To find the total playback time of Jim's music library in seconds, we start by calculating the total time in minutes and then convert that to seconds.
- Total number of songs: 1,900 songs
- Average length of each song: 3.5 minutes
Now, we calculate the total length of the playlist in minutes:
\[ \text{Total time in minutes} = \text{Number of songs} \times \text{Average time per song} = 1900 \times 3.5 \]
Calculating this:
\[ 1900 \times 3.5 = 6650 \text{ minutes} \]
Next, we convert the total time from minutes to seconds. Since 1 minute has 60 seconds:
\[ \text{Total time in seconds} = 6650 \times 60 \]
Calculating this:
\[ 6650 \times 60 = 399000 \text{ seconds} \]
Now we express \(399000\) in scientific notation. We can rewrite \(399000\) as:
\[ 399000 = 3.99 \times 10^5 \]
Thus, the total number of seconds the playlist will play is:
\[ \boxed{3.99 \times 10^5 \text{ seconds}} \]