Express 0.007777777..... In rational number?

Question

1937 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-25T07:38:22

$7/900$

$" let "x=0.007777777....$

since only one digit recurs multiply by $10$

$10x=0.07color(red)(777...)$

$color(white)(aa)x=0.00color(red)(77777..)$

subtract, the digits in red cancel

$:.9x=0.07$

$=>x=0.07/9xx100/100$

$x=7/900$