The given numbers have equal number of digits (3).
So, we start by comparing the digits at the hundreds place.
Since 9>8, we have 968, 986 and 998 to be greater than 899 and 889.
Now, we compare the digits at the tens place for 968, 986 and 998. Since 6<8<9, we have 968<986<998.
Doing the same for 899 and 889, since 8<9, we have 889<899.
∴889<899<968<986<998