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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 66}

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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   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{68}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{48}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,027  ~ \(\times\)  ~ 10
\item   0,771  ~ \(\times\)  ~ 10
\item   0,049  ~ \(\times\)  ~ 10
\item   948  ~ \(\times\)  ~ 1 000
\item   38,1  ~ \(\times\)  ~ 100
\item   0,754  ~ \(\times\)  ~ 1 000
\item   526  ~ \(\times\)  ~ 1 000
\item   0,123  ~ \(\times\)  ~ 10
\item   388  ~ \(\times\)  ~ 10
\item   73,6  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   776,9  ~ : ~ 1 000
\item   5,318  ~ : ~ 100
\item   33,99  ~ : ~ 10
\item   33,67  ~ : ~ 1 000
\item   5,886  ~ : ~ 10
\item   5 187  ~ : ~ 100
\item   4 578  ~ : ~ 1 000
\item   20,32  ~ : ~ 100
\item   6 900  ~ : ~ 1 000
\item   6 623  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,088  ~ \(\times\)  ~ ... ~ = ~ 8,8
\item   0,332  ~ \(\times\)  ~ ... ~ = ~ 33,2
\item   8,19  ~ \(\times\)  ~ ... ~ = ~ 8 190
\item   23,2  ~ \(\times\)  ~ ... ~ = ~ 232
\item   9,48  ~ \(\times\)  ~ ... ~ = ~ 948
\item   852  ~ \(\times\)  ~ ... ~ = ~ 85 200
\item   4,93  ~ \(\times\)  ~ ... ~ = ~ 4 930
\item   0,77  ~ \(\times\)  ~ ... ~ = ~ 77
\item   0,004  ~ \(\times\)  ~ ... ~ = ~ 4
\item   65,6  ~ \(\times\)  ~ ... ~ = ~ 65 600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   48,23  ~ \(\times\)  ~ 0,1
\item   5 726  ~ \(\times\)  ~ 0,01
\item   1 979  ~ \(\times\)  ~ 0,01
\item   48,5  ~ \(\times\)  ~ 0,1
\item   913  ~ \(\times\)  ~ 0,001
\item   1,759  ~ \(\times\)  ~ 0,1
\item   9 276  ~ \(\times\)  ~ 0,01
\item   643,6  ~ \(\times\)  ~ 0,1
\item   1,121  ~ \(\times\)  ~ 0,001
\item   155,7  ~ \(\times\)  ~ 0,001
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,83  ~ \(\times\)  ~ ... ~ = ~  7,983
\item   17,23  ~ \(\times\)  ~ ... ~ = ~  0,172 3
\item   35,8  ~ \(\times\)  ~ ... ~ = ~  0,358
\item   13,88  ~ \(\times\)  ~ ... ~ = ~  1,388
\item   667,2  ~ \(\times\)  ~ ... ~ = ~  0,667 2
\item   357,3  ~ \(\times\)  ~ ... ~ = ~  0,357 3
\item   4 111  ~ \(\times\)  ~ ... ~ = ~  411,1
\item   2,074  ~ \(\times\)  ~ ... ~ = ~  0,207 4
\item   912,1  ~ \(\times\)  ~ ... ~ = ~  0,912 1
\item   4,488  ~ \(\times\)  ~ ... ~ = ~  0,044 88
\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~ = ...~cm
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 250,4 ~dam~ = ...~dm
\item   8 584,7 ~cm~ = ...~dam
\item   3 908 ~cL~ = ...~hL
\item   132,52 ~dam~ = ...~km
\item   914,75 ~dg~ = ...~hg
\item   2 259,6 ~dag~ = ...~kg
\item   541,57 ~hL~ = ...~mL
\item   9 750,8 ~kg~ = ...~mg
\item   353,69 ~dag~ = ...~dg
\item   2 146,1 ~cL~ = ...~mL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 = \(\dfrac{20}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{6600}{100}\) = \(\dfrac{660}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{68}{10}\) = \(\dfrac{680}{100}\)
\item   \(\dfrac{48}{100}\) = \(\dfrac{480}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,027  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,27}
\item   0,771  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,71}
\item   0,049  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,49}
\item   948  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 948 000}
\item   38,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 810}
\item   0,754  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 754}
\item   526  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 526 000}
\item   0,123  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,23}
\item   388  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 880}
\item   73,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 73 600}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   776,9 ~ : ~ 1 000 ~ = ~{\color{red} 0,776 9}
\item   5,318 ~ : ~ 100 ~ = ~{\color{red} 0,053 18}
\item   33,99 ~ : ~ 10 ~ = ~{\color{red} 3,399}
\item   33,67 ~ : ~ 1 000 ~ = ~{\color{red} 0,033 67}
\item   5,886 ~ : ~ 10 ~ = ~{\color{red} 0,588 6}
\item   5 187 ~ : ~ 100 ~ = ~{\color{red} 51,87}
\item   4 578 ~ : ~ 1 000 ~ = ~{\color{red} 4,578}
\item   20,32 ~ : ~ 100 ~ = ~{\color{red} 0,203 2}
\item   6 900 ~ : ~ 1 000 ~ = ~{\color{red} 6,9}
\item   6 623 ~ : ~ 1 000 ~ = ~{\color{red} 6,623}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,088 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8,8
\item   0,332 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~33,2
\item   8,19 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8 190
\item   23,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~232
\item   9,48 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~948
\item   852 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~85 200
\item   4,93 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 930
\item   0,77 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~77
\item   0,004 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4
\item   65,6 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~65 600
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   48,23 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,823
}\item   5 726 ~ \(\times\)  0,01 ~ = ~{\color{red} 57,26
}\item   1 979 ~ \(\times\)  0,01 ~ = ~{\color{red} 19,79
}\item   48,5 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,85
}\item   913 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,913
}\item   1,759 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,175 9
}\item   9 276 ~ \(\times\)  0,01 ~ = ~{\color{red} 92,76
}\item   643,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 64,36
}\item   1,121 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 121
}\item   155,7 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,155 7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   79,83 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,983
\item   17,23 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,172 3
\item   35,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,358
\item   13,88 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,388
\item   667,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,667 2
\item   357,3 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,357 3
\item   4 111 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 411,1
\item   2,074 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,207 4
\item   912,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,912 1
\item   4,488 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,044 88
\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~ = ~ {\color{red}  100 ~ }cm
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 250,4 ~dam~ = {\color{red}  525 040 }~dm
\item   8 584,7 ~cm~ = {\color{red}  8,584 7 }~dam
\item   3 908 ~cL~ = {\color{red}  0,390 8 }~hL
\item   132,52 ~dam~ = {\color{red}  1,325 2 }~km
\item   914,75 ~dg~ = {\color{red}  0,914 75 }~hg
\item   2 259,6 ~dag~ = {\color{red}  22,596 }~kg
\item   541,57 ~hL~ = {\color{red}  54 157 000 }~mL
\item   9 750,8 ~kg~ = {\color{red}  9 750 800 000 }~mg
\item   353,69 ~dag~ = {\color{red}  35 369 }~dg
\item   2 146,1 ~cL~ = {\color{red}  21 461 }~mL
\end{itemize}
\end{multicols}
\end{document}
