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.

To find the approximate value of the question mark (?), let's analyze the given equation step-by-step:

$44.44÷4.4÷10.1={(?)}^2÷100$

Step 1: Simplify the left-hand side (LHS) by using approximate values.

We can round off the numbers to their nearest simple whole numbers or decimals to perform quick estimation:

$44.44\approx 44.4$

$4.4\approx 4.4$

$10.1\approx 10$

First, calculate

$44.44÷4.4\approx 10.1$

Next, divide this result by 10.1:

$10.1÷10.1=1$

So, the approximate value of the LHS is 1.

Step 2: Set up the equation with LHS = 1.

$1={(?)}^2÷100$

Step 3: Solve for (?).

Multiply both sides by 100:

${(?)}^2=1\times 100$

${(?)}^2=100$

Take the square root of both sides:

$?=\sqrt{100}$

$?=10$

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