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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 210}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   2 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\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   \(\dfrac{32}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,29  ~ \(\times\)  ~ 10
\item   4,9  ~ \(\times\)  ~ 10
\item   0,562  ~ \(\times\)  ~ 1 000
\item   877  ~ \(\times\)  ~ 1 000
\item   0,086  ~ \(\times\)  ~ 10
\item   0,68  ~ \(\times\)  ~ 10
\item   0,036  ~ \(\times\)  ~ 10
\item   0,84  ~ \(\times\)  ~ 1 000
\item   9,87  ~ \(\times\)  ~ 100
\item   807  ~ \(\times\)  ~ 100
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,79  ~ : ~ 1 000
\item   1,98  ~ : ~ 1 000
\item   3 825  ~ : ~ 10
\item   415,1  ~ : ~ 100
\item   8,258  ~ : ~ 10
\item   571  ~ : ~ 10
\item   911  ~ : ~ 100
\item   691,8  ~ : ~ 100
\item   26,17  ~ : ~ 1 000
\item   2,484  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,007  ~ \(\times\)  ~ ... ~ = ~ 0,07
\item   591  ~ \(\times\)  ~ ... ~ = ~ 5 910
\item   0,51  ~ \(\times\)  ~ ... ~ = ~ 5,1
\item   2,91  ~ \(\times\)  ~ ... ~ = ~ 2 910
\item   0,044  ~ \(\times\)  ~ ... ~ = ~ 44
\item   0,044  ~ \(\times\)  ~ ... ~ = ~ 44
\item   502  ~ \(\times\)  ~ ... ~ = ~ 50 200
\item   587  ~ \(\times\)  ~ ... ~ = ~ 5 870
\item   0,558  ~ \(\times\)  ~ ... ~ = ~ 55,8
\item   0,075  ~ \(\times\)  ~ ... ~ = ~ 0,75
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 565  ~ \(\times\)  ~ 0,1
\item   271  ~ \(\times\)  ~ 0,01
\item   7 185  ~ \(\times\)  ~ 0,001
\item   8,96  ~ \(\times\)  ~ 0,1
\item   134  ~ \(\times\)  ~ 0,01
\item   5 249  ~ \(\times\)  ~ 0,01
\item   9,668  ~ \(\times\)  ~ 0,1
\item   8 709  ~ \(\times\)  ~ 0,001
\item   8,029  ~ \(\times\)  ~ 0,01
\item   177,2  ~ \(\times\)  ~ 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   8,803  ~ \(\times\)  ~ ... ~ = ~  0,880 3
\item   5,971  ~ \(\times\)  ~ ... ~ = ~  0,059 71
\item   68,8  ~ \(\times\)  ~ ... ~ = ~  6,88
\item   9 624  ~ \(\times\)  ~ ... ~ = ~  96,24
\item   731,2  ~ \(\times\)  ~ ... ~ = ~  7,312
\item   2 101  ~ \(\times\)  ~ ... ~ = ~  210,1
\item   4,61  ~ \(\times\)  ~ ... ~ = ~  0,461
\item   7,199  ~ \(\times\)  ~ ... ~ = ~  0,007 199
\item   49,2  ~ \(\times\)  ~ ... ~ = ~  0,049 2
\item   686,7  ~ \(\times\)  ~ ... ~ = ~  0,686 7
\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~ = ...~dm
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~km
\item   1 ~cm~ = ...~m
\item   1 ~dam~ = ...~m
\item   1 ~hm~ = ...~cm
\item   1 ~hm~ = ...~m
\item   1 ~hm~ = ...~dam
\item   1 ~km~ = ...~m
\item   1 ~hm~ = ...~km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   357,56 ~mm~ = ...~dm
\item   614,59 ~g~ = ...~dg
\item   834,3 ~hL~ = ...~daL
\item   2 798,8 ~mL~ = ...~dL
\item   8 898,8 ~L~ = ...~dL
\item   485,89 ~cm~ = ...~km
\item   4 098,5 ~dag~ = ...~kg
\item   1 829,4 ~cg~ = ...~g
\item   978,16 ~dag~ = ...~mg
\item   749,2 ~dag~ = ...~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   7 = \(\dfrac{70}{10}\)
\item   2 = \(\dfrac{200}{100}\)
\item   \(\dfrac{9800}{100}\) = \(\dfrac{980}{10}\)
\item   \(\dfrac{7}{10}\) = \(\dfrac{700}{1\,000}\)
\item   \(\dfrac{32}{10}\) = \(\dfrac{320}{100}\)
\item   \(\dfrac{99}{100}\) = \(\dfrac{990}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,29  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2,9}
\item   4,9  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 49}
\item   0,562  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 562}
\item   877  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 877 000}
\item   0,086  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,86}
\item   0,68  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6,8}
\item   0,036  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,36}
\item   0,84  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 840}
\item   9,87  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 987}
\item   807  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 80 700}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   7,79 ~ : ~ 1 000 ~ = ~{\color{red} 0,007 79}
\item   1,98 ~ : ~ 1 000 ~ = ~{\color{red} 0,001 98}
\item   3 825 ~ : ~ 10 ~ = ~{\color{red} 382,5}
\item   415,1 ~ : ~ 100 ~ = ~{\color{red} 4,151}
\item   8,258 ~ : ~ 10 ~ = ~{\color{red} 0,825 8}
\item   571 ~ : ~ 10 ~ = ~{\color{red} 57,1}
\item   911 ~ : ~ 100 ~ = ~{\color{red} 9,11}
\item   691,8 ~ : ~ 100 ~ = ~{\color{red} 6,918}
\item   26,17 ~ : ~ 1 000 ~ = ~{\color{red} 0,026 17}
\item   2,484 ~ : ~ 10 ~ = ~{\color{red} 0,248 4}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,007 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,07
\item   591 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 910
\item   0,51 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5,1
\item   2,91 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~2 910
\item   0,044 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~44
\item   0,044 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~44
\item   502 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~50 200
\item   587 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~5 870
\item   0,558 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~55,8
\item   0,075 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,75
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1 565 ~ \(\times\)  0,1 ~ = ~{\color{red} 156,5
}\item   271 ~ \(\times\)  0,01 ~ = ~{\color{red} 2,71
}\item   7 185 ~ \(\times\)  0,001 ~ = ~{\color{red} 7,185
}\item   8,96 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,896
}\item   134 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,34
}\item   5 249 ~ \(\times\)  0,01 ~ = ~{\color{red} 52,49
}\item   9,668 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,966 8
}\item   8 709 ~ \(\times\)  0,001 ~ = ~{\color{red} 8,709
}\item   8,029 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,080 29
}\item   177,2 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,772
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   8,803 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,880 3
\item   5,971 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,059 71
\item   68,8 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 6,88
\item   9 624 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 96,24
\item   731,2 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 7,312
\item   2 101 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 210,1
\item   4,61 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,461
\item   7,199 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,007 199
\item   49,2 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,049 2
\item   686,7 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,686 7
\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}  10 000 ~ }dm
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{100\,000}\) ~ km
\item   1 ~cm~ = ~  \(\dfrac{1}{100}\) ~ m
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 000 ~ }cm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\item   1 ~km~ = ~ {\color{red}  1 000 ~ }m
\item   1 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   357,56 ~mm~ = {\color{red}  3,575 6 }~dm
\item   614,59 ~g~ = {\color{red}  6 145,9 }~dg
\item   834,3 ~hL~ = {\color{red}  8 343 }~daL
\item   2 798,8 ~mL~ = {\color{red}  27,988 }~dL
\item   8 898,8 ~L~ = {\color{red}  88 988 }~dL
\item   485,89 ~cm~ = {\color{red}  0,004 858 9 }~km
\item   4 098,5 ~dag~ = {\color{red}  40,985 }~kg
\item   1 829,4 ~cg~ = {\color{red}  18,294 }~g
\item   978,16 ~dag~ = {\color{red}  9 781 600 }~mg
\item   749,2 ~dag~ = {\color{red}  74,92 }~hg
\end{itemize}
\end{multicols}
\end{document}
