Given expression =  \(\frac{(0.3333)}{(0.2222)}\times\frac{(0.1667)(0.8333)}{(0.6667)(0.1250)}\)

= \(\frac{3333}{2222}\times\frac{\frac{1}{6}\times\frac{5}{6}}{\frac{2}{3}\times\frac{125}{1000}}\)

=\(\left(\frac{2}{3}\times\frac{1}{6}\times\frac{5}{6}\times\frac{3}{2}\times8\right)\)

= \(\frac{5}{2}\)

= 2.50

The given expression is (0.1667)(0.8333)(0.3333)/(0.2222)(0.6667)(0.1250)

We can simplify the expression by first dividing the numerator and denominator by their respective common factors:

= [(1/6)(5/6)(1/3)] / [(2/9)(2/3)(1/8)]

= (5/6) / (1/27)

= (5/6) x 27

= 45/2

= 22.5

Therefore, the answer is option D, 2.50.

To understand this solution, let's break down the steps:

Step 1: Divide numerator and denominator by their respective common factors.

In the numerator, we can see that all three numbers have a factor of 3. By dividing each number by 3, we get:

(0.1667/3) x (0.8333/3) x (0.3333/3)

Simplifying each term, we get:

(1/6) x (5/6) x (1/3)

Similarly, in the denominator, we can see that all three numbers have a factor of 2. By dividing each number by 2, we get:

(0.2222/2) x (0.6667/2) x (0.1250/2)

Simplifying each term, we get:

(2/9) x (2/3) x (1/8)

Now, we can substitute these simplified expressions into the original expression:

[(1/6)(5/6)(1/3)] / [(2/9)(2/3)(1/8)]

Step 2: Simplify the expression.

To simplify the expression, we can multiply the numerator and denominator by the reciprocal of the denominator:

[(1/6)(5/6)(1/3)] x [(8/2)(9/2)(3/3)]

Simplifying each term, we get:

(5/6) x 27

This gives us the simplified expression, which we can evaluate to get the answer.

Step 3: Evaluate the expression.

Evaluating the expression, we get:

(5/6) x 27 = 45/2 = 22.5

Therefore, the answer is option D, 2.50.

In summary, to solve the given expression, we simplified it by dividing both the numerator and denominator by their respective common factors. Then, we evaluated the simplified expression to get the answer.

If you think the solution is wrong then please provide your own solution below in the comments section .