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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 271}

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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   8 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,575  ~ \(\times\)  ~ 10
\item   0,088  ~ \(\times\)  ~ 10
\item   0,847  ~ \(\times\)  ~ 1 000
\item   771  ~ \(\times\)  ~ 100
\item   0,808  ~ \(\times\)  ~ 10
\item   3,36  ~ \(\times\)  ~ 10
\item   0,636  ~ \(\times\)  ~ 10
\item   0,862  ~ \(\times\)  ~ 100
\item   942  ~ \(\times\)  ~ 1 000
\item   0,159  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   160,2  ~ : ~ 10
\item   768,3  ~ : ~ 1 000
\item   900,3  ~ : ~ 100
\item   4 422  ~ : ~ 1 000
\item   35,3  ~ : ~ 1 000
\item   459  ~ : ~ 100
\item   4 979  ~ : ~ 10
\item   25,74  ~ : ~ 100
\item   4,02  ~ : ~ 100
\item   653  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,154  ~ \(\times\)  ~ ... ~ = ~ 1,54
\item   0,008  ~ \(\times\)  ~ ... ~ = ~ 8
\item   9,78  ~ \(\times\)  ~ ... ~ = ~ 978
\item   9,52  ~ \(\times\)  ~ ... ~ = ~ 95,2
\item   0,038  ~ \(\times\)  ~ ... ~ = ~ 0,38
\item   0,975  ~ \(\times\)  ~ ... ~ = ~ 975
\item   0,622  ~ \(\times\)  ~ ... ~ = ~ 62,2
\item   965  ~ \(\times\)  ~ ... ~ = ~ 965 000
\item   0,048  ~ \(\times\)  ~ ... ~ = ~ 48
\item   0,87  ~ \(\times\)  ~ ... ~ = ~ 8,7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 015  ~ \(\times\)  ~ 0,001
\item   971  ~ \(\times\)  ~ 0,1
\item   5,17  ~ \(\times\)  ~ 0,01
\item   571,9  ~ \(\times\)  ~ 0,01
\item   7,039  ~ \(\times\)  ~ 0,01
\item   89,12  ~ \(\times\)  ~ 0,001
\item   306,4  ~ \(\times\)  ~ 0,01
\item   43,51  ~ \(\times\)  ~ 0,01
\item   7 289  ~ \(\times\)  ~ 0,01
\item   7 887  ~ \(\times\)  ~ 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   783,5  ~ \(\times\)  ~ ... ~ = ~  78,35
\item   248,1  ~ \(\times\)  ~ ... ~ = ~  0,248 1
\item   3,365  ~ \(\times\)  ~ ... ~ = ~  0,003 365
\item   2 019  ~ \(\times\)  ~ ... ~ = ~  2,019
\item   918,3  ~ \(\times\)  ~ ... ~ = ~  91,83
\item   641  ~ \(\times\)  ~ ... ~ = ~  6,41
\item   91,31  ~ \(\times\)  ~ ... ~ = ~  0,913 1
\item   13,58  ~ \(\times\)  ~ ... ~ = ~  0,013 58
\item   96,95  ~ \(\times\)  ~ ... ~ = ~  9,695
\item   12,16  ~ \(\times\)  ~ ... ~ = ~  1,216
\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~ = ...~m
\item   1 ~dam~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~dm~ = ...~m
\item   1 ~dam~ = ...~km
\item   1 ~dam~ = ...~hm
\item   1 ~dm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   674,53 ~hg~ = ...~dg
\item   186,15 ~dag~ = ...~kg
\item   639,68 ~mg~ = ...~kg
\item   2 060,4 ~mg~ = ...~dag
\item   1 411,1 ~g~ = ...~kg
\item   797 ~cL~ = ...~mL
\item   5 239,3 ~hm~ = ...~m
\item   2 640,8 ~cm~ = ...~m
\item   9 720,5 ~dag~ = ...~mg
\item   460,72 ~cm~ = ...~hm
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   8 = \(\dfrac{80}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{5400}{100}\) = \(\dfrac{540}{10}\)
\item   \(\dfrac{3}{10}\) = \(\dfrac{300}{1\,000}\)
\item   \(\dfrac{58}{10}\) = \(\dfrac{580}{100}\)
\item   \(\dfrac{78}{100}\) = \(\dfrac{780}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,575  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 5,75}
\item   0,088  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,88}
\item   0,847  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 847}
\item   771  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 77 100}
\item   0,808  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8,08}
\item   3,36  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 33,6}
\item   0,636  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,36}
\item   0,862  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 86,2}
\item   942  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 942 000}
\item   0,159  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 1,59}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   160,2 ~ : ~ 10 ~ = ~{\color{red} 16,02}
\item   768,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,768 3}
\item   900,3 ~ : ~ 100 ~ = ~{\color{red} 9,003}
\item   4 422 ~ : ~ 1 000 ~ = ~{\color{red} 4,422}
\item   35,3 ~ : ~ 1 000 ~ = ~{\color{red} 0,035 3}
\item   459 ~ : ~ 100 ~ = ~{\color{red} 4,59}
\item   4 979 ~ : ~ 10 ~ = ~{\color{red} 497,9}
\item   25,74 ~ : ~ 100 ~ = ~{\color{red} 0,257 4}
\item   4,02 ~ : ~ 100 ~ = ~{\color{red} 0,040 2}
\item   653 ~ : ~ 1 000 ~ = ~{\color{red} 0,653}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,154 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~1,54
\item   0,008 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~8
\item   9,78 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~978
\item   9,52 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~95,2
\item   0,038 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,38
\item   0,975 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~975
\item   0,622 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~62,2
\item   965 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~965 000
\item   0,048 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~48
\item   0,87 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,7
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 015 ~ \(\times\)  0,001 ~ = ~{\color{red} 3,015
}\item   971 ~ \(\times\)  0,1 ~ = ~{\color{red} 97,1
}\item   5,17 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,051 7
}\item   571,9 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,719
}\item   7,039 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,070 39
}\item   89,12 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,089 12
}\item   306,4 ~ \(\times\)  0,01 ~ = ~{\color{red} 3,064
}\item   43,51 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,435 1
}\item   7 289 ~ \(\times\)  0,01 ~ = ~{\color{red} 72,89
}\item   7 887 ~ \(\times\)  0,1 ~ = ~{\color{red} 788,7
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   783,5 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 78,35
\item   248,1 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,248 1
\item   3,365 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 365
\item   2 019 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 2,019
\item   918,3 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 91,83
\item   641 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 6,41
\item   91,31 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,913 1
\item   13,58 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,013 58
\item   96,95 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 9,695
\item   12,16 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,216
\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}  1 000 ~ }m
\item   1 ~dam~ = ~ {\color{red}  1 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   674,53 ~hg~ = {\color{red}  674 530 }~dg
\item   186,15 ~dag~ = {\color{red}  1,861 5 }~kg
\item   639,68 ~mg~ = {\color{red}  0,000 639 68 }~kg
\item   2 060,4 ~mg~ = {\color{red}  0,206 04 }~dag
\item   1 411,1 ~g~ = {\color{red}  1,411 1 }~kg
\item   797 ~cL~ = {\color{red}  7 970 }~mL
\item   5 239,3 ~hm~ = {\color{red}  523 930 }~m
\item   2 640,8 ~cm~ = {\color{red}  26,408 }~m
\item   9 720,5 ~dag~ = {\color{red}  97 205 000 }~mg
\item   460,72 ~cm~ = {\color{red}  0,046 072 }~hm
\end{itemize}
\end{multicols}
\end{document}
