If p/q degrees Celsius = q/p degrees Fahrenheit (p and q are positive), then determine the minimum positive integer value of p such that:

The base ten expansion of q is an integer if rounded to two decimal places.
To three decimal places?

Note:
To convert from degrees Fahrenheit to Celsius, subtract 32 then multiply by 5/9. To convert the other way, simply do the opposite (multiply by 9/5 and add 32). Ignore leading zeroes.