Jims music library on his phone holds 1,900 songs. The songs have an average time of 3.5 minutes. Use scientific notation to find the total number of seconds the playlist will play. Express the answer to the exact decimal place.

Answer 1

To find the total playtime of Jim's music library in seconds, we can follow these steps:

1. Calculate the total playtime in minutes: \[ \text{Total playtime in minutes} = \text{Number of songs} \times \text{Average time per song} \] \[ = 1900 , \text{songs} \times 3.5 , \text{minutes/song} = 6650 , \text{minutes} \]

2. Convert the total playtime to seconds: Since there are 60 seconds in a minute, we multiply the total playtime in minutes by 60: \[ \text{Total playtime in seconds} = 6650 , \text{minutes} \times 60 , \text{seconds/minute} = 399000 , \text{seconds} \]

3. Express this number in scientific notation: \[ 399000 = 3.99000 \times 10^5 \text{ seconds} \] We can round this to three significant figures: \[ 3.99 \times 10^5 \text{ seconds} \]

So, the total playtime of Jim's music library is \( \mathbf{3.99 \times 10^5} \) seconds.