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Chapter 6: Problem 8

Write \(\frac{4}{9}\) as a percent. A. \(4 . \overline{4} \%\) 8\. \(0 . \overline{4} \%\) C. 44496 \(44 . \overline{4} \%\)

Short Answer

Expert verified
The answer is D) \(44.\overline{4}\%\).

Step by step solution

01

Understand the Problem

The exercise asks us to convert a fraction, \( \frac{4}{9} \), into a percentage. A percentage is a way of expressing a number as a fraction of 100, meaning we want to multiply the fraction by 100 to find its percentage form.
02

Convert the Fraction to a Decimal

To convert \( \frac{4}{9} \) to a percentage, first convert the fraction to a decimal by dividing the numerator by the denominator: \( 4 \div 9 = 0.4444\ldots \). This is a repeating decimal, which can be written as \( 0.\overline{4} \).
03

Multiply by 100 to Find the Percentage

To convert the decimal \( 0.\overline{4} \) into a percentage, multiply it by 100: \( 0.\overline{4} \times 100 = 44.\overline{4} \). This calculation results in \( 44.\overline{4} \% \), where the repeated decimal 4 continues infinitely in the tenths place.
04

Select the Correct Answer

Compare the calculated percentage \( 44.\overline{4}\% \) with the given options. The correct choice is D) \( 44.\overline{4} \% \).

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Key Concepts

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

Converting Fractions
Converting fractions into other forms, such as decimals or percentages, is a critical math skill. Fractions represent division, so the first step in converting a fraction like \( \frac{4}{9} \) to a decimal is to actually perform the division:
  • Divide the numerator (4) by the denominator (9).
  • This gives you the decimal form of the fraction: \( 0.4444\ldots \).
  • The decimal repeats and can be represented as \( 0.\overline{4} \).
Once you have the decimal, converting to a percentage is straightforward. Remember your goal is to express the fraction as a part of 100:
  • Multiply the decimal by 100 to convert it to a percentage.
  • For instance, \( 0.\overline{4} \times 100 = 44.\overline{4} \% \).
Understanding these foundational steps can help you tackle any conversion problem with fractions.
Repeating Decimals
A repeating decimal is a decimal representation of a number that has digits that repeat forever. They appear frequently when converting fractions to decimals. For example, when you divide 4 by 9, you get 0.4444. The 4 repeats indefinitely, so it is denoted by a line above the repeating digit as \( 0.\overline{4} \). This notation clearly indicates which part of the decimal repeats.Repeating decimals offer a unique challenge in terms of notation and understanding but can be managed with practice. To convert them to fractions or percentages, we use methodologies like:
  • Identifying the repeating part of the decimal.
  • Using the repeat notation to handle calculations conveniently.
When dealing with repeating decimals, patience and attention to notation can make the process much smoother.
Percents
The concept of percents involves expressing numbers as parts out of 100. It is a convenient way of understanding proportions. In mathematics, converting numbers into percent form provides a common baseline for comparison.To illustrate, any decimal number can be converted into a percent by multiplying it by 100:
  • For example, \( 0.75 \) becomes \( 75\% \).
  • Similarly, \( 0.\overline{4} \) becomes \( 44.\overline{4}\% \).
This conversion helps in visualizing and interpreting proportions or changes in data. Whether you are working with whole numbers, decimals, or fractions, percent form makes numbers easier to compare, analyze, and discuss, which is crucial in fields like finance, statistics, and everyday decision-making.

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Most popular questions from this chapter

\(4 \%\) of what number is \(60 ?\) A. 15 B. 240 C. 1500 D. 150

If the sales tax rate is \(7 \%\) and the sales tax on an item is \(\$ 35,\) find the cost of the item. A. \(\$ 500\) B. \(\$ 24.50\) C. \(\$ 0.05\) D. \(\$ 5.00\)

Write 8 as a percent. A. \(0.8 \%\) B. \(800 \%\) C. \(80 \%\) D. \(8 \%\)

Write \(22.2 \%\) as a decimal. A. 0.0222 B. 2.22 C. 0.222 D. 22.2

A person bought a motorcycle for \(\$ 8,000\) and made a \(25 \%\) down payment. How much was the down payment? A. \(\$ 320\) B. \(\$ 200\) C. \(\$ 3,200\) D. \(\$ 2,000\)
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