The given formula of nickel oxide is Ni_0.98O_1.00

Thus, the ratio of the number of Ni atoms to the number of O atoms is,

Ni : O = 0.98 : 1.00 = 98 : 100

Now, Total charge on 100 O^2- ions = 100 × (-2) = -200

Let the number of Ni²⁺ ions = x.

So, the number of Ni³⁺ ions is 98 - x.

Now, Total charge on Ni²⁺ ions = x(+2) = +2x

Similarly, total charge on Ni³⁺ ions = (98 - x)(+3) = 294 - 3x

As, the compound is neutral,

we can write: 2x + (294 - 3x) + (-200) = 0

⇒ −x + 94 = 0

⇒ x = 94

Therefore, number of Ni²⁺ ions = 94

And, number of Ni³⁺ ions = 98 − 94 = 4

Thus, the fraction of nickel that exists as Ni²⁺= 94/98 = 0.0959

And, the fraction of nickel that exists as Ni³⁺ = 4/98 = 0.041