Evaluate (8.25 + 0.498) / (1 - 0.498).

Step-by-step solution

1. 1

   Evaluate the two grouped expressions first. Parentheses outrank the division bar:

   $8.25+0.498=8.748,\qquad 1-0.498=0.502$

2. 2

   Predict the size of the quotient. The denominator $0.502$ is just above $\tfrac12$, so dividing by it should roughly double the numerator: expect something near $2\times8.748\approx17.5$.

3. 3

   Convert to an exact fraction. Multiplying top and bottom by $1000$ and reducing by $2$:

   $\frac{8.748}{0.502}=\frac{8748}{502}=\frac{4374}{251}$

   Since $251$ is prime and does not divide $4374$, this is fully reduced.

4. 4

   Divide out to the required precision.

   $\frac{4374}{251}=17.426294820\ldots$

   Rounded to four decimals: $17.4263$ (the next digit $9$ rounds $2$ up to $3$).

5. 5

   Compare with the prediction. The estimate was about $17.5$ and the exact value is $17.4263$ — close enough to confirm the setup, and the small gap is explained by $0.502$ being slightly more than $\tfrac12$, which pulls the quotient slightly below double.