Estimate the approximate value that should replace the question mark (?) in the mathematical expression below. (Note: Precise calculation of the exact value is not required.)

$59.90\%\text{of}1020.11-9.88\%\text{of}79.91=?{}^3+92.01$

The correct option is 8.

To find the approximate value of the question mark (?), we can round each number in the expression to its nearest convenient whole number for easier calculation:

• 59.90% ≈ 60%

• 1020.11 ≈ 1020

• 9.88% ≈ 10%

• 79.91 ≈ 80

• 92.01 ≈ 92

Now, substitute these approximate values into the given equation:

$(60\%\text{of}1020)-(10\%\text{of}80)={?}^3+92$

Calculate each part step-by-step:

1. 60% of 1020:

$\frac{60}{100}\times 1020=6\times 102=612$

2. 10% of 80:

$\frac{10}{100}\times 80=8$

Substitute these values back into the left side of the equation:

$612-8={?}^3+92$

$604={?}^3+92$

Subtract 92 from both sides to solve for ?³:

${?}^3=604-92$

${?}^3=512$

Taking the cube root of both sides:

$?=\sqrt[3]{512}=8$

Therefore, the approximate value that should replace the question mark (?) is 8.