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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 176}

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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   \(\dfrac{3900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{60}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,033  ~ \(\times\)  ~ 100
\item   110  ~ \(\times\)  ~ 10
\item   0,033  ~ \(\times\)  ~ 100
\item   0,331  ~ \(\times\)  ~ 100
\item   2,79  ~ \(\times\)  ~ 1 000
\item   0,661  ~ \(\times\)  ~ 100
\item   768  ~ \(\times\)  ~ 10
\item   47  ~ \(\times\)  ~ 1 000
\item   0,714  ~ \(\times\)  ~ 10
\item   864  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,281  ~ : ~ 1 000
\item   54,93  ~ : ~ 1 000
\item   5,323  ~ : ~ 100
\item   0,738  ~ : ~ 100
\item   1,707  ~ : ~ 100
\item   1,159  ~ : ~ 10
\item   6 788  ~ : ~ 10
\item   91,83  ~ : ~ 100
\item   84,59  ~ : ~ 100
\item   855  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,032  ~ \(\times\)  ~ ... ~ = ~ 3,2
\item   5,6  ~ \(\times\)  ~ ... ~ = ~ 56
\item   270  ~ \(\times\)  ~ ... ~ = ~ 270 000
\item   0,315  ~ \(\times\)  ~ ... ~ = ~ 3,15
\item   0,541  ~ \(\times\)  ~ ... ~ = ~ 54,1
\item   0,13  ~ \(\times\)  ~ ... ~ = ~ 130
\item   0,897  ~ \(\times\)  ~ ... ~ = ~ 89,7
\item   0,648  ~ \(\times\)  ~ ... ~ = ~ 6,48
\item   82,2  ~ \(\times\)  ~ ... ~ = ~ 822
\item   31,3  ~ \(\times\)  ~ ... ~ = ~ 313
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   137,8  ~ \(\times\)  ~ 0,1
\item   569  ~ \(\times\)  ~ 0,01
\item   755,8  ~ \(\times\)  ~ 0,1
\item   98,28  ~ \(\times\)  ~ 0,001
\item   6 829  ~ \(\times\)  ~ 0,01
\item   22,8  ~ \(\times\)  ~ 0,1
\item   428,6  ~ \(\times\)  ~ 0,1
\item   8,889  ~ \(\times\)  ~ 0,01
\item   1 120  ~ \(\times\)  ~ 0,01
\item   4 510  ~ \(\times\)  ~ 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   615,8  ~ \(\times\)  ~ ... ~ = ~  6,158
\item   566  ~ \(\times\)  ~ ... ~ = ~  5,66
\item   9 147  ~ \(\times\)  ~ ... ~ = ~  9,147
\item   52,4  ~ \(\times\)  ~ ... ~ = ~  5,24
\item   7,795  ~ \(\times\)  ~ ... ~ = ~  0,077 95
\item   113,3  ~ \(\times\)  ~ ... ~ = ~  1,133
\item   70,37  ~ \(\times\)  ~ ... ~ = ~  7,037
\item   179,2  ~ \(\times\)  ~ ... ~ = ~  1,792
\item   58,15  ~ \(\times\)  ~ ... ~ = ~  0,581 5
\item   9 519  ~ \(\times\)  ~ ... ~ = ~  95,19
\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~ = ...~m
\item   1 ~cm~ = ...~km
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~hm
\item   1 ~dam~ = ...~dm
\item   1 ~cm~ = ...~dm
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 484,9 ~mL~ = ...~dL
\item   5 547,8 ~daL~ = ...~cL
\item   129,68 ~dg~ = ...~mg
\item   260,99 ~cm~ = ...~km
\item   7 179,2 ~cL~ = ...~kL
\item   9 601,7 ~km~ = ...~m
\item   340,39 ~mm~ = ...~cm
\item   979,47 ~dag~ = ...~dg
\item   356,12 ~hm~ = ...~dam
\item   971,86 ~dm~ = ...~m
\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   \(\dfrac{3900}{100}\) = \(\dfrac{390}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{60}{10}\) = \(\dfrac{600}{100}\)
\item   \(\dfrac{92}{100}\) = \(\dfrac{920}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,033  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,3}
\item   110  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1 100}
\item   0,033  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3,3}
\item   0,331  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 33,1}
\item   2,79  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 2 790}
\item   0,661  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66,1}
\item   768  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 680}
\item   47  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 47 000}
\item   0,714  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,14}
\item   864  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 86 400}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,281 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 281}
\item   54,93 ~ : ~ 1 000 ~ = ~{\color{red} 0,054 93}
\item   5,323 ~ : ~ 100 ~ = ~{\color{red} 0,053 23}
\item   0,738 ~ : ~ 100 ~ = ~{\color{red} 0,007 38}
\item   1,707 ~ : ~ 100 ~ = ~{\color{red} 0,017 07}
\item   1,159 ~ : ~ 10 ~ = ~{\color{red} 0,115 9}
\item   6 788 ~ : ~ 10 ~ = ~{\color{red} 678,8}
\item   91,83 ~ : ~ 100 ~ = ~{\color{red} 0,918 3}
\item   84,59 ~ : ~ 100 ~ = ~{\color{red} 0,845 9}
\item   855 ~ : ~ 1 000 ~ = ~{\color{red} 0,855}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,032 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3,2
\item   5,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~56
\item   270 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~270 000
\item   0,315 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~3,15
\item   0,541 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~54,1
\item   0,13 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~130
\item   0,897 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~89,7
\item   0,648 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6,48
\item   82,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~822
\item   31,3 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~313
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   137,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 13,78
}\item   569 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,69
}\item   755,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 75,58
}\item   98,28 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,098 28
}\item   6 829 ~ \(\times\)  0,01 ~ = ~{\color{red} 68,29
}\item   22,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 2,28
}\item   428,6 ~ \(\times\)  0,1 ~ = ~{\color{red} 42,86
}\item   8,889 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,088 89
}\item   1 120 ~ \(\times\)  0,01 ~ = ~{\color{red} 11,2
}\item   4 510 ~ \(\times\)  0,01 ~ = ~{\color{red} 45,1
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   615,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,158
\item   566 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,66
\item   9 147 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 9,147
\item   52,4 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 5,24
\item   7,795 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,077 95
\item   113,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,133
\item   70,37 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 7,037
\item   179,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 1,792
\item   58,15 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,581 5
\item   9 519 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 95,19
\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~ = ~ {\color{red}  10 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  100 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 484,9 ~mL~ = {\color{red}  94,849 }~dL
\item   5 547,8 ~daL~ = {\color{red}  5 547 800 }~cL
\item   129,68 ~dg~ = {\color{red}  12 968 }~mg
\item   260,99 ~cm~ = {\color{red}  0,002 609 9 }~km
\item   7 179,2 ~cL~ = {\color{red}  0,071 792 }~kL
\item   9 601,7 ~km~ = {\color{red}  9 601 700 }~m
\item   340,39 ~mm~ = {\color{red}  34,039 }~cm
\item   979,47 ~dag~ = {\color{red}  97 947 }~dg
\item   356,12 ~hm~ = {\color{red}  3 561,2 }~dam
\item   971,86 ~dm~ = {\color{red}  97,186 }~m
\end{itemize}
\end{multicols}
\end{document}
