To write the ratio of 20 inches to 3 feet using fractional notation, we first need to convert the feet to inches using the conversion \(1 \text{ foot} = 12 \text{ inches}\).
Calculating the inches in 3 feet:
\[ 3 \text{ feet} = 3 \times 12 \text{ inches} = 36 \text{ inches} \]
Now we can express the ratio of 20 inches to 36 inches as a fraction:
\[ \frac{20 \text{ inches}}{36 \text{ inches}} = \frac{20}{36} \]
Next, we simplify the fraction \(\frac{20}{36}\) by finding the greatest common divisor (GCD) of 20 and 36. The GCD of 20 and 36 is 4.
Dividing both the numerator and the denominator by their GCD:
\[ \frac{20 \div 4}{36 \div 4} = \frac{5}{9} \]
Thus, the simplified ratio of 20 inches to 3 feet is:
\[ \frac{5}{9} \]
The correct answer is \( \boxed{A} \).