A map shows the distance between Dallas and Houston as 2 inches. The actual distance is 240 miles. If there are 63,360 inches in a mile, find the ratio of the distance on the map to the actual distance between Dallas and Houston.

To determine the ratio of the distance on the map to the actual distance between Dallas and Houston, follow these steps:

1. **Calculate the actual distance in inches:**
The actual distance between Dallas and Houston is 240 miles. Since there are 63,360 inches in a mile, the total distance in inches can be calculated as:
\[
240 \text{ miles} \times 63,360 \text{ inches/mile} = 15,206,400 \text{ inches}
\]

2. **Given distance on the map:**
The map shows the distance as 2 inches.

3. **Form the ratio:**
The ratio of the distance on the map to the actual distance is:
\[
\text{Ratio on map to actual distance} = \frac{2 \text{ inches}}{15,206,400 \text{ inches}}
\]

4. **Simplify the ratio:**
Divide both the numerator and the denominator by 2:
\[
\frac{2 \text{ inches}}{15,206,400 \text{ inches}} = \frac{1 \text{ inch}}{7,603,200 \text{ inches}}
\]

Thus, the ratio of the distance shown on the map to the actual distance between Dallas and Houston is:
\[
\boxed{\frac{1}{7,603,200}}
\]