30.8k views
1 vote
Show that 2.373737... =2.37 canbe expressed in the form p/q where pand q are integers and q≠0​

1 Answer

2 votes

Answer:


2.373737....=(235)/(99)

Explanation:


2.373737....=2.\overline{37}


Let\: x=2.\overline{37}...(1)


\therefore 100x=237.\overline{37}...(2)

Subtracting equation (1) from equation (2), we find:


\therefore 100x-x=237.\overline{37}-2.\overline{37}


\therefore 99x=237+0.\overline{37}-2-0.\overline{37}


\therefore 99x=235


\therefore x=(235)/(99)


\implies 2.373737....=(235)/(99)

User RndmTsk
by
7.1k points