First, we need to find out how much Jimwell spent. He spent four-tenths of $20.
To calculate the amount spent:
\[ \text{Amount spent} = 0.4 \times 20 = 8 \]
Next, we determine how much money is left after the spending:
\[ \text{Amount left} = 20 - 8 = 12 \]
Now, we need to express the remaining amount, $12, as a fractional part of $20. This can be done by dividing 12 by 20:
\[ \frac{12}{20} = 0.6 \]
Therefore, the fractional part of $20 that is left, expressed in decimal form, is:
\[ \boxed{0.6} \]