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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 173}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9600}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{87}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   91,8  ~ \(\times\)  ~ 100
\item   748  ~ \(\times\)  ~ 100
\item   723  ~ \(\times\)  ~ 10
\item   0,764  ~ \(\times\)  ~ 10
\item   47,3  ~ \(\times\)  ~ 1 000
\item   207  ~ \(\times\)  ~ 1 000
\item   590  ~ \(\times\)  ~ 100
\item   1,58  ~ \(\times\)  ~ 100
\item   0,109  ~ \(\times\)  ~ 10
\item   322  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,318  ~ : ~ 1 000
\item   18,9  ~ : ~ 100
\item   7 795  ~ : ~ 10
\item   3,255  ~ : ~ 1 000
\item   35,7  ~ : ~ 100
\item   33,7  ~ : ~ 100
\item   45,59  ~ : ~ 10
\item   3,624  ~ : ~ 100
\item   3,709  ~ : ~ 100
\item   17,75  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   731  ~ \(\times\)  ~ ... ~ = ~ 731 000
\item   0,853  ~ \(\times\)  ~ ... ~ = ~ 85,3
\item   49,4  ~ \(\times\)  ~ ... ~ = ~ 49 400
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 27
\item   0,716  ~ \(\times\)  ~ ... ~ = ~ 71,6
\item   5,64  ~ \(\times\)  ~ ... ~ = ~ 56,4
\item   8,55  ~ \(\times\)  ~ ... ~ = ~ 85,5
\item   33,7  ~ \(\times\)  ~ ... ~ = ~ 3 370
\item   0,099  ~ \(\times\)  ~ ... ~ = ~ 99
\item   0,019  ~ \(\times\)  ~ ... ~ = ~ 19
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   83,27  ~ \(\times\)  ~ 0,1
\item   80,31  ~ \(\times\)  ~ 0,1
\item   9 066  ~ \(\times\)  ~ 0,01
\item   1 337  ~ \(\times\)  ~ 0,001
\item   7 761  ~ \(\times\)  ~ 0,01
\item   92,64  ~ \(\times\)  ~ 0,1
\item   6,07  ~ \(\times\)  ~ 0,1
\item   3,674  ~ \(\times\)  ~ 0,001
\item   704  ~ \(\times\)  ~ 0,1
\item   32,67  ~ \(\times\)  ~ 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   4 967  ~ \(\times\)  ~ ... ~ = ~  4,967
\item   1,9  ~ \(\times\)  ~ ... ~ = ~  0,019
\item   489,5  ~ \(\times\)  ~ ... ~ = ~  48,95
\item   718,6  ~ \(\times\)  ~ ... ~ = ~  7,186
\item   4,375  ~ \(\times\)  ~ ... ~ = ~  0,043 75
\item   77,51  ~ \(\times\)  ~ ... ~ = ~  0,077 51
\item   659,6  ~ \(\times\)  ~ ... ~ = ~  65,96
\item   820,1  ~ \(\times\)  ~ ... ~ = ~  0,820 1
\item   1 954  ~ \(\times\)  ~ ... ~ = ~  19,54
\item   6,987  ~ \(\times\)  ~ ... ~ = ~  0,069 87
\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~ = ...~cm
\item   1 ~dm~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~cm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~m~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~dm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 898,9 ~hg~ = ...~mg
\item   3 525,4 ~cm~ = ...~km
\item   284,51 ~kL~ = ...~hL
\item   3 642,3 ~kg~ = ...~cg
\item   7 931,6 ~cL~ = ...~dL
\item   503,63 ~m~ = ...~km
\item   2 258,6 ~daL~ = ...~L
\item   9 315,7 ~cL~ = ...~mL
\item   216,57 ~kL~ = ...~cL
\item   3 475,4 ~mL~ = ...~kL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   9 = \(\dfrac{900}{100}\)
\item   \(\dfrac{9600}{100}\) = \(\dfrac{960}{10}\)
\item   \(\dfrac{9}{10}\) = \(\dfrac{900}{1\,000}\)
\item   \(\dfrac{87}{10}\) = \(\dfrac{870}{100}\)
\item   \(\dfrac{57}{100}\) = \(\dfrac{570}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   91,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9 180}
\item   748  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 74 800}
\item   723  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7 230}
\item   0,764  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 7,64}
\item   47,3  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 47 300}
\item   207  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 207 000}
\item   590  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 59 000}
\item   1,58  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 158}
\item   0,109  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,09}
\item   322  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 32 200}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   6,318 ~ : ~ 1 000 ~ = ~{\color{red} 0,006 318}
\item   18,9 ~ : ~ 100 ~ = ~{\color{red} 0,189}
\item   7 795 ~ : ~ 10 ~ = ~{\color{red} 779,5}
\item   3,255 ~ : ~ 1 000 ~ = ~{\color{red} 0,003 255}
\item   35,7 ~ : ~ 100 ~ = ~{\color{red} 0,357}
\item   33,7 ~ : ~ 100 ~ = ~{\color{red} 0,337}
\item   45,59 ~ : ~ 10 ~ = ~{\color{red} 4,559}
\item   3,624 ~ : ~ 100 ~ = ~{\color{red} 0,036 24}
\item   3,709 ~ : ~ 100 ~ = ~{\color{red} 0,037 09}
\item   17,75 ~ : ~ 1 000 ~ = ~{\color{red} 0,017 75}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   731 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~731 000
\item   0,853 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~85,3
\item   49,4 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~49 400
\item   0,027 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27
\item   0,716 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~71,6
\item   5,64 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~56,4
\item   8,55 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~85,5
\item   33,7 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 370
\item   0,099 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~99
\item   0,019 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~19
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   83,27 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,327
}\item   80,31 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,031
}\item   9 066 ~ \(\times\)  0,01 ~ = ~{\color{red} 90,66
}\item   1 337 ~ \(\times\)  0,001 ~ = ~{\color{red} 1,337
}\item   7 761 ~ \(\times\)  0,01 ~ = ~{\color{red} 77,61
}\item   92,64 ~ \(\times\)  0,1 ~ = ~{\color{red} 9,264
}\item   6,07 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,607
}\item   3,674 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,003 674
}\item   704 ~ \(\times\)  0,1 ~ = ~{\color{red} 70,4
}\item   32,67 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,326 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   4 967 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 4,967
\item   1,9 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,019
\item   489,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 48,95
\item   718,6 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,186
\item   4,375 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,043 75
\item   77,51 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,077 51
\item   659,6 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 65,96
\item   820,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,820 1
\item   1 954 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 19,54
\item   6,987 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,069 87
\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}  100 000 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 898,9 ~hg~ = {\color{red}  289 890 000 }~mg
\item   3 525,4 ~cm~ = {\color{red}  0,035 254 }~km
\item   284,51 ~kL~ = {\color{red}  2 845,1 }~hL
\item   3 642,3 ~kg~ = {\color{red}  364 230 000 }~cg
\item   7 931,6 ~cL~ = {\color{red}  793,16 }~dL
\item   503,63 ~m~ = {\color{red}  0,503 63 }~km
\item   2 258,6 ~daL~ = {\color{red}  22 586 }~L
\item   9 315,7 ~cL~ = {\color{red}  93 157 }~mL
\item   216,57 ~kL~ = {\color{red}  21 657 000 }~cL
\item   3 475,4 ~mL~ = {\color{red}  0,003 475 4 }~kL
\end{itemize}
\end{multicols}
\end{document}
