First, we need to find out how much money Jim spent. He spent four-tenths of $20.
Calculating that, we have:
\[ \text{Amount spent} = 0.4 \times 20 = 8 \]
Now, we can find out how much money is left by subtracting the amount spent from the total amount:
\[ \text{Amount left} = 20 - 8 = 12 \]
Next, to find the fractional part of $20 that is left, we can express the amount left as a fraction of $20:
\[ \text{Fractional part left} = \frac{12}{20} \]
Now, to simplify \(\frac{12}{20}\):
\[ \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \]
To write this as a decimal, we convert \(\frac{3}{5}\):
\[ \frac{3}{5} = 0.6 \]
Thus, the fractional part of $20 that is left, expressed in decimal form, is \(0.6\).