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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 58}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   5 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9300}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{16}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{35}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,469  ~ \(\times\)  ~ 100
\item   9,75  ~ \(\times\)  ~ 100
\item   0,047  ~ \(\times\)  ~ 100
\item   0,03  ~ \(\times\)  ~ 10
\item   0,021  ~ \(\times\)  ~ 10
\item   490  ~ \(\times\)  ~ 100
\item   0,575  ~ \(\times\)  ~ 1 000
\item   385  ~ \(\times\)  ~ 10
\item   81,1  ~ \(\times\)  ~ 100
\item   4,4  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   518,4  ~ : ~ 1 000
\item   4 081  ~ : ~ 10
\item   3,401  ~ : ~ 10
\item   223,2  ~ : ~ 1 000
\item   3 826  ~ : ~ 100
\item   4 206  ~ : ~ 100
\item   83,07  ~ : ~ 1 000
\item   5,556  ~ : ~ 10
\item   47,77  ~ : ~ 10
\item   768  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,242  ~ \(\times\)  ~ ... ~ = ~ 242
\item   643  ~ \(\times\)  ~ ... ~ = ~ 6 430
\item   956  ~ \(\times\)  ~ ... ~ = ~ 95 600
\item   7,47  ~ \(\times\)  ~ ... ~ = ~ 747
\item   0,72  ~ \(\times\)  ~ ... ~ = ~ 72
\item   0,271  ~ \(\times\)  ~ ... ~ = ~ 2,71
\item   804  ~ \(\times\)  ~ ... ~ = ~ 8 040
\item   0,005  ~ \(\times\)  ~ ... ~ = ~ 0,05
\item   0,43  ~ \(\times\)  ~ ... ~ = ~ 4,3
\item   4,7  ~ \(\times\)  ~ ... ~ = ~ 4 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 231  ~ \(\times\)  ~ 0,1
\item   8 135  ~ \(\times\)  ~ 0,001
\item   4,679  ~ \(\times\)  ~ 0,001
\item   55,35  ~ \(\times\)  ~ 0,001
\item   10,84  ~ \(\times\)  ~ 0,1
\item   223,3  ~ \(\times\)  ~ 0,1
\item   34,57  ~ \(\times\)  ~ 0,01
\item   1,796  ~ \(\times\)  ~ 0,1
\item   342,9  ~ \(\times\)  ~ 0,1
\item   82,1  ~ \(\times\)  ~ 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   10,26  ~ \(\times\)  ~ ... ~ = ~  0,102 6
\item   6,197  ~ \(\times\)  ~ ... ~ = ~  0,619 7
\item   6 092  ~ \(\times\)  ~ ... ~ = ~  6,092
\item   6,612  ~ \(\times\)  ~ ... ~ = ~  0,066 12
\item   6 950  ~ \(\times\)  ~ ... ~ = ~  69,5
\item   209,7  ~ \(\times\)  ~ ... ~ = ~  2,097
\item   2 195  ~ \(\times\)  ~ ... ~ = ~  219,5
\item   6 306  ~ \(\times\)  ~ ... ~ = ~  630,6
\item   3 514  ~ \(\times\)  ~ ... ~ = ~  3,514
\item   652,7  ~ \(\times\)  ~ ... ~ = ~  6,527
\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 ~dm~ = ...~dam
\item   1 ~hm~ = ...~dm
\item   1 ~dm~ = ...~hm
\item   1 ~km~ = ...~cm
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~m
\item   1 ~cm~ = ...~dm
\item   1 ~m~ = ...~hm
\item   1 ~dam~ = ...~hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 926,2 ~dam~ = ...~cm
\item   377,32 ~L~ = ...~hL
\item   652,1 ~kg~ = ...~dag
\item   5 171,8 ~km~ = ...~cm
\item   5 097,9 ~kL~ = ...~cL
\item   7 365,9 ~dag~ = ...~kg
\item   490,41 ~mL~ = ...~dL
\item   720,16 ~daL~ = ...~mL
\item   266,46 ~cL~ = ...~L
\item   419,93 ~cg~ = ...~hg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   4 = \(\dfrac{40}{10}\)
\item   5 = \(\dfrac{500}{100}\)
\item   \(\dfrac{9300}{100}\) = \(\dfrac{930}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{16}{10}\) = \(\dfrac{160}{100}\)
\item   \(\dfrac{35}{100}\) = \(\dfrac{350}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,469  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 46,9}
\item   9,75  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 975}
\item   0,047  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,7}
\item   0,03  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,3}
\item   0,021  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,21}
\item   490  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 49 000}
\item   0,575  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 575}
\item   385  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3 850}
\item   81,1  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 8 110}
\item   4,4  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 440}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   518,4 ~ : ~ 1 000 ~ = ~{\color{red} 0,518 4}
\item   4 081 ~ : ~ 10 ~ = ~{\color{red} 408,1}
\item   3,401 ~ : ~ 10 ~ = ~{\color{red} 0,340 1}
\item   223,2 ~ : ~ 1 000 ~ = ~{\color{red} 0,223 2}
\item   3 826 ~ : ~ 100 ~ = ~{\color{red} 38,26}
\item   4 206 ~ : ~ 100 ~ = ~{\color{red} 42,06}
\item   83,07 ~ : ~ 1 000 ~ = ~{\color{red} 0,083 07}
\item   5,556 ~ : ~ 10 ~ = ~{\color{red} 0,555 6}
\item   47,77 ~ : ~ 10 ~ = ~{\color{red} 4,777}
\item   768 ~ : ~ 1 000 ~ = ~{\color{red} 0,768}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,242 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~242
\item   643 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~6 430
\item   956 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~95 600
\item   7,47 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~747
\item   0,72 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~72
\item   0,271 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~2,71
\item   804 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8 040
\item   0,005 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,05
\item   0,43 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4,3
\item   4,7 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~4 700
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 231 ~ \(\times\)  0,1 ~ = ~{\color{red} 123,1
}\item   8 135 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,135
}\item   4,679 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,004 679
}\item   55,35 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,055 35
}\item   10,84 ~ \(\times\)  0,1 ~ = ~{\color{red} 1,084
}\item   223,3 ~ \(\times\)  0,1 ~ = ~{\color{red} 22,33
}\item   34,57 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,345 7
}\item   1,796 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,179 6
}\item   342,9 ~ \(\times\)  0,1 ~ = ~{\color{red} 34,29
}\item   82,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,082 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   10,26 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,102 6
\item   6,197 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,619 7
\item   6 092 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 6,092
\item   6,612 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,066 12
\item   6 950 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 69,5
\item   209,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 2,097
\item   2 195 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 219,5
\item   6 306 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 630,6
\item   3 514 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 3,514
\item   652,7 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,527
\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 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  1 000 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{1\,000}\) ~ hm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 926,2 ~dam~ = {\color{red}  5 926 200 }~cm
\item   377,32 ~L~ = {\color{red}  3,773 2 }~hL
\item   652,1 ~kg~ = {\color{red}  65 210 }~dag
\item   5 171,8 ~km~ = {\color{red}  517 180 000 }~cm
\item   5 097,9 ~kL~ = {\color{red}  509 790 000 }~cL
\item   7 365,9 ~dag~ = {\color{red}  73,659 }~kg
\item   490,41 ~mL~ = {\color{red}  4,904 1 }~dL
\item   720,16 ~daL~ = {\color{red}  7 201 600 }~mL
\item   266,46 ~cL~ = {\color{red}  2,664 6 }~L
\item   419,93 ~cg~ = {\color{red}  0,041 993 }~hg
\end{itemize}
\end{multicols}
\end{document}
