Question

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

Answer 1

Answer:

$2.373737....=\frac{235}{99}$

Step-by-step 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:

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

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

$\therefore 99x=235$

$\therefore x=\frac{235}{99}$

$\implies 2.373737....=\frac{235}{99}$