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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 258}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,4  ~ \(\times\)  ~ 1 000
\item   0,009  ~ \(\times\)  ~ 100
\item   0,023  ~ \(\times\)  ~ 100
\item   79,1  ~ \(\times\)  ~ 10
\item   56,2  ~ \(\times\)  ~ 10
\item   747  ~ \(\times\)  ~ 10
\item   78,7  ~ \(\times\)  ~ 10
\item   0,59  ~ \(\times\)  ~ 1 000
\item   0,026  ~ \(\times\)  ~ 10
\item   0,092  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   48,09  ~ : ~ 10
\item   73,08  ~ : ~ 100
\item   9 318  ~ : ~ 100
\item   82,04  ~ : ~ 10
\item   558,6  ~ : ~ 1 000
\item   5 635  ~ : ~ 1 000
\item   57,23  ~ : ~ 100
\item   76,22  ~ : ~ 10
\item   8,65  ~ : ~ 100
\item   571,6  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   812  ~ \(\times\)  ~ ... ~ = ~ 8 120
\item   0,002  ~ \(\times\)  ~ ... ~ = ~ 0,2
\item   1,13  ~ \(\times\)  ~ ... ~ = ~ 11,3
\item   28,2  ~ \(\times\)  ~ ... ~ = ~ 282
\item   13,3  ~ \(\times\)  ~ ... ~ = ~ 13 300
\item   0,213  ~ \(\times\)  ~ ... ~ = ~ 213
\item   6,82  ~ \(\times\)  ~ ... ~ = ~ 682
\item   28,2  ~ \(\times\)  ~ ... ~ = ~ 28 200
\item   0,003  ~ \(\times\)  ~ ... ~ = ~ 0,03
\item   16,3  ~ \(\times\)  ~ ... ~ = ~ 16 300
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 680  ~ \(\times\)  ~ 0,001
\item   58,91  ~ \(\times\)  ~ 0,01
\item   3 983  ~ \(\times\)  ~ 0,001
\item   4,227  ~ \(\times\)  ~ 0,1
\item   1 350  ~ \(\times\)  ~ 0,001
\item   3 260  ~ \(\times\)  ~ 0,01
\item   3,268  ~ \(\times\)  ~ 0,01
\item   7,239  ~ \(\times\)  ~ 0,001
\item   5,18  ~ \(\times\)  ~ 0,01
\item   3,938  ~ \(\times\)  ~ 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   24,29  ~ \(\times\)  ~ ... ~ = ~  0,242 9
\item   594,3  ~ \(\times\)  ~ ... ~ = ~  5,943
\item   2,038  ~ \(\times\)  ~ ... ~ = ~  0,002 038
\item   6 693  ~ \(\times\)  ~ ... ~ = ~  66,93
\item   867,6  ~ \(\times\)  ~ ... ~ = ~  8,676
\item   1 514  ~ \(\times\)  ~ ... ~ = ~  1,514
\item   297,1  ~ \(\times\)  ~ ... ~ = ~  0,297 1
\item   6 346  ~ \(\times\)  ~ ... ~ = ~  634,6
\item   726,4  ~ \(\times\)  ~ ... ~ = ~  0,726 4
\item   304,9  ~ \(\times\)  ~ ... ~ = ~  30,49
\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~ = ...~km
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~dm
\item   1 ~cm~ = ...~hm
\item   1 ~km~ = ...~dam
\item   1 ~cm~ = ...~km
\item   1 ~m~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 056,9 ~cg~ = ...~dg
\item   450,53 ~mL~ = ...~hL
\item   1 270,1 ~hg~ = ...~dg
\item   5 028,8 ~dag~ = ...~g
\item   4 465,6 ~dam~ = ...~mm
\item   2 004,9 ~kg~ = ...~mg
\item   187,07 ~g~ = ...~dg
\item   9 161,1 ~daL~ = ...~dL
\item   7 895,5 ~dg~ = ...~dag
\item   165,13 ~km~ = ...~cm
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{7900}{100}\) = \(\dfrac{790}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{36}{10}\) = \(\dfrac{360}{100}\)
\item   \(\dfrac{28}{100}\) = \(\dfrac{280}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   69,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 69 400}
\item   0,009  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 0,9}
\item   0,023  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 2,3}
\item   79,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 791}
\item   56,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 562}
\item   747  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 470}
\item   78,7  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 787}
\item   0,59  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 590}
\item   0,026  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,26}
\item   0,092  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   48,09 ~ : ~ 10 ~ = ~{\color{red} 4,809}
\item   73,08 ~ : ~ 100 ~ = ~{\color{red} 0,730 8}
\item   9 318 ~ : ~ 100 ~ = ~{\color{red} 93,18}
\item   82,04 ~ : ~ 10 ~ = ~{\color{red} 8,204}
\item   558,6 ~ : ~ 1 000 ~ = ~{\color{red} 0,558 6}
\item   5 635 ~ : ~ 1 000 ~ = ~{\color{red} 5,635}
\item   57,23 ~ : ~ 100 ~ = ~{\color{red} 0,572 3}
\item   76,22 ~ : ~ 10 ~ = ~{\color{red} 7,622}
\item   8,65 ~ : ~ 100 ~ = ~{\color{red} 0,086 5}
\item   571,6 ~ : ~ 10 ~ = ~{\color{red} 57,16}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   812 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 120
\item   0,002 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~0,2
\item   1,13 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~11,3
\item   28,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~282
\item   13,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~13 300
\item   0,213 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~213
\item   6,82 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~682
\item   28,2 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~28 200
\item   0,003 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,03
\item   16,3 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~16 300
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 680 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,68
}\item   58,91 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,589 1
}\item   3 983 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,983
}\item   4,227 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,422 7
}\item   1 350 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,35
}\item   3 260 ~ \(\times\)  0,01 ~ = ~{\color{red} 32,6
}\item   3,268 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,032 68
}\item   7,239 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 239
}\item   5,18 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,051 8
}\item   3,938 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,039 38
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   24,29 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,242 9
\item   594,3 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 5,943
\item   2,038 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,002 038
\item   6 693 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 66,93
\item   867,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,676
\item   1 514 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 1,514
\item   297,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,297 1
\item   6 346 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 634,6
\item   726,4 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,726 4
\item   304,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 30,49
\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~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~cm~ = ~  \(\dfrac{1}{10\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 056,9 ~cg~ = {\color{red}  805,69 }~dg
\item   450,53 ~mL~ = {\color{red}  0,004 505 3 }~hL
\item   1 270,1 ~hg~ = {\color{red}  1 270 100 }~dg
\item   5 028,8 ~dag~ = {\color{red}  50 288 }~g
\item   4 465,6 ~dam~ = {\color{red}  44 656 000 }~mm
\item   2 004,9 ~kg~ = {\color{red}  2 004 900 000 }~mg
\item   187,07 ~g~ = {\color{red}  1 870,7 }~dg
\item   9 161,1 ~daL~ = {\color{red}  916 110 }~dL
\item   7 895,5 ~dg~ = {\color{red}  78,955 }~dag
\item   165,13 ~km~ = {\color{red}  16 513 000 }~cm
\end{itemize}
\end{multicols}
\end{document}
