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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 372}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{37}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,738  ~ \(\times\)  ~ 100
\item   0,062  ~ \(\times\)  ~ 1 000
\item   0,23  ~ \(\times\)  ~ 10
\item   0,097  ~ \(\times\)  ~ 100
\item   2,57  ~ \(\times\)  ~ 10
\item   0,015  ~ \(\times\)  ~ 100
\item   31,9  ~ \(\times\)  ~ 100
\item   1,64  ~ \(\times\)  ~ 100
\item   0,069  ~ \(\times\)  ~ 1 000
\item   93  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   45,58  ~ : ~ 1 000
\item   24,18  ~ : ~ 100
\item   2,686  ~ : ~ 1 000
\item   944,9  ~ : ~ 10
\item   90,39  ~ : ~ 10
\item   8 039  ~ : ~ 10
\item   9,202  ~ : ~ 10
\item   90,4  ~ : ~ 1 000
\item   4 892  ~ : ~ 1 000
\item   7,822  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   50,2  ~ \(\times\)  ~ ... ~ = ~ 502
\item   72,1  ~ \(\times\)  ~ ... ~ = ~ 721
\item   61  ~ \(\times\)  ~ ... ~ = ~ 6 100
\item   38,6  ~ \(\times\)  ~ ... ~ = ~ 3 860
\item   453  ~ \(\times\)  ~ ... ~ = ~ 453 000
\item   540  ~ \(\times\)  ~ ... ~ = ~ 5 400
\item   0,045  ~ \(\times\)  ~ ... ~ = ~ 4,5
\item   0,532  ~ \(\times\)  ~ ... ~ = ~ 532
\item   0,083  ~ \(\times\)  ~ ... ~ = ~ 0,83
\item   670  ~ \(\times\)  ~ ... ~ = ~ 670 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 090  ~ \(\times\)  ~ 0,01
\item   8 871  ~ \(\times\)  ~ 0,1
\item   5 073  ~ \(\times\)  ~ 0,001
\item   97,01  ~ \(\times\)  ~ 0,001
\item   8,626  ~ \(\times\)  ~ 0,01
\item   58,69  ~ \(\times\)  ~ 0,1
\item   5,575  ~ \(\times\)  ~ 0,01
\item   45,6  ~ \(\times\)  ~ 0,01
\item   41,98  ~ \(\times\)  ~ 0,001
\item   9,096  ~ \(\times\)  ~ 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   93,87  ~ \(\times\)  ~ ... ~ = ~  0,093 87
\item   4 073  ~ \(\times\)  ~ ... ~ = ~  40,73
\item   4,071  ~ \(\times\)  ~ ... ~ = ~  0,407 1
\item   6 140  ~ \(\times\)  ~ ... ~ = ~  614
\item   9 550  ~ \(\times\)  ~ ... ~ = ~  95,5
\item   9,61  ~ \(\times\)  ~ ... ~ = ~  0,961
\item   8,089  ~ \(\times\)  ~ ... ~ = ~  0,808 9
\item   3,317  ~ \(\times\)  ~ ... ~ = ~  0,331 7
\item   3 308  ~ \(\times\)  ~ ... ~ = ~  330,8
\item   71,89  ~ \(\times\)  ~ ... ~ = ~  0,718 9
\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~ = ...~dm
\item   1 ~dam~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~dm~ = ...~km
\item   1 ~m~ = ...~hm
\item   1 ~hm~ = ...~m
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~km
\item   1 ~dam~ = ...~cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 264,8 ~cg~ = ...~kg
\item   5 196,7 ~kg~ = ...~hg
\item   9 527,6 ~kL~ = ...~L
\item   245,79 ~dag~ = ...~kg
\item   7 346,9 ~hL~ = ...~L
\item   8 604,5 ~dm~ = ...~km
\item   5 674,4 ~dag~ = ...~mg
\item   129,54 ~cm~ = ...~dam
\item   231,98 ~kL~ = ...~mL
\item   5 271,4 ~kg~ = ...~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   2 = \(\dfrac{20}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{4200}{100}\) = \(\dfrac{420}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{78}{10}\) = \(\dfrac{780}{100}\)
\item   \(\dfrac{37}{100}\) = \(\dfrac{370}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,738  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 73,8}
\item   0,062  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 62}
\item   0,23  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,3}
\item   0,097  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,7}
\item   2,57  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 25,7}
\item   0,015  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1,5}
\item   31,9  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 3 190}
\item   1,64  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 164}
\item   0,069  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 69}
\item   93  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 930}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   45,58 ~ : ~ 1 000 ~ = ~{\color{red} 0,045 58}
\item   24,18 ~ : ~ 100 ~ = ~{\color{red} 0,241 8}
\item   2,686 ~ : ~ 1 000 ~ = ~{\color{red} 0,002 686}
\item   944,9 ~ : ~ 10 ~ = ~{\color{red} 94,49}
\item   90,39 ~ : ~ 10 ~ = ~{\color{red} 9,039}
\item   8 039 ~ : ~ 10 ~ = ~{\color{red} 803,9}
\item   9,202 ~ : ~ 10 ~ = ~{\color{red} 0,920 2}
\item   90,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,090 4}
\item   4 892 ~ : ~ 1 000 ~ = ~{\color{red} 4,892}
\item   7,822 ~ : ~ 10 ~ = ~{\color{red} 0,782 2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   50,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~502
\item   72,1 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~721
\item   61 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~6 100
\item   38,6 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~3 860
\item   453 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~453 000
\item   540 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 400
\item   0,045 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~4,5
\item   0,532 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~532
\item   0,083 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,83
\item   670 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~670 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 090 ~ \(\times\)  0,01 ~ = ~{\color{red} 40,9
}\item   8 871 ~ \(\times\)  0,1 ~ = ~{\color{red} 887,1
}\item   5 073 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,073
}\item   97,01 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,097 01
}\item   8,626 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,086 26
}\item   58,69 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,869
}\item   5,575 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,055 75
}\item   45,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,456
}\item   41,98 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,041 98
}\item   9,096 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,909 6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   93,87 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,093 87
\item   4 073 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 40,73
\item   4,071 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,407 1
\item   6 140 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 614
\item   9 550 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 95,5
\item   9,61 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,961
\item   8,089 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,808 9
\item   3,317 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,331 7
\item   3 308 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 330,8
\item   71,89 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,718 9
\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~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 264,8 ~cg~ = {\color{red}  0,042 648 }~kg
\item   5 196,7 ~kg~ = {\color{red}  51 967 }~hg
\item   9 527,6 ~kL~ = {\color{red}  9 527 600 }~L
\item   245,79 ~dag~ = {\color{red}  2,457 9 }~kg
\item   7 346,9 ~hL~ = {\color{red}  734 690 }~L
\item   8 604,5 ~dm~ = {\color{red}  0,860 45 }~km
\item   5 674,4 ~dag~ = {\color{red}  56 744 000 }~mg
\item   129,54 ~cm~ = {\color{red}  0,129 54 }~dam
\item   231,98 ~kL~ = {\color{red}  231 980 000 }~mL
\item   5 271,4 ~kg~ = {\color{red}  5 271 400 }~g
\end{itemize}
\end{multicols}
\end{document}
