The dielectric constant for air is 1.006. The speed of em wave travelling in air is `axx10^8ms^-1`, where a is about:

Explanation

To solve the problem, we need to find the value of \( a \) in the expression for the speed of electromagnetic waves in air, which is given as \( a \times 10^8 \, \text{ms}^{-1} \).

### Step-by-Step Solution:

1. **Understand the relationship between speed of light and dielectric constant**:
The speed of electromagnetic waves in a medium is given by the formula:
\[ v = \frac{c}{\sqrt{\epsilon_r}} \]
where \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \, \text{ms}^{-1} \)) and \( \epsilon_r \) is the dielectric constant of the medium.

2. **Identify the dielectric constant for air**:
The problem states that the dielectric constant for air is \( \epsilon_r = 1.006 \).

3. **Calculate the speed of EM waves in air**:
Using the formula, we can substitute the values:
\[ v = \frac{3 \times 10^8}{\sqrt{1.006}} \]

4. **Calculate \( \sqrt{1.006} \)**:
Approximating \( \sqrt{1.006} \):
\[ \sqrt{1.006} \approx 1.003 \]

5. **Substitute back into the speed formula**:
Now, substituting this back into the equation for \( v \):
\[ v \approx \frac{3 \times 10^8}{1.003} \approx 2.99 \times 10^8 \, \text{ms}^{-1} \]

6. **Express the speed in the form \( a \times 10^8 \)**:
We can express \( 2.99 \times 10^8 \) as:
\[ v \approx 2.99 \times 10^8 \, \text{ms}^{-1} \implies a \approx 2.99 \]

7. **Round \( a \) to a suitable value**:
Since the problem asks for \( a \) to be about a certain value, we can round \( 2.99 \) to \( 3 \).

### Final Answer:
Thus, the value of \( a \) is approximately \( 3 \).