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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 316}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   505  ~ \(\times\)  ~ 100
\item   551  ~ \(\times\)  ~ 100
\item   0,097  ~ \(\times\)  ~ 1 000
\item   23,5  ~ \(\times\)  ~ 10
\item   87,9  ~ \(\times\)  ~ 100
\item   86,5  ~ \(\times\)  ~ 1 000
\item   0,052  ~ \(\times\)  ~ 1 000
\item   0,756  ~ \(\times\)  ~ 100
\item   455  ~ \(\times\)  ~ 100
\item   0,016  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 366  ~ : ~ 100
\item   52,62  ~ : ~ 1 000
\item   7,283  ~ : ~ 1 000
\item   167,8  ~ : ~ 100
\item   5,111  ~ : ~ 1 000
\item   6,091  ~ : ~ 1 000
\item   1 946  ~ : ~ 10
\item   2 047  ~ : ~ 100
\item   11,81  ~ : ~ 100
\item   18,4  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,4  ~ \(\times\)  ~ ... ~ = ~ 874
\item   2,82  ~ \(\times\)  ~ ... ~ = ~ 2 820
\item   88  ~ \(\times\)  ~ ... ~ = ~ 8 800
\item   4,98  ~ \(\times\)  ~ ... ~ = ~ 498
\item   0,188  ~ \(\times\)  ~ ... ~ = ~ 18,8
\item   0,844  ~ \(\times\)  ~ ... ~ = ~ 84,4
\item   8,07  ~ \(\times\)  ~ ... ~ = ~ 807
\item   809  ~ \(\times\)  ~ ... ~ = ~ 8 090
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 0,4
\item   88,3  ~ \(\times\)  ~ ... ~ = ~ 8 830
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,49  ~ \(\times\)  ~ 0,01
\item   26,7  ~ \(\times\)  ~ 0,1
\item   7 154  ~ \(\times\)  ~ 0,01
\item   7 429  ~ \(\times\)  ~ 0,001
\item   9 465  ~ \(\times\)  ~ 0,01
\item   5,176  ~ \(\times\)  ~ 0,1
\item   5,205  ~ \(\times\)  ~ 0,1
\item   72,48  ~ \(\times\)  ~ 0,001
\item   1 088  ~ \(\times\)  ~ 0,001
\item   74,62  ~ \(\times\)  ~ 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   36,54  ~ \(\times\)  ~ ... ~ = ~  3,654
\item   4,749  ~ \(\times\)  ~ ... ~ = ~  0,004 749
\item   5 060  ~ \(\times\)  ~ ... ~ = ~  50,6
\item   2,492  ~ \(\times\)  ~ ... ~ = ~  0,249 2
\item   445,3  ~ \(\times\)  ~ ... ~ = ~  44,53
\item   78,55  ~ \(\times\)  ~ ... ~ = ~  0,785 5
\item   93,96  ~ \(\times\)  ~ ... ~ = ~  0,939 6
\item   5 178  ~ \(\times\)  ~ ... ~ = ~  51,78
\item   3,022  ~ \(\times\)  ~ ... ~ = ~  0,030 22
\item   9 667  ~ \(\times\)  ~ ... ~ = ~  96,67
\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 ~km~ = ...~m
\item   1 ~dam~ = ...~m
\item   1 ~m~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~dm~ = ...~dam
\item   1 ~dam~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 797,7 ~mL~ = ...~dL
\item   1 889,9 ~cg~ = ...~g
\item   566,96 ~dag~ = ...~cg
\item   3 142,6 ~hL~ = ...~dL
\item   8 595,6 ~kg~ = ...~dag
\item   5 905,3 ~dg~ = ...~mg
\item   1 406,2 ~daL~ = ...~L
\item   384,02 ~mL~ = ...~cL
\item   8 384,9 ~cL~ = ...~kL
\item   984,36 ~kL~ = ...~dL
\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   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{510}{10}\)
\item   \(\dfrac{1}{10}\) = \(\dfrac{100}{1\,000}\)
\item   \(\dfrac{39}{10}\) = \(\dfrac{390}{100}\)
\item   \(\dfrac{42}{100}\) = \(\dfrac{420}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   505  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 50 500}
\item   551  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 55 100}
\item   0,097  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 97}
\item   23,5  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 235}
\item   87,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 790}
\item   86,5  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 86 500}
\item   0,052  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 52}
\item   0,756  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 75,6}
\item   455  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 45 500}
\item   0,016  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 16}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 366 ~ : ~ 100 ~ = ~{\color{red} 63,66}
\item   52,62 ~ : ~ 1 000 ~ = ~{\color{red} 0,052 62}
\item   7,283 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 283}
\item   167,8 ~ : ~ 100 ~ = ~{\color{red} 1,678}
\item   5,111 ~ : ~ 1 000 ~ = ~{\color{red} 0,005 111}
\item   6,091 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 091}
\item   1 946 ~ : ~ 10 ~ = ~{\color{red} 194,6}
\item   2 047 ~ : ~ 100 ~ = ~{\color{red} 20,47}
\item   11,81 ~ : ~ 100 ~ = ~{\color{red} 0,118 1}
\item   18,4 ~ : ~ 100 ~ = ~{\color{red} 0,184}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   87,4 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~874
\item   2,82 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 820
\item   88 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 800
\item   4,98 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~498
\item   0,188 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~18,8
\item   0,844 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~84,4
\item   8,07 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~807
\item   809 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 090
\item   0,004 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,4
\item   88,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 830
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,49 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,094 9
}\item   26,7 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,67
}\item   7 154 ~ \(\times\)  0,01 ~ = ~{\color{red} 71,54
}\item   7 429 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,429
}\item   9 465 ~ \(\times\)  0,01 ~ = ~{\color{red} 94,65
}\item   5,176 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,517 6
}\item   5,205 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,520 5
}\item   72,48 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,072 48
}\item   1 088 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,088
}\item   74,62 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,462
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   36,54 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 3,654
\item   4,749 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,004 749
\item   5 060 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 50,6
\item   2,492 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,249 2
\item   445,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 44,53
\item   78,55 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,785 5
\item   93,96 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,939 6
\item   5 178 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 51,78
\item   3,022 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,030 22
\item   9 667 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 96,67
\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 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 797,7 ~mL~ = {\color{red}  87,977 }~dL
\item   1 889,9 ~cg~ = {\color{red}  18,899 }~g
\item   566,96 ~dag~ = {\color{red}  566 960 }~cg
\item   3 142,6 ~hL~ = {\color{red}  3 142 600 }~dL
\item   8 595,6 ~kg~ = {\color{red}  859 560 }~dag
\item   5 905,3 ~dg~ = {\color{red}  590 530 }~mg
\item   1 406,2 ~daL~ = {\color{red}  14 062 }~L
\item   384,02 ~mL~ = {\color{red}  38,402 }~cL
\item   8 384,9 ~cL~ = {\color{red}  0,083 849 }~kL
\item   984,36 ~kL~ = {\color{red}  9 843 600 }~dL
\end{itemize}
\end{multicols}
\end{document}
