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### Problem Summary
Spotify pays an artist or band €0.0084 for each time their song is played. At the end of 2015, the five most played songs had the following number of streams:

1. Major Lazer - *Lean On* (feat. MØ & DJ Snake): 586 million streams
2. Ed Sheeran - *Thinking Out Loud*: 556 million streams
3. OMI - *Cheerleader* (Felix Jaehn Remix): 507 million streams
4. Mark Ronson - *Uptown Funk*: 498 million streams
5. Hozier - *Take Me to Church*: 476 million streams

The questions are:

### a) Do you think these numbers have been rounded? Why do you think so?
Yes, it is highly likely that these numbers have been rounded for simplicity, especially since all of them are multiples of one million. When dealing with such large numbers, it is common to round them to the nearest million for ease of communication and readability. Moreover, the exact number of streams is likely to fluctuate slightly, so reporting rounded figures simplifies the data.

### b) Do you think the simplification of the number affects how much the artists are paid? Why or why not?
The rounding or simplification of the numbers does not affect how much the artists are actually paid because the payment is based on the exact number of streams. Spotify's internal system would track the exact number of plays for each song down to individual streams. The rounded numbers are only for presentation purposes. Therefore, the artists are still paid based on the precise number of streams rather than the rounded figures reported.

### c) How much was each artist paid? Show your calculations.

To find how much each artist was paid, we need to multiply the number of streams by the payment rate of €0.0084 per stream.

#### Major Lazer - *Lean On* (586 million streams):
\[
586 \, \text{million} \times 0.0084 = 586 \times 10^6 \times 0.0084 = 4,922,400 \, \text{€}
\]

#### Ed Sheeran - *Thinking Out Loud* (556 million streams):
\[
556 \, \text{million} \times 0.0084 = 556 \times 10^6 \times 0.0084 = 4,670,400 \, \text{€}
\]

#### OMI - *Cheerleader* (507 million streams):
\[
507 \, \text{million} \times 0.0084 = 507 \times 10^6 \times 0.0084 = 4,258,800 \, \text{€}
\]

#### Mark Ronson - *Uptown Funk* (498 million streams):
\[
498 \, \text{million} \times 0.0084 = 498 \times 10^6 \times 0.0084 = 4,183,200 \, \text{€}
\]

#### Hozier - *Take Me to Church* (476 million streams):
\[
476 \, \text{million} \times 0.0084 = 476 \times 10^6 \times 0.0084 = 3,998,400 \, \text{€}
\]

### d) Provide your answer in standard form as well.

The artists' earnings in standard form are as follows:

1. Major Lazer - *Lean On*: \( 4.9224 \times 10^6 \, \text{€} \)
2. Ed Sheeran - *Thinking Out Loud*: \( 4.6704 \times 10^6 \, \text{€} \)
3. OMI - *Cheerleader*: \( 4.2588 \times 10^6 \, \text{€} \)
4. Mark Ronson - *Uptown Funk*: \( 4.1832 \times 10^6 \, \text{€} \)
5. Hozier - *Take Me to Church*: \( 3.9984 \times 10^6 \, \text{€} \)

Would you like further clarification on any part of the solution?

Here are some related questions to consider:

1. How would the total earnings change if Spotify increased the payout per stream to €0.01?
2. What would the earnings be for a song with 1 billion streams?
3. If an artist has multiple songs, how can you calculate their total Spotify earnings for all their tracks combined?
4. How does the payment per stream in this problem compare to streaming payouts on other platforms like Apple Music or YouTube?
5. How many more streams would a song with 400 million streams need to match the earnings of Hozier's *Take Me to Church*?

**Tip**: When calculating large sums, be mindful of the rounding method used, as it could affect your final total, even when not immediately visible in simple cases.

El servicio de reproducción de música Spotify paga a un músico o una banda cada vez que alguien reproduce su canción. Pagan 0.0084€ por reproducción de una canción. A finales de 2015, las cinco canciones más reproducidas fueron:
1. Major Lazer - 'Lean On' (feat. MØ & DJ Snake) - 586 millones de reproducciones
2. Ed Sheeran - 'Thinking Out Loud' - 556 millones de reproducciones
3. OMI - 'Cheerleader' (Felix Jaehn Remix) - 507 millones de reproducciones
4. Mark Ronson - 'Uptown Funk' - 498 millones de reproducciones
5. Hozier - 'Take Me to Church' - 476 millones de reproducciones

a) ¿Crees que estos números se han redondeado? ¿Por qué crees eso?
b) ¿Crees que la simplificación del número afecta a la cantidad de dinero que reciben los artistas? ¿por qué sí o por qué no?
c) ¿Cuánto se pagó a cada uno de estos artistas? Muestra tus cálculos. Elija un nivel apropiado de exactitud para tus respuestas
d) Dé su respuesta en forma estándar también.

Discover how much Spotify paid artists for their most-streamed songs in 2015. Calculate the earnings based on the number of streams and learn about rounding impacts. Explore detailed calculations for songs like 'Lean On' and 'Thinking Out Loud'. Suitable for middle school math students.

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