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Chapter 4: Problem 84

Find the number of FM high-definition radio stations that transmitted iTunes- tagging UFID codes. Round to the nearest whole number. Of about 1,600 FM HD Radio stations in early 2009, most delivered song and artist metadata, and about two-thirds of those transmitted iTunes-tagging UFID codes. (Source: www.twice.com, March 9, 2009)

Short Answer

Expert verified
1067

Step by step solution

01

Understand total FM HD Radio stations

The problem states that there are about 1,600 FM HD Radio stations.
02

Calculate radios transmitting metadata

It is given that most FM HD Radio stations delivered song and artist metadata. 'Most' usually refers to a significant majority, but for this exercise, we can assume it is close to all. Therefore, assume all 1,600 deliver metadata.
03

Determine stations with iTunes-tagging UFID codes

About two-thirds of the stations delivering metadata transmitted iTunes-tagging UFID codes. Two-thirds is calculated as follows: \( \text{Number of stations} = \frac{2}{3} \times 1600 \)
04

Perform the multiplication

Multiply 1600 by two-thirds: \( \frac{2}{3} \times 1600 = \frac{3200}{3} = 1066.67 \)
05

Round to the nearest whole number

Since the result is 1066.67, round to the nearest whole number: 1067.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

basic algebra calculations
Understanding basic algebra calculations is essential for solving many problems. In this exercise, we start by identifying the total number of FM HD Radio stations. The problem states that there are about 1,600 stations, which means we start our calculations with this number.

We then need to determine how many of these stations transmitted iTunes-tagging UFID codes. We are given that about two-thirds of the stations transmitted these codes. To find two-thirds of 1600, we set up the fraction multiplication problem: \( \frac{2}{3} \times 1600 \).

Performing this multiplication gives us the next step in our calculation.
fractions multiplication
The next key concept is fractions multiplication. Multiplying fractions by whole numbers is a common operation in algebra. For our problem, we need to multiply 1600 by two-thirds to find the number of stations transmitting iTunes-tagging codes.

Here is the step-by-step multiplication process:
  • First, represent two-thirds as a fraction: \( \frac{2}{3} \).
  • Next, multiply this fraction by 1600: \( \frac{2}{3} \times 1600 \).
  • We do this by multiplying the numerator (2) by 1600, which gives us 3200, and then divide by the denominator (3), resulting in: \( \frac{3200}{3} = 1066.67 \).
This process converts our problem into a solvable equation.
rounding numbers
The final concept in our problem is rounding numbers. After performing our fraction multiplication, we end up with the number 1066.67. Depending on the context, it is often necessary to round this number to make it more practical for reporting or further calculations.

Rounding involves approximating a number to its nearest whole number, ten, hundred, etc. In our case, we round to the nearest whole number:
  • Since 1066.67 is closer to 1067 than 1066, we round up to 1067.
  • Thus, the rounded number of stations transmitting iTunes-tagging codes is 1067.
This final step ensures we have a clear, understandable answer to the problem.

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