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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 214}

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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   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{6400}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{93}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{80}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,8  ~ \(\times\)  ~ 10
\item   427  ~ \(\times\)  ~ 100
\item   22,2  ~ \(\times\)  ~ 10
\item   70,3  ~ \(\times\)  ~ 100
\item   0,068  ~ \(\times\)  ~ 1 000
\item   834  ~ \(\times\)  ~ 10
\item   0,084  ~ \(\times\)  ~ 1 000
\item   889  ~ \(\times\)  ~ 10
\item   9,31  ~ \(\times\)  ~ 1 000
\item   6,88  ~ \(\times\)  ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,777  ~ : ~ 100
\item   7 532  ~ : ~ 1 000
\item   134,8  ~ : ~ 1 000
\item   6,783  ~ : ~ 10
\item   505  ~ : ~ 1 000
\item   71,56  ~ : ~ 10
\item   96,37  ~ : ~ 10
\item   2,641  ~ : ~ 100
\item   9 373  ~ : ~ 100
\item   3 256  ~ : ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,51  ~ \(\times\)  ~ ... ~ = ~ 1 510
\item   0,058  ~ \(\times\)  ~ ... ~ = ~ 58
\item   8,25  ~ \(\times\)  ~ ... ~ = ~ 82,5
\item   65,2  ~ \(\times\)  ~ ... ~ = ~ 652
\item   0,092  ~ \(\times\)  ~ ... ~ = ~ 92
\item   7,65  ~ \(\times\)  ~ ... ~ = ~ 7 650
\item   9,55  ~ \(\times\)  ~ ... ~ = ~ 955
\item   0,804  ~ \(\times\)  ~ ... ~ = ~ 8,04
\item   827  ~ \(\times\)  ~ ... ~ = ~ 82 700
\item   0,22  ~ \(\times\)  ~ ... ~ = ~ 22
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,49  ~ \(\times\)  ~ 0,01
\item   6 149  ~ \(\times\)  ~ 0,001
\item   225,4  ~ \(\times\)  ~ 0,1
\item   150  ~ \(\times\)  ~ 0,1
\item   6 943  ~ \(\times\)  ~ 0,1
\item   9,446  ~ \(\times\)  ~ 0,001
\item   83,74  ~ \(\times\)  ~ 0,1
\item   72,92  ~ \(\times\)  ~ 0,01
\item   7,151  ~ \(\times\)  ~ 0,001
\item   8 660  ~ \(\times\)  ~ 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   12,31  ~ \(\times\)  ~ ... ~ = ~  1,231
\item   5,95  ~ \(\times\)  ~ ... ~ = ~  0,595
\item   9,006  ~ \(\times\)  ~ ... ~ = ~  0,900 6
\item   3,091  ~ \(\times\)  ~ ... ~ = ~  0,030 91
\item   7,376  ~ \(\times\)  ~ ... ~ = ~  0,073 76
\item   3,436  ~ \(\times\)  ~ ... ~ = ~  0,003 436
\item   443,8  ~ \(\times\)  ~ ... ~ = ~  0,443 8
\item   37,63  ~ \(\times\)  ~ ... ~ = ~  0,376 3
\item   43,11  ~ \(\times\)  ~ ... ~ = ~  0,431 1
\item   8 954  ~ \(\times\)  ~ ... ~ = ~  895,4
\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 ~hm~ = ...~km
\item   1 ~km~ = ...~dm
\item   1 ~hm~ = ...~m
\item   1 ~m~ = ...~km
\item   1 ~dam~ = ...~m
\item   1 ~km~ = ...~dam
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~dm
\item   1 ~dm~ = ...~km
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 802,6 ~dL~ = ...~daL
\item   751,35 ~dag~ = ...~hg
\item   145,14 ~km~ = ...~cm
\item   742,92 ~mm~ = ...~cm
\item   4 245,3 ~hL~ = ...~L
\item   354,14 ~L~ = ...~dL
\item   9 382,8 ~hL~ = ...~daL
\item   2 979,3 ~mg~ = ...~g
\item   8 803,3 ~g~ = ...~dg
\item   418,75 ~dag~ = ...~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   9 = \(\dfrac{90}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{6400}{100}\) = \(\dfrac{640}{10}\)
\item   \(\dfrac{5}{10}\) = \(\dfrac{500}{1\,000}\)
\item   \(\dfrac{93}{10}\) = \(\dfrac{930}{100}\)
\item   \(\dfrac{80}{100}\) = \(\dfrac{800}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,8  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8}
\item   427  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 42 700}
\item   22,2  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 222}
\item   70,3  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 7 030}
\item   0,068  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 68}
\item   834  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 340}
\item   0,084  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 84}
\item   889  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 8 890}
\item   9,31  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 9 310}
\item   6,88  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 68,8}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,777 ~ : ~ 100 ~ = ~{\color{red} 0,007 77}
\item   7 532 ~ : ~ 1 000 ~ = ~{\color{red} 7,532}
\item   134,8 ~ : ~ 1 000 ~ = ~{\color{red} 0,134 8}
\item   6,783 ~ : ~ 10 ~ = ~{\color{red} 0,678 3}
\item   505 ~ : ~ 1 000 ~ = ~{\color{red} 0,505}
\item   71,56 ~ : ~ 10 ~ = ~{\color{red} 7,156}
\item   96,37 ~ : ~ 10 ~ = ~{\color{red} 9,637}
\item   2,641 ~ : ~ 100 ~ = ~{\color{red} 0,026 41}
\item   9 373 ~ : ~ 100 ~ = ~{\color{red} 93,73}
\item   3 256 ~ : ~ 1 000 ~ = ~{\color{red} 3,256}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   1,51 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~1 510
\item   0,058 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~58
\item   8,25 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~82,5
\item   65,2 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~652
\item   0,092 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~92
\item   7,65 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~7 650
\item   9,55 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~955
\item   0,804 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~8,04
\item   827 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~82 700
\item   0,22 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~22
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   51,49 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,514 9
}\item   6 149 ~ \(\times\)  0,001 ~ = ~{\color{red} 6,149
}\item   225,4 ~ \(\times\)  0,1 ~ = ~{\color{red} 22,54
}\item   150 ~ \(\times\)  0,1 ~ = ~{\color{red} 15
}\item   6 943 ~ \(\times\)  0,1 ~ = ~{\color{red} 694,3
}\item   9,446 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,009 446
}\item   83,74 ~ \(\times\)  0,1 ~ = ~{\color{red} 8,374
}\item   72,92 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,729 2
}\item   7,151 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,007 151
}\item   8 660 ~ \(\times\)  0,01 ~ = ~{\color{red} 86,6
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   12,31 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 1,231
\item   5,95 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,595
\item   9,006 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 0,900 6
\item   3,091 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,030 91
\item   7,376 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,073 76
\item   3,436 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,003 436
\item   443,8 ~ \(\times\) ~ {\color{red}  0,001 } ~ = ~ 0,443 8
\item   37,63 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,376 3
\item   43,11 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,431 1
\item   8 954 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 895,4
\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 ~hm~ = ~  \(\dfrac{1}{10}\) ~ km
\item   1 ~km~ = ~ {\color{red}  10 000 ~ }dm
\item   1 ~hm~ = ~ {\color{red}  100 ~ }m
\item   1 ~m~ = ~  \(\dfrac{1}{1\,000}\) ~ km
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~km~ = ~ {\color{red}  100 ~ }dam
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~ {\color{red}  10 ~ }dm
\item   1 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   2 802,6 ~dL~ = {\color{red}  28,026 }~daL
\item   751,35 ~dag~ = {\color{red}  75,135 }~hg
\item   145,14 ~km~ = {\color{red}  14 514 000 }~cm
\item   742,92 ~mm~ = {\color{red}  74,292 }~cm
\item   4 245,3 ~hL~ = {\color{red}  424 530 }~L
\item   354,14 ~L~ = {\color{red}  3 541,4 }~dL
\item   9 382,8 ~hL~ = {\color{red}  93 828 }~daL
\item   2 979,3 ~mg~ = {\color{red}  2,979 3 }~g
\item   8 803,3 ~g~ = {\color{red}  88 033 }~dg
\item   418,75 ~dag~ = {\color{red}  41 875 }~dg
\end{itemize}
\end{multicols}
\end{document}
