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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 117}

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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   4 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{62}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{31}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,58  ~ \(\times\)  ~ 1 000
\item   0,013  ~ \(\times\)  ~ 1 000
\item   3,47  ~ \(\times\)  ~ 100
\item   839  ~ \(\times\)  ~ 10
\item   0,392  ~ \(\times\)  ~ 10
\item   0,176  ~ \(\times\)  ~ 100
\item   0,666  ~ \(\times\)  ~ 100
\item   1,6  ~ \(\times\)  ~ 1 000
\item   44,4  ~ \(\times\)  ~ 1 000
\item   76,8  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,118  ~ : ~ 100
\item   390  ~ : ~ 100
\item   1 943  ~ : ~ 1 000
\item   455  ~ : ~ 10
\item   55,55  ~ : ~ 100
\item   43,76  ~ : ~ 100
\item   62,52  ~ : ~ 10
\item   25,22  ~ : ~ 10
\item   44,89  ~ : ~ 1 000
\item   0,829  ~ : ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,21  ~ \(\times\)  ~ ... ~ = ~ 21
\item   877  ~ \(\times\)  ~ ... ~ = ~ 877 000
\item   0,902  ~ \(\times\)  ~ ... ~ = ~ 902
\item   198  ~ \(\times\)  ~ ... ~ = ~ 19 800
\item   0,561  ~ \(\times\)  ~ ... ~ = ~ 561
\item   0,097  ~ \(\times\)  ~ ... ~ = ~ 97
\item   0,03  ~ \(\times\)  ~ ... ~ = ~ 30
\item   408  ~ \(\times\)  ~ ... ~ = ~ 4 080
\item   9,34  ~ \(\times\)  ~ ... ~ = ~ 93,4
\item   0,611  ~ \(\times\)  ~ ... ~ = ~ 61,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,975  ~ \(\times\)  ~ 0,001
\item   45,36  ~ \(\times\)  ~ 0,1
\item   33,54  ~ \(\times\)  ~ 0,001
\item   746,4  ~ \(\times\)  ~ 0,001
\item   7 691  ~ \(\times\)  ~ 0,001
\item   93,66  ~ \(\times\)  ~ 0,01
\item   5 475  ~ \(\times\)  ~ 0,01
\item   77,46  ~ \(\times\)  ~ 0,1
\item   85,64  ~ \(\times\)  ~ 0,001
\item   4 071  ~ \(\times\)  ~ 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   985  ~ \(\times\)  ~ ... ~ = ~  98,5
\item   5,905  ~ \(\times\)  ~ ... ~ = ~  0,005 905
\item   8,747  ~ \(\times\)  ~ ... ~ = ~  0,008 747
\item   4 632  ~ \(\times\)  ~ ... ~ = ~  46,32
\item   5,848  ~ \(\times\)  ~ ... ~ = ~  0,058 48
\item   8 736  ~ \(\times\)  ~ ... ~ = ~  873,6
\item   3,481  ~ \(\times\)  ~ ... ~ = ~  0,003 481
\item   1,074  ~ \(\times\)  ~ ... ~ = ~  0,001 074
\item   2 520  ~ \(\times\)  ~ ... ~ = ~  252
\item   2,666  ~ \(\times\)  ~ ... ~ = ~  0,026 66
\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~ = ...~km
\item   1 ~hm~ = ...~km
\item   1 ~dm~ = ...~m
\item   1 ~cm~ = ...~dam
\item   1 ~km~ = ...~dam
\item   1 ~hm~ = ...~cm
\item   1 ~cm~ = ...~m
\item   1 ~m~ = ...~dm
\item   1 ~km~ = ...~dm
\item   1 ~dam~ = ...~dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   547,19 ~m~ = ...~km
\item   788,37 ~hg~ = ...~g
\item   415,71 ~cg~ = ...~dg
\item   852,69 ~mm~ = ...~km
\item   314,57 ~dam~ = ...~km
\item   260,59 ~cm~ = ...~km
\item   2 676,4 ~dm~ = ...~hm
\item   8 239,4 ~dL~ = ...~hL
\item   669,09 ~hL~ = ...~L
\item   7 588,9 ~g~ = ...~dg
\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   4 = \(\dfrac{400}{100}\)
\item   \(\dfrac{3200}{100}\) = \(\dfrac{320}{10}\)
\item   \(\dfrac{4}{10}\) = \(\dfrac{400}{1\,000}\)
\item   \(\dfrac{62}{10}\) = \(\dfrac{620}{100}\)
\item   \(\dfrac{31}{100}\) = \(\dfrac{310}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,58  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 580}
\item   0,013  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 13}
\item   3,47  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 347}
\item   839  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 390}
\item   0,392  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 3,92}
\item   0,176  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 17,6}
\item   0,666  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 66,6}
\item   1,6  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 1 600}
\item   44,4  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 44 400}
\item   76,8  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 680}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   9,118 ~ : ~ 100 ~ = ~{\color{red} 0,091 18}
\item   390 ~ : ~ 100 ~ = ~{\color{red} 3,9}
\item   1 943 ~ : ~ 1 000 ~ = ~{\color{red} 1,943}
\item   455 ~ : ~ 10 ~ = ~{\color{red} 45,5}
\item   55,55 ~ : ~ 100 ~ = ~{\color{red} 0,555 5}
\item   43,76 ~ : ~ 100 ~ = ~{\color{red} 0,437 6}
\item   62,52 ~ : ~ 10 ~ = ~{\color{red} 6,252}
\item   25,22 ~ : ~ 10 ~ = ~{\color{red} 2,522}
\item   44,89 ~ : ~ 1 000 ~ = ~{\color{red} 0,044 89}
\item   0,829 ~ : ~ 100 ~ = ~{\color{red} 0,008 29}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,21 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~21
\item   877 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~877 000
\item   0,902 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~902
\item   198 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~19 800
\item   0,561 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~561
\item   0,097 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~97
\item   0,03 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~30
\item   408 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~4 080
\item   9,34 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~93,4
\item   0,611 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~61,1
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,975 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,001 975
}\item   45,36 ~ \(\times\)  0,1 ~ = ~{\color{red} 4,536
}\item   33,54 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,033 54
}\item   746,4 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,746 4
}\item   7 691 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,691
}\item   93,66 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,936 6
}\item   5 475 ~ \(\times\)  0,01 ~ = ~{\color{red} 54,75
}\item   77,46 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,746
}\item   85,64 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,085 64
}\item   4 071 ~ \(\times\)  0,01 ~ = ~{\color{red} 40,71
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   985 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 98,5
\item   5,905 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,005 905
\item   8,747 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,008 747
\item   4 632 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 46,32
\item   5,848 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,058 48
\item   8 736 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 873,6
\item   3,481 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 481
\item   1,074 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,001 074
\item   2 520 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 252
\item   2,666 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,026 66
\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~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~dam~ = ~ {\color{red}  100 ~ }dm
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   547,19 ~m~ = {\color{red}  0,547 19 }~km
\item   788,37 ~hg~ = {\color{red}  78 837 }~g
\item   415,71 ~cg~ = {\color{red}  41,571 }~dg
\item   852,69 ~mm~ = {\color{red}  0,000 852 69 }~km
\item   314,57 ~dam~ = {\color{red}  3,145 7 }~km
\item   260,59 ~cm~ = {\color{red}  0,002 605 9 }~km
\item   2 676,4 ~dm~ = {\color{red}  2,676 4 }~hm
\item   8 239,4 ~dL~ = {\color{red}  8,239 4 }~hL
\item   669,09 ~hL~ = {\color{red}  66 909 }~L
\item   7 588,9 ~g~ = {\color{red}  75 889 }~dg
\end{itemize}
\end{multicols}
\end{document}
