To express the ratio of 20 inches to 3 feet using fractional notation, we first convert 3 feet into inches. Since 1 foot equals 12 inches, we can calculate:
\[ 3 \text{ feet} = 3 \times 12 \text{ inches} = 36 \text{ inches} \]
Now, we can write 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 \(\frac{20}{36}\). We can find the greatest common divisor (GCD) of 20 and 36, which is 4. We divide 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 in fractional notation is:
\[ \frac{5}{9} \]