Question

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

Answer 1

`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)`