Find the approximate value that should replace the question mark (?) in the equation below (note that an exact calculation is not required).

$44.44÷4.4÷10.1={(?)}^2÷100$

The correct option is 10.

We are asked to find the approximate value of the question mark (?) in the following equation:

$44.44÷4.4÷10.1={(?)}^2÷100$

Step 1: Approximate the numbers to simplify calculations.
Let us round off the numbers to their nearest manageable values:
- $44.44$ can be approximated as $44$
- $4.4$ can be approximated as $4.4$ (or notice that $44.44÷4.4=10.1$ directly)
- $10.1$ can be approximated as $10$

Step 2: Evaluate the left side of the equation.
Calculating exact division on the left-hand side:
First, $44.44÷4.4=10.1$
Next, divide by $10.1$:
$10.1÷10.1=1$

Step 3: Substitute back into the equation to solve for (?).
Now the equation becomes:
$1={(?)}^2÷100$

Multiplying both sides by $100$:
${(?)}^2=100$

Taking the square root on both sides:
$?=\sqrt{100}=10$

Hence, the approximate value that replaces the question mark is 10.