How do you c

onvert the decimal expansion 0.1777 ... into a rational number. (simplify)

Step-by-step 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.