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\newcommand{\titre}{Conversions}
\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 155}

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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   9 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{9800}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{80}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,043  ~ \(\times\)  ~ 100
\item   82,9  ~ \(\times\)  ~ 1 000
\item   899  ~ \(\times\)  ~ 1 000
\item   0,003  ~ \(\times\)  ~ 10
\item   19,1  ~ \(\times\)  ~ 10
\item   919  ~ \(\times\)  ~ 10
\item   545  ~ \(\times\)  ~ 1 000
\item   61,3  ~ \(\times\)  ~ 100
\item   0,091  ~ \(\times\)  ~ 10
\item   0,007  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 664  ~ : ~ 10
\item   71,45  ~ : ~ 1 000
\item   19,56  ~ : ~ 1 000
\item   7,977  ~ : ~ 10
\item   0,179  ~ : ~ 10
\item   303  ~ : ~ 1 000
\item   8,744  ~ : ~ 10
\item   5 510  ~ : ~ 100
\item   63,57  ~ : ~ 100
\item   973,2  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,252  ~ \(\times\)  ~ ... ~ = ~ 25,2
\item   7,34  ~ \(\times\)  ~ ... ~ = ~ 73,4
\item   0,067  ~ \(\times\)  ~ ... ~ = ~ 67
\item   0,007  ~ \(\times\)  ~ ... ~ = ~ 7
\item   41,6  ~ \(\times\)  ~ ... ~ = ~ 416
\item   88,2  ~ \(\times\)  ~ ... ~ = ~ 8 820
\item   0,75  ~ \(\times\)  ~ ... ~ = ~ 75
\item   0,038  ~ \(\times\)  ~ ... ~ = ~ 38
\item   408  ~ \(\times\)  ~ ... ~ = ~ 40 800
\item   5,17  ~ \(\times\)  ~ ... ~ = ~ 517
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   50,15  ~ \(\times\)  ~ 0,1
\item   5,168  ~ \(\times\)  ~ 0,01
\item   9 737  ~ \(\times\)  ~ 0,1
\item   8 943  ~ \(\times\)  ~ 0,001
\item   12,61  ~ \(\times\)  ~ 0,01
\item   76,55  ~ \(\times\)  ~ 0,1
\item   9,571  ~ \(\times\)  ~ 0,001
\item   8,816  ~ \(\times\)  ~ 0,001
\item   89,05  ~ \(\times\)  ~ 0,1
\item   9 423  ~ \(\times\)  ~ 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   84,03  ~ \(\times\)  ~ ... ~ = ~  0,840 3
\item   0,163  ~ \(\times\)  ~ ... ~ = ~  0,016 3
\item   73,56  ~ \(\times\)  ~ ... ~ = ~  0,735 6
\item   43,69  ~ \(\times\)  ~ ... ~ = ~  0,436 9
\item   6,384  ~ \(\times\)  ~ ... ~ = ~  0,006 384
\item   2,827  ~ \(\times\)  ~ ... ~ = ~  0,028 27
\item   717,6  ~ \(\times\)  ~ ... ~ = ~  0,717 6
\item   5 991  ~ \(\times\)  ~ ... ~ = ~  5,991
\item   510,8  ~ \(\times\)  ~ ... ~ = ~  0,510 8
\item   3,647  ~ \(\times\)  ~ ... ~ = ~  0,003 647
\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 ~dam~ = ...~m
\item   1 ~m~ = ...~dam
\item   1 ~hm~ = ...~dam
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~hm
\item   1 ~dm~ = ...~cm
\item   1 ~dm~ = ...~dam
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   130,91 ~kg~ = ...~dg
\item   219,3 ~hg~ = ...~dag
\item   596,72 ~daL~ = ...~mL
\item   9 144,7 ~mg~ = ...~g
\item   894,78 ~dag~ = ...~g
\item   500,63 ~kg~ = ...~g
\item   5 777,6 ~km~ = ...~dm
\item   938,2 ~L~ = ...~hL
\item   435,64 ~cg~ = ...~dg
\item   6 599,6 ~L~ = ...~cL
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   9 = \(\dfrac{90}{10}\)
\item   6 = \(\dfrac{600}{100}\)
\item   \(\dfrac{9800}{100}\) = \(\dfrac{980}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{80}{10}\) = \(\dfrac{800}{100}\)
\item   \(\dfrac{79}{100}\) = \(\dfrac{790}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,043  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 4,3}
\item   82,9  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 82 900}
\item   899  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 899 000}
\item   0,003  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,03}
\item   19,1  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 191}
\item   919  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 9 190}
\item   545  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 545 000}
\item   61,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 6 130}
\item   0,091  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,91}
\item   0,007  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 7}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 664 ~ : ~ 10 ~ = ~{\color{red} 366,4}
\item   71,45 ~ : ~ 1 000 ~ = ~{\color{red} 0,071 45}
\item   19,56 ~ : ~ 1 000 ~ = ~{\color{red} 0,019 56}
\item   7,977 ~ : ~ 10 ~ = ~{\color{red} 0,797 7}
\item   0,179 ~ : ~ 10 ~ = ~{\color{red} 0,017 9}
\item   303 ~ : ~ 1 000 ~ = ~{\color{red} 0,303}
\item   8,744 ~ : ~ 10 ~ = ~{\color{red} 0,874 4}
\item   5 510 ~ : ~ 100 ~ = ~{\color{red} 55,1}
\item   63,57 ~ : ~ 100 ~ = ~{\color{red} 0,635 7}
\item   973,2 ~ : ~ 10 ~ = ~{\color{red} 97,32}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,252 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~25,2
\item   7,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~73,4
\item   0,067 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~67
\item   0,007 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7
\item   41,6 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~416
\item   88,2 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~8 820
\item   0,75 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~75
\item   0,038 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~38
\item   408 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~40 800
\item   5,17 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~517
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   50,15 ~ \(\times\)  0,1 ~ = ~{\color{red} 5,015
}\item   5,168 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,051 68
}\item   9 737 ~ \(\times\)  0,1 ~ = ~{\color{red} 973,7
}\item   8 943 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,943
}\item   12,61 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,126 1
}\item   76,55 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,655
}\item   9,571 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 571
}\item   8,816 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,008 816
}\item   89,05 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,905
}\item   9 423 ~ \(\times\)  0,001 ~ = ~{\color{red} 9,423
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   84,03 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,840 3
\item   0,163 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,016 3
\item   73,56 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,735 6
\item   43,69 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,436 9
\item   6,384 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,006 384
\item   2,827 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,028 27
\item   717,6 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,717 6
\item   5 991 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 5,991
\item   510,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,510 8
\item   3,647 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 647
\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 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{10}\) ~ dam
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 ~ }hm
\item   1 ~dm~ = ~ {\color{red}  10 ~ }cm
\item   1 ~dm~ = ~  \(\dfrac{1}{100}\) ~ dam
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   130,91 ~kg~ = {\color{red}  1 309 100 }~dg
\item   219,3 ~hg~ = {\color{red}  2 193 }~dag
\item   596,72 ~daL~ = {\color{red}  5 967 200 }~mL
\item   9 144,7 ~mg~ = {\color{red}  9,144 7 }~g
\item   894,78 ~dag~ = {\color{red}  8 947,8 }~g
\item   500,63 ~kg~ = {\color{red}  500 630 }~g
\item   5 777,6 ~km~ = {\color{red}  57 776 000 }~dm
\item   938,2 ~L~ = {\color{red}  9,382 }~hL
\item   435,64 ~cg~ = {\color{red}  43,564 }~dg
\item   6 599,6 ~L~ = {\color{red}  659 960 }~cL
\end{itemize}
\end{multicols}
\end{document}
