Problem 17 - Prealgebra

Question

In a survey, \(55 \%\) of those surveyed said that they get the news from their local television station, three-fifths said that they get the news from a daily newspaper, and 0.4 said they got their news from the Internet. Which news source has the most users?

Step-by-Step Solution

Answer

The daily newspaper has the most users with 0.6 or 60%.

Step 1: Convert Percentages to Decimals

First, we need to convert any percentage values from the survey results into decimals to compare them easily. The percentage of people who get their news from their local television station is given as \(55\%\). To convert \(55\%\) to a decimal, divide by 100: \(55\% = 0.55\). For the daily newspaper, it is given as a fraction \(\frac{3}{5}\), which is already in decimal form as \(0.6\). The Internet users are given directly as \(0.4\).

Step 2: Compare the Decimal Values

Now that we have all the values in decimal form, we can compare them to determine which source has the most users. We have: Local TV: \(0.55\), Newspaper: \(0.6\), Internet: \(0.4\).

Step 3: Identify the Largest Value

Compare the decimal values to find the largest one. \(0.6 > 0.55 > 0.4\). Thus, the fraction for the daily newspaper converts to the decimal 0.6, which is the largest among the three news sources.

Key Concepts

Percentage Conversion

Turning percentage values into decimals is a crucial first step when you need to make comparisons on the same scale. It makes data easier to work with and compare.
To convert a percentage to a decimal, you simply divide the percentage value by 100. This is because 'percent' refers to 'per hundred'. Here is a simple formula you can use:

• Convert: \( X\% = \frac{X}{100} \)

For example, if we want to convert \(55\%\) to a decimal, we do the following calculation:

• \(55\% = \frac{55}{100} = 0.55\)

This mathematically reduces the percentage to a form where it can be easily compared with other decimal values.

Decimal Comparison

Once all values are converted to decimals, comparing them is as simple as comparing any basic numbers. This step allows us to see which decimal is largest or smallest.
When comparing decimal numbers, you can line up the decimal points and compare digit by digit, starting from the left. Here’s a tip: focus first on the whole number part, if they are the same, move to the tenths place, then to the hundredths, and so on.
For instance, to compare \(0.55\), \(0.6\), and \(0.4\):

• Start by comparing the tenths digit (0.5, 0.6, 0.4).
• The largest tenths digit is 0.6.
• Thus, \(0.6\) represents the largest proportion of users.

With this method, it becomes clear which number is greater or lesser, helping you draw meaningful conclusions from your data.

Fractions to Decimals

Converting fractions into decimals is another essential skill in basic arithmetic. It can make arithmetic operations and comparisons significantly easier.
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number).

• For example, convert \(\frac{3}{5}\) into a decimal: \(\frac{3}{5} = 0.6\).

Using this approach, anyone can transform a fractional value into a decimal form accurately and efficiently.
Once you have all values in the same form, whether decimal, fraction, or percentage converted to decimals, they become easy to compare, as shown in our original exercise about news source preferences.