Jimwell spent four-tenths of $20. First, we calculate how much he spent:
\[ \text{Amount spent} = \frac{4}{10} \times 20 = 0.4 \times 20 = 8 \]
Next, we find out how much money is left from the initial $20:
\[ \text{Amount left} = 20 - 8 = 12 \]
Now, to find the fractional part of $20 that was left, we express the amount left as a fraction of the original $20:
\[ \text{Fraction left} = \frac{12}{20} = \frac{3}{5} \]
To convert this fraction into decimal form:
\[ \frac{3}{5} = 0.6 \]
Thus, the decimal form of the fractional part of $20 that was left is:
\[ \boxed{0.6} \]