One way to think of this is to think of your number line. 9/10 is to the right of zero. For the moment think of it as 1 unit to the right of zero, because 9/10 is only 1/10 left of 1, so it's close to 1.
Now, adding -9 means we move 9 units to the left of 1. That brings us 8 units to the left of zero. That's -8. But, if you remember, 9/10 is 1/10 short of 1 (to the left of 1), so we have to go another 1/10 to the left of -8, which makes it more negative by 1/10. So we make 8 bigger to 8 1/10, but it's bigger negative so that's -8 1/10.