Convert 0.66 to a Reduced Fraction: Step-by-Step Solution

To solve this problem, let's convert the decimal number 0.66 to a fraction and then reduce it:

Step 1: Convert the decimal to a fraction.
The decimal 0.66 can be expressed as $\frac{66}{100}$ because it has two decimal places. This places the 66 over 100.

Step 2: Simplify the fraction $\frac{66}{100}$.
To simplify, we need to find the greatest common divisor (GCD) of the numerator 66 and the denominator 100.

The prime factorization of 66: $66 = 2 \times 3 \times 11$
The prime factorization of 100: $100 = 2 \times 2 \times 5 \times 5$

The common factor between them is 2. Thus, the GCD is 2.
Now, divide both the numerator and the denominator by the GCD, which is 2.

$\frac{66}{100} = \frac{66 \div 2}{100 \div 2} = \frac{33}{50}$

Therefore, the fraction $\frac{33}{50}$ is the simplest form of 0.66.

The final, reduced fraction is: $\frac{33}{50}$.