Question

How do you c
onvert the decimal expansion 0.1777... into a rational number. (simplify)

Answer 1

Explanation:

converting a repeating decimal to ratio of integers

Hi,

This is 0.1+0.077777=110+7100+71000+... where you have a GP to sum.

Or Let x=0.0777.. so that 10x=0.777.. .

Subtracting gives 9x=0.7 and so x=790 . Now just add 110+790 and simplify.