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\newcommand{\soustitre}{Cycle 3 --- Fiche n\textdegree 170}

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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   6 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   7 = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\item   \(\dfrac{42}{10}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{100}\)
\item   \(\dfrac{52}{100}\) = \(\dfrac{\fbox{\rule[-0.45ex]{0pt}{1.8ex}\hspace{1.4em}}}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,028  ~ \(\times\)  ~ 10
\item   232  ~ \(\times\)  ~ 100
\item   0,094  ~ \(\times\)  ~ 100
\item   0,6  ~ \(\times\)  ~ 10
\item   5,39  ~ \(\times\)  ~ 1 000
\item   261  ~ \(\times\)  ~ 10
\item   0,85  ~ \(\times\)  ~ 100
\item   0,189  ~ \(\times\)  ~ 1 000
\item   19  ~ \(\times\)  ~ 100
\item   0,011  ~ \(\times\)  ~ 1 000
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,336  ~ : ~ 1 000
\item   9 031  ~ : ~ 100
\item   9 597  ~ : ~ 10
\item   8 800  ~ : ~ 100
\item   65,86  ~ : ~ 10
\item   5 721  ~ : ~ 10
\item   5 606  ~ : ~ 10
\item   87,07  ~ : ~ 1 000
\item   897,7  ~ : ~ 10
\item   5,562  ~ : ~ 10
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,8  ~ \(\times\)  ~ ... ~ = ~ 178
\item   306  ~ \(\times\)  ~ ... ~ = ~ 306 000
\item   607  ~ \(\times\)  ~ ... ~ = ~ 607 000
\item   585  ~ \(\times\)  ~ ... ~ = ~ 58 500
\item   965  ~ \(\times\)  ~ ... ~ = ~ 96 500
\item   740  ~ \(\times\)  ~ ... ~ = ~ 740 000
\item   0,073  ~ \(\times\)  ~ ... ~ = ~ 0,73
\item   604  ~ \(\times\)  ~ ... ~ = ~ 604 000
\item   0,027  ~ \(\times\)  ~ ... ~ = ~ 27
\item   18  ~ \(\times\)  ~ ... ~ = ~ 180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 957  ~ \(\times\)  ~ 0,01
\item   5 600  ~ \(\times\)  ~ 0,001
\item   181,6  ~ \(\times\)  ~ 0,01
\item   72,42  ~ \(\times\)  ~ 0,1
\item   8,886  ~ \(\times\)  ~ 0,1
\item   575,7  ~ \(\times\)  ~ 0,01
\item   779,1  ~ \(\times\)  ~ 0,001
\item   966,1  ~ \(\times\)  ~ 0,001
\item   213,8  ~ \(\times\)  ~ 0,1
\item   44,73  ~ \(\times\)  ~ 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   5 860  ~ \(\times\)  ~ ... ~ = ~  58,6
\item   2 192  ~ \(\times\)  ~ ... ~ = ~  21,92
\item   862,9  ~ \(\times\)  ~ ... ~ = ~  86,29
\item   1,13  ~ \(\times\)  ~ ... ~ = ~  0,011 3
\item   3,42  ~ \(\times\)  ~ ... ~ = ~  0,034 2
\item   810,8  ~ \(\times\)  ~ ... ~ = ~  8,108
\item   542,1  ~ \(\times\)  ~ ... ~ = ~  54,21
\item   308,9  ~ \(\times\)  ~ ... ~ = ~  30,89
\item   42,82  ~ \(\times\)  ~ ... ~ = ~  4,282
\item   6 324  ~ \(\times\)  ~ ... ~ = ~  632,4
\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 ~dm~ = ...~km
\item   1 ~dam~ = ...~km
\item   1 ~km~ = ...~cm
\item   1 ~cm~ = ...~dam
\item   1 ~cm~ = ...~dm
\item   1 ~dam~ = ...~m
\item   1 ~dam~ = ...~hm
\item   1 ~m~ = ...~hm
\item   1 ~dm~ = ...~m
\item   1 ~hm~ = ...~dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 325,8 ~kL~ = ...~daL
\item   634,21 ~mm~ = ...~dm
\item   973,28 ~cm~ = ...~km
\item   6 211,1 ~dL~ = ...~cL
\item   790,08 ~mg~ = ...~dg
\item   228 ~dam~ = ...~cm
\item   364,57 ~cm~ = ...~m
\item   822,45 ~dag~ = ...~mg
\item   1 944,3 ~hL~ = ...~daL
\item   5 986,1 ~kg~ = ...~cg
\end{itemize}
\end{multicols}
\newpage
\section*{\textcolor{red}{Correction}}

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

\begin{multicols}{2}
\begin{itemize}
\item   6 = \(\dfrac{60}{10}\)
\item   7 = \(\dfrac{700}{100}\)
\item   \(\dfrac{5100}{100}\) = \(\dfrac{510}{10}\)
\item   \(\dfrac{2}{10}\) = \(\dfrac{200}{1\,000}\)
\item   \(\dfrac{42}{10}\) = \(\dfrac{420}{100}\)
\item   \(\dfrac{52}{100}\) = \(\dfrac{520}{1\,000}\)
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,028  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 0,28}
\item   232  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 23 200}
\item   0,094  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 9,4}
\item   0,6  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 6}
\item   5,39  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 5 390}
\item   261  ~ \(\times\)  ~ 10 ~ = ~{\color{red} 2 610}
\item   0,85  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 85}
\item   0,189  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 189}
\item   19  ~ \(\times\)  ~ 100 ~ = ~{\color{red} 1 900}
\item   0,011  ~ \(\times\)  ~ 1 000 ~ = ~{\color{red} 11}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   0,336 ~ : ~ 1 000 ~ = ~{\color{red} 0,000 336}
\item   9 031 ~ : ~ 100 ~ = ~{\color{red} 90,31}
\item   9 597 ~ : ~ 10 ~ = ~{\color{red} 959,7}
\item   8 800 ~ : ~ 100 ~ = ~{\color{red} 88}
\item   65,86 ~ : ~ 10 ~ = ~{\color{red} 6,586}
\item   5 721 ~ : ~ 10 ~ = ~{\color{red} 572,1}
\item   5 606 ~ : ~ 10 ~ = ~{\color{red} 560,6}
\item   87,07 ~ : ~ 1 000 ~ = ~{\color{red} 0,087 07}
\item   897,7 ~ : ~ 10 ~ = ~{\color{red} 89,77}
\item   5,562 ~ : ~ 10 ~ = ~{\color{red} 0,556 2}
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   17,8 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~178
\item   306 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~306 000
\item   607 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~607 000
\item   585 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~58 500
\item   965 ~ \(\times\)  ~ {\color{red} 100 ~ }= ~96 500
\item   740 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~740 000
\item   0,073 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~0,73
\item   604 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~604 000
\item   0,027 ~ \(\times\)  ~ {\color{red} 1 000 ~ }= ~27
\item   18 ~ \(\times\)  ~ {\color{red} 10 ~ }= ~180
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 957 ~ \(\times\)  0,01 ~ = ~{\color{red} 39,57
}\item   5 600 ~ \(\times\)  0,001 ~ = ~{\color{red} 5,6
}\item   181,6 ~ \(\times\)  0,01 ~ = ~{\color{red} 1,816
}\item   72,42 ~ \(\times\)  0,1 ~ = ~{\color{red} 7,242
}\item   8,886 ~ \(\times\)  0,1 ~ = ~{\color{red} 0,888 6
}\item   575,7 ~ \(\times\)  0,01 ~ = ~{\color{red} 5,757
}\item   779,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,779 1
}\item   966,1 ~ \(\times\)  0,001 ~ = ~{\color{red} 0,966 1
}\item   213,8 ~ \(\times\)  0,1 ~ = ~{\color{red} 21,38
}\item   44,73 ~ \(\times\)  0,01 ~ = ~{\color{red} 0,447 3
}\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   5 860 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 58,6
\item   2 192 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 21,92
\item   862,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 86,29
\item   1,13 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,011 3
\item   3,42 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 0,034 2
\item   810,8 ~ \(\times\) ~ {\color{red}  0,01 } ~ = ~ 8,108
\item   542,1 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 54,21
\item   308,9 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 30,89
\item   42,82 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 4,282
\item   6 324 ~ \(\times\) ~ {\color{red}  0,1 } ~ = ~ 632,4
\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 ~dm~ = ~  \(\dfrac{1}{10\,000}\) ~ km
\item   1 ~dam~ = ~  \(\dfrac{1}{100}\) ~ km
\item   1 ~km~ = ~ {\color{red}  100 000 ~ }cm
\item   1 ~cm~ = ~  \(\dfrac{1}{1\,000}\) ~ dam
\item   1 ~cm~ = ~  \(\dfrac{1}{10}\) ~ dm
\item   1 ~dam~ = ~ {\color{red}  10 ~ }m
\item   1 ~dam~ = ~  \(\dfrac{1}{10}\) ~ hm
\item   1 ~m~ = ~  \(\dfrac{1}{100}\) ~ hm
\item   1 ~dm~ = ~  \(\dfrac{1}{10}\) ~ m
\item   1 ~hm~ = ~ {\color{red}  10 ~ }dam
\end{itemize}
\end{multicols}

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

\begin{multicols}{2}
\begin{itemize}
\item   3 325,8 ~kL~ = {\color{red}  332 580 }~daL
\item   634,21 ~mm~ = {\color{red}  6,342 1 }~dm
\item   973,28 ~cm~ = {\color{red}  0,009 732 8 }~km
\item   6 211,1 ~dL~ = {\color{red}  62 111 }~cL
\item   790,08 ~mg~ = {\color{red}  7,900 8 }~dg
\item   228 ~dam~ = {\color{red}  228 000 }~cm
\item   364,57 ~cm~ = {\color{red}  3,645 7 }~m
\item   822,45 ~dag~ = {\color{red}  8 224 500 }~mg
\item   1 944,3 ~hL~ = {\color{red}  19 443 }~daL
\item   5 986,1 ~kg~ = {\color{red}  598 610 000 }~cg
\end{itemize}
\end{multicols}
\end{document}
