(\times\)  ~ ... ~ = ~ 9,02
\item   40,7  ~ \(\times\)  ~ ... ~ = ~ 4 070
\item   13,7  ~ \(\times\)  ~ ... ~ = ~ 1 370
\item   8,37  ~ \(\times\)  ~ ... ~ = ~ 837
\item   0,955  ~ \(\times\)  ~ ... ~ = ~ 95,5
\item   57  ~ \(\times\)  ~ ... ~ = ~ 57 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,643  ~ \(\times\)  ~ 0,001
\item   356  ~ \(\times\)  ~ 0,001
\item   33,88  ~ \(\times\)  ~ 0,01
\item   405,8  ~ \(\times\)  ~ 0,1
\item   90,97  ~ \(\times\)  ~ 0,001
\item   20,99  ~ \(\times\)  ~ 0,1
\item   2 934  ~ \(\times\)  ~ 0,1
\item   8 936  ~ \(\times\)  ~ 0,1
\item   734,6  ~ \(\times\)  ~ 0,1
\item   3,104  ~ \(\times\)  ~ 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   56,28  ~ \(\times\)  ~ ... ~ = ~  0,056 28
\item   896,4  ~ \(\times\)  ~ ... ~ = ~  89,64
\item   5,3  ~ \(\times\)  ~ ... ~ = ~  0,053
\item   83,56  ~ \(\times\)  ~ ... ~ = ~  0,835 6
\item   3,077  ~ \(\times\)  ~ ... ~ = ~  0,003 077
\item   7 785  ~ \(\times\)  ~ ... ~ = ~  7,785
\item   877,7  ~ \(\times\)  ~ ... ~ = ~  87,77
\item   960,1  ~ \(\times\)  ~ ... ~ = ~  96,01
\item   9,749  ~ \(\times\)  ~ ... ~ = ~  0,974 9
\item   3 585  ~ \(\times\)  ~ ... ~ = ~  358,5
\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 ~dm~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~km
\item   1 ~hm~ = ...~dm
\item   1 ~m~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~km
\item   1 ~hm~ = ...~dam
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 891,3 ~cg~ = ...~dg
\item   5 460,3 ~kL~ = ...~daL
\item   4 722,6 ~daL~ = ...~mL
\item   4 813,8 ~cg~ = ...~g
\item   280,38 ~hg~ = ...~cg
\item   265,54 ~dag~ = ...~dg
\item   355,77 ~km~ = ...~cm
\item   4 069,4 ~kg~ = ...~cg
\item   6 156,7 ~kg~ = ...~g
\item   2 443,8 ~daL~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{2700}{100}\) = \(\dfrac{270}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{13}{10}\) = \(\dfrac{130}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{990}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,02  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,2}
\item   0,005  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,5}
\item   475  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 4 750}
\item   0,099  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,9}
\item   83,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 83 400}
\item   64,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 648}
\item   0,608  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 60,8}
\item   0,051  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 51}
\item   0,032  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,2}
\item   314  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 140}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   691,8 ~ : ~ 100 ~ = ~{\color{red} 6,918}
\item   82,25 ~ : ~ 10 ~ = ~{\color{red} 8,225}
\item   48,37 ~ : ~ 100 ~ = ~{\color{red} 0,483 7}
\item   5,73 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 73}
\item   16,31 ~ : ~ 100 ~ = ~{\color{red} 0,163 1}
\item   47,43 ~ : ~ 100 ~ = ~{\color{red} 0,474 3}
\item   52,18 ~ : ~ 100 ~ = ~{\color{red} 0,521 8}
\item   97,52 ~ : ~ 10 ~ = ~{\color{red} 9,752}
\item   28,87 ~ : ~ 1 000 ~ = ~{\color{red} 0,028 87}
\item   605 ~ : ~ 100 ~ = ~{\color{red} 6,05}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,883 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,83
\item   0,347 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,47
\item   0,044 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~44
\item   0,774 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~774
\item   0,902 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~9,02
\item   40,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4 070
\item   13,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 370
\item   8,37 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~837
\item   0,955 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~95,5
\item   57 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~57 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2,643 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,002 643
}\item   356 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,356
}\item   33,88 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,338 8
}\item   405,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 40,58
}\item   90,97 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,090 97
}\item   20,99 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,099
}\item   2 934 ~ \(\times\)  0,1 ~ = ~{\color{red} 293,4
}\item   8 936 ~ \(\times\)  0,1 ~ = ~{\color{red} 893,6
}\item   734,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 73,46
}\item   3,104 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,031 04
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   56,28 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,056 28
\item   896,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 89,64
\item   5,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,053
\item   83,56 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,835 6
\item   3,077 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 077
\item   7 785 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 7,785
\item   877,7 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 87,77
\item   960,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 96,01
\item   9,749 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,974 9
\item   3 585 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 358,5
\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 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 891,3 ~cg~ = {\color{red}  489,13 }~dg
\item   5 460,3 ~kL~ = {\color{red}  546 030 }~daL
\item   4 722,6 ~daL~ = {\color{red}  47 226 000 }~mL
\item   4 813,8 ~cg~ = {\color{red}  48,138 }~g
\item   280,38 ~hg~ = {\color{red}  2 803 800 }~cg
\item   265,54 ~dag~ = {\color{red}  26 554 }~dg
\item   355,77 ~km~ = {\color{red}  35 577 000 }~cm
\item   4 069,4 ~kg~ = {\color{red}  406 940 000 }~cg
\item   6 156,7 ~kg~ = {\color{red}  6 156 700 }~g
\item   2 443,8 ~daL~ = {\color{red}  24,438 }~kL
\end{itemize}
\end{multicols}
\end{document}
