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Chapter 7: Problem 61

Convert the given fraction to a percent. $$ \frac{9}{4} $$

Short Answer

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Step by step solution

01

Understanding the Problem

We are given a fraction, \( \frac{9}{4} \), and we need to express it as a percentage. Percent means 'per hundred', so our goal is to express the fraction with a denominator of 100.
02

Convert Fraction to Decimal

To convert the fraction \( \frac{9}{4} \) to a decimal, divide the numerator by the denominator: \( 9 \div 4 = 2.25 \). So, \( \frac{9}{4} \) is equal to 2.25 as a decimal.
03

Convert Decimal to Percent

To convert the decimal 2.25 to a percent, multiply by 100: \( 2.25 \times 100 = 225 \).
04

State the Solution

Therefore, \( \frac{9}{4} \) as a percentage is 225%.

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Key Concepts

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

Fraction to Decimal Conversion
Converting a fraction to a decimal is a foundational math skill that involves division. When you have a fraction like \( \frac{9}{4} \), you can transform it into a decimal by dividing the numerator (9) by the denominator (4). This division will result in a decimal number.Here, when you perform the division, 9 divided by 4 gives you 2.25. This tells us that \( \frac{9}{4} \) is equivalent to 2.25 in decimal form. Understanding this conversion
  • Makes it easier to handle fractions in various mathematical problems.
  • Simplifies the comparison of fractional values.
  • Assists in converting to other formats, such as percentages.
Multiplying Decimals by 100
Once your fraction is converted to a decimal, an important step to convert it to a percentage is multiplying it by 100. This step is crucial because the term "percent" reflects a value "out of a hundred."For example, when dealing with the decimal 2.25:
  • Multiply 2.25 by 100: \(2.25 \times 100 = 225\)
  • Now, 2.25 converted into percentage form is 225%
This multiplication is nothing but shifting the decimal point two positions to the right. It's similar to saying that each whole number in the decimal is equivalent to 100% when multiplied appropriately.Therefore, the result helps you understand where the decimal portion fits within a whole number scale.
Understanding Percentages
Percentages are a way of expressing a number as a fraction of 100. They give a quick glance at how one quantity stands in relation to 100, making complex ratios or comparisons more comprehensible. When you see a percentage like 225%, it means that the original number (in this case, 2.25) is equivalent to 225 per every 100 parts. This concept helps in various fields:
  • Grades and scores often use percentages.
  • Financial calculations, including interest rates, use percentages for clarity.
  • Percentages simplify the process of comparing different quantities.
By understanding percentages, you gain powerful insights into data and can make informed decisions based on quantitative analysis.

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Most popular questions from this chapter

In an election for class president, Kamili received 14 votes, Jamal received 9 votes, and Jose received the remaining 27 votes cast. If a pie chart is created for this voting data, what will be the degree measure of the central angle of the sector representing Kamili's share of the vote? Round your answer to the nearest degree.

A business owner borrows $$\$ 3,200$$ for 6 months. At the end of the 6 -month loan period, the interest owed is $$\$ 96$$. What was the simple yearly interest rate (as a percent)?

A business owner borrows $$\$ 3,200$$ for 4 months at a \(9 \%\) per year simple interest rate. At the end of the 4 -month loan period, how much interest is owed?

In an election for class president, Jamal received \(30 \%\) of the votes, Luisa received \(20 \%\), Kamili received \(28 \%\) of the votes, and \(22 \%\) of the votes were received by other candidates. If a pie chart is created for this data, what will be the degree measure of the central angle of the sector representing Jamal's share of the vote? Round your answer to the nearest degree.

Due to a textile mill closure, the population of Ghosttown decreases by \(6.1 \%\). If the original population was 14,320 hardy souls, what is the new population, correct to the nearest person?
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