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Chapter 3: Problem 5

Convert the decimal or fraction to a percent. $$\frac{4}{5}$$

Short Answer

Expert verified
The fraction \(\frac{4}{5}\) is equivalent to \(80\%\) in percentage form.

Step by step solution

01

Convert the fraction to a decimal

To convert a fraction to a decimal, the numerator is divided by the denominator. Here, \(4\) (numerator) is divided by \(5\) (denominator), which results to \(0.8\).
02

Convert the decimal to a percentage

Now take the decimal resulted from Step 1, which is \(0.8\) and multiply it by \(100\) to convert it to a percentage. Doing so gives \(0.8 * 100 = 80\).
03

Add the percentage symbol

Finally, add the percentage symbol (%) to the result obtained from Step 2. Our result thus becomes \(80\%\).

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Key Concepts

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

Converting Fractions to Decimals
Converting a fraction to a decimal is a straightforward process. Fractions consist of two parts: a numerator and a denominator. Think of the numerator as how many parts you have and the denominator as the total parts that make a whole.
To change a fraction into a decimal, divide the numerator by the denominator. For example, with the fraction \( \frac{4}{5} \), you would calculate \( 4 \div 5 \).
This division gives you the decimal \( 0.8 \). This method is helpful in everyday situations where you might prefer to work with a single, continuous number (a decimal) rather than a fraction.
Decimal Conversion to Percentage
Changing a decimal to a percentage involves a simple multiplication.
Since a percentage represents a number out of 100, you can easily convert a decimal to a percentage by multiplying it by 100.
For example, if you have the decimal \( 0.8 \), you multiply \( 0.8 \times 100 \) to get\( 80 \).
  • This transformation signifies that \( 0.8 \) is essentially \( 80\% \) of a whole value.
  • Transforming decimals into percentages is useful in understanding statistical data and comparing different sets of information easily.
Percentage Calculation and Understanding
Once you have the numerical value from the decimal conversion, adding the percent symbol \((\%)\) is the final touch in turning it into a percentage.
The percent symbol essentially means "per 100," so it's showing the fraction of a hundred parts.
Percentages are extremely helpful in various real-life contexts, like sales, discounts, and statistics.
  • The number \( 80\% \) means you have 80 parts out of 100.
  • Remember, percentages offer a simple way to compare quantities easily.
By understanding how to convert fractions to decimals and then to percentages, you can navigate many mathematical challenges effortlessly!

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