Find the Opposite Number: Converting 13.5 to Its Negative Value

To solve this problem, we'll find the reciprocal of the given number 13.5:

• Step 1: Convert the decimal $13.5$ to a fraction.
• Step 2: Determine the reciprocal of that fraction.
• Step 3: Simplify the fraction to its lowest terms.

Let's work through these steps:

Step 1: Convert $13.5$ to a fraction.
The decimal $13.5$ can be expressed as the fraction $\frac{135}{10}$.

Step 2: Write the reciprocal of $\frac{135}{10}$.
The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$. Thus, the reciprocal of $\frac{135}{10}$ is $\frac{10}{135}$.

Step 3: Simplify $\frac{10}{135}$.
Divide both the numerator and the denominator by their greatest common divisor, which is 5:
$\frac{10 \div 5}{135 \div 5} = \frac{2}{27}$.

Therefore, the opposite (reciprocal) number of $13.5$ is $\frac{2}{27}$.