Question

When the repeating decimal 0.575757.......is written in simplest fraction form p/q find p_q

Answer 1

Here,

$\sf 'x '\: = 0.\overline{57}$ _____________ ( i )

$\sf 100x = 57.\overline{57}$________ ( ii )

Subtract  (1 ) from ( 2 ) :

$\sf 100x = 57.\overline{57}$

$\sf - x = 0.\overline{57}$

_________

99x = 57.0

∴ x = 57/99

here,

• p = 57
• q = 99

Now, move towards the second part of the question. We've to find ' p - q '

= 57 - 99

= - 42

Therefore,

Answer : - 42

$\rule{200}2$