College

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

A. [tex]3.99 \times 10^5[/tex] seconds
B. [tex]0.399 \times 10^6[/tex] seconds
C. [tex]3.99 \times 10^3[/tex] seconds
D. [tex]3.99 \times 10^4[/tex] seconds

Answer :

To solve the problem, let's calculate the total number of seconds Jim's playlist will play:

1. Determine the total number of songs: Jim has a total of 1,900 songs in his music library.

2. Average duration of each song: Each song has an average playing time of 3.5 minutes.

3. Convert the average time from minutes to seconds: There are 60 seconds in a minute, so we need to convert the time for each song into seconds:
[tex]\[
3.5 \text{ minutes} \times 60 \text{ seconds/minute} = 210 \text{ seconds}
\][/tex]

4. Calculate the total playing time in seconds: Multiply the number of songs by the average song duration in seconds:
[tex]\[
1,900 \text{ songs} \times 210 \text{ seconds/song} = 399,000 \text{ seconds}
\][/tex]

5. Express the total playing time in scientific notation: The number 399,000 can be expressed as:
[tex]\[
3.99 \times 10^5
\][/tex]

So, the total number of seconds the playlist will play, expressed in scientific notation, is [tex]\(3.99 \times 10^5\)[/tex] seconds. Therefore, the correct answer is:
- [tex]\(3.99 \times 10^5\)[/tex] seconds.