/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 79 Convert \(17 / 27\) to a percent... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 79

Convert \(17 / 27\) to a percent, and round your answer to the nearest hundredth of a percent.

Short Answer

Expert verified
The fraction 17/27 converted to a percent is approximately 62.96%.

Step by step solution

01

Understand the Conversion Factor

To convert a fraction to a percent, you need to multiply the fraction by 100. This is because percent means per hundred.
02

Multiply by 100

Take the fraction \(\frac{17}{27}\) and multiply it by 100 to convert it into a percentage. Perform the multiplication: \(\frac{17}{27} \times 100\).
03

Perform the Division

Divide 17 by 27 to get the decimal form of the fraction. \(17 \div 27 \approx 0.62963\).
04

Multiply the Decimal by 100

Take the decimal result from Step 3, which is approximately 0.62963, and multiply it by 100 to get the percentage: \(0.62963 \times 100 = 62.963\).
05

Round to the Nearest Hundredth

The result from Step 4 gives us 62.963. To round this to the nearest hundredth, look at the third decimal place, which is 3. Since it's less than 5, round down, resulting in 62.96%.

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Key Concepts

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

Converting Fractions to Percents
When you want to convert a fraction to a percent, think of it as finding out how much of a whole (or 100%) the fraction represents. Since "percent" means "out of 100," the conversion process involves a simple multiplication by 100. Here's how you can do it:
  • Take the given fraction. In our case, it's \(\frac{17}{27}\).
  • Multiply this fraction by 100. You do this to adjust the fraction into a percentage.
After performing these steps, you should get the percentage value. Remember that converting to a percent is just finding a part of 100; it's a skill that becomes quite intuitive with practice. This helps you see fractions in contexts that involve grading, discounts, and statistics.
Rounding Decimals to the Nearest Hundredth
Rounding numbers helps simplify values and make them easier to use. Rounding to the nearest hundredth is particularly useful in percentages for clarity and precision. Here鈥檚 how you can do it:
  • Look at the number you need to round, for example, 62.963.
  • Identify the digit in the hundredth place, here it is 9.
  • Check the next digit to the right, which is 3.
If the digit is less than 5, you keep the hundredth digit as it is. If it were 5 or more, you would increase the hundredth place by one. So, in our example, rounding 62.963 to the nearest hundredth gives us 62.96. This process ensures that your percentages are accurate without being overly complex.
Math Calculations and Their Importance
Performing math calculations, such as converting fractions to percentages or rounding decimals, is integral for daily life and various academic pursuits. Math calculations allow you to:
  • Interpret data and understand probabilities in statistics.
  • Calculate discounts and prices in shopping.
  • Determine angles and measurements in geometry.
Performing calculations helps develop logical thinking and is foundational for understanding more complex mathematical concepts. It also enhances problem-solving skills and allows for more accurate decision-making. Through practice, you can become more confident and efficient at these calculations, improving both speed and accuracy.

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Most popular questions from this chapter

In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Bernardo } & 38 \\ \text { Fernando } & 49 \\ \text { Aisha } & 44 \\ \hline \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.

The balance on a 4-year loan is $$\$ 5,720$$. If the principal borrowed was $$\$ 4,400$$, what was the simple interest rate (as a percent)?

In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Bernardo } & 54 \\ \text { Mabel } & 38 \\ \text { Henry } & 49 \\ \hline \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.

A business owner borrows $$\$ 4,200$$ for 4 months. At the end of the 4 -month loan period, the interest owed is $$\$ 63$$. What was the simple yearly interest rate (as a percent)?

A business owner takes out a 6-month loan at a 8% per year simple interest rate. At the end of the 6-month loan period, the interest owed is $68. What was the principal amount borrowed?
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