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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 365}

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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   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{76}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{60}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,6  ~ \(\times\)  ~ 1 000
\item   57,4  ~ \(\times\)  ~ 10
\item   215  ~ \(\times\)  ~ 10
\item   0,024  ~ \(\times\)  ~ 1 000
\item   9,1  ~ \(\times\)  ~ 10
\item   4,05  ~ \(\times\)  ~ 1 000
\item   0,005  ~ \(\times\)  ~ 10
\item   2,3  ~ \(\times\)  ~ 10
\item   8,14  ~ \(\times\)  ~ 1 000
\item   49  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,2  ~ : ~ 10
\item   955,3  ~ : ~ 1 000
\item   2 523  ~ : ~ 10
\item   45,25  ~ : ~ 1 000
\item   663,9  ~ : ~ 100
\item   6,16  ~ : ~ 100
\item   479,7  ~ : ~ 1 000
\item   676,9  ~ : ~ 10
\item   4,54  ~ : ~ 100
\item   6 652  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   35,3  ~ \(\times\)  ~ ... ~ = ~ 3 530
\item   95,3  ~ \(\times\)  ~ ... ~ = ~ 9 530
\item   13,4  ~ \(\times\)  ~ ... ~ = ~ 1 340
\item   785  ~ \(\times\)  ~ ... ~ = ~ 785 000
\item   4,3  ~ \(\times\)  ~ ... ~ = ~ 4 300
\item   2,08  ~ \(\times\)  ~ ... ~ = ~ 20,8
\item   0,432  ~ \(\times\)  ~ ... ~ = ~ 4,32
\item   8,22  ~ \(\times\)  ~ ... ~ = ~ 82,2
\item   8,34  ~ \(\times\)  ~ ... ~ = ~ 83,4
\item   0,749  ~ \(\times\)  ~ ... ~ = ~ 749
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,98  ~ \(\times\)  ~ 0,01
\item   875,2  ~ \(\times\)  ~ 0,001
\item   3,561  ~ \(\times\)  ~ 0,01
\item   3,34  ~ \(\times\)  ~ 0,001
\item   59,91  ~ \(\times\)  ~ 0,1
\item   8,346  ~ \(\times\)  ~ 0,01
\item   528,4  ~ \(\times\)  ~ 0,01
\item   352,5  ~ \(\times\)  ~ 0,001
\item   5 348  ~ \(\times\)  ~ 0,01
\item   7 024  ~ \(\times\)  ~ 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   8 814  ~ \(\times\)  ~ ... ~ = ~  88,14
\item   8,969  ~ \(\times\)  ~ ... ~ = ~  0,008 969
\item   54  ~ \(\times\)  ~ ... ~ = ~  0,054
\item   1 919  ~ \(\times\)  ~ ... ~ = ~  1,919
\item   4 256  ~ \(\times\)  ~ ... ~ = ~  425,6
\item   27,4  ~ \(\times\)  ~ ... ~ = ~  2,74
\item   64,31  ~ \(\times\)  ~ ... ~ = ~  0,643 1
\item   6,065  ~ \(\times\)  ~ ... ~ = ~  0,060 65
\item   653,4  ~ \(\times\)  ~ ... ~ = ~  0,653 4
\item   7,715  ~ \(\times\)  ~ ... ~ = ~  0,077 15
\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 ~hm~ = ...~km
\item   1 ~dam~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~dm
\item   1 ~dm~ = ...~dam
\item   1 ~km~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~dm~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~cm~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   704,25 ~mL~ = ...~hL
\item   148,29 ~m~ = ...~dm
\item   459,93 ~kL~ = ...~mL
\item   8 562,4 ~kg~ = ...~g
\item   1 983,5 ~dm~ = ...~dam
\item   620,15 ~kL~ = ...~dL
\item   798,07 ~dm~ = ...~km
\item   418,98 ~dg~ = ...~g
\item   8 734,6 ~dam~ = ...~mm
\item   2 109,1 ~cg~ = ...~g
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 = \(\dfrac{50}{10}\)
\item   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{4700}{100}\) = \(\dfrac{470}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{76}{10}\) = \(\dfrac{760}{100}\)
\item   \(\dfrac{60}{100}\) = \(\dfrac{600}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 600}
\item   57,4  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 574}
\item   215  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 150}
\item   0,024  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 24}
\item   9,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 91}
\item   4,05  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 4 050}
\item   0,005  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,05}
\item   2,3  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 23}
\item   8,14  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 8 140}
\item   49  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 490}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,2 ~ : ~ 10 ~ = ~{\color{red} 5,52}
\item   955,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,955 3}
\item   2 523 ~ : ~ 10 ~ = ~{\color{red} 252,3}
\item   45,25 ~ : ~ 1 000 ~ = ~{\color{red} 0,045 25}
\item   663,9 ~ : ~ 100 ~ = ~{\color{red} 6,639}
\item   6,16 ~ : ~ 100 ~ = ~{\color{red} 0,061 6}
\item   479,7 ~ : ~ 1 000 ~ = ~{\color{red} 0,479 7}
\item   676,9 ~ : ~ 10 ~ = ~{\color{red} 67,69}
\item   4,54 ~ : ~ 100 ~ = ~{\color{red} 0,045 4}
\item   6 652 ~ : ~ 10 ~ = ~{\color{red} 665,2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   35,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 530
\item   95,3 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~9 530
\item   13,4 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~1 340
\item   785 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~785 000
\item   4,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 300
\item   2,08 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~20,8
\item   0,432 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,32
\item   8,22 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~82,2
\item   8,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~83,4
\item   0,749 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~749
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   55,98 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,559 8
}\item   875,2 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,875 2
}\item   3,561 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,035 61
}\item   3,34 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 34
}\item   59,91 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,991
}\item   8,346 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,083 46
}\item   528,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,284
}\item   352,5 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,352 5
}\item   5 348 ~ \(\times\)  0,01 ~ = ~{\color{red} 53,48
}\item   7 024 ~ \(\times\)  0,1 ~ = ~{\color{red} 702,4
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 814 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 88,14
\item   8,969 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 969
\item   54 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,054
\item   1 919 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,919
\item   4 256 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 425,6
\item   27,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 2,74
\item   64,31 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,643 1
\item   6,065 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,060 65
\item   653,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,653 4
\item   7,715 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,077 15
\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 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\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   704,25 ~mL~ = {\color{red}  0,007 042 5 }~hL
\item   148,29 ~m~ = {\color{red}  1 482,9 }~dm
\item   459,93 ~kL~ = {\color{red}  459 930 000 }~mL
\item   8 562,4 ~kg~ = {\color{red}  8 562 400 }~g
\item   1 983,5 ~dm~ = {\color{red}  19,835 }~dam
\item   620,15 ~kL~ = {\color{red}  6 201 500 }~dL
\item   798,07 ~dm~ = {\color{red}  0,079 807 }~km
\item   418,98 ~dg~ = {\color{red}  41,898 }~g
\item   8 734,6 ~dam~ = {\color{red}  87 346 000 }~mm
\item   2 109,1 ~cg~ = {\color{red}  21,091 }~g
\end{itemize}
\end{multicols}
\end{document}
