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Chapter 7: Problem 77

Convert \(9 / 23\) to a percent, and round your answer to the nearest tenth of a percent.

Short Answer

Expert verified
9/23 is approximately 39.1% when rounded to the nearest tenth of a percent.

Step by step solution

01

Understanding Percent Conversion

When you want to convert a fraction to a percentage, you multiply the fraction by 100. This is because 'percent' means 'per hundred'. The goal is to express the given fraction as a part of 100.
02

Multiply the Fraction by 100

Convert the fraction \(\frac{9}{23}\) to a percent by multiplying it by 100: \[ \frac{9}{23} \times 100 \] Doing this will give you the percentage equivalent of the fraction.
03

Perform the Multiplication

Calculate \(\frac{9}{23} \times 100\). First, divide 9 by 23, which equals approximately 0.3913. Then multiply this result by 100. The calculation is: \[ 0.3913 \times 100 = 39.13 \]
04

Rounding to the Nearest Tenth

The calculated percentage is 39.13%. To round to the nearest tenth of a percent, look at the hundredths place, which is 3. Since it is less than 5, you round down, keeping the tenths place the same, which gives you 39.1%.

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Key Concepts

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

Fraction to Percent
Converting a fraction to a percent is a process of expressing the fraction as a part out of 100. The word "percent" literally means "per hundred," and fractions are often used to represent parts of a whole. To convert a fraction, such as \( \frac{9}{23} \), into a percent, you use the relationship between fractions and percentages. This conversion helps in understanding the proportion of the given fraction in terms of 100, making it easier to compare and interpret.
  • A fraction represents a division problem; \( \frac{9}{23} \) means 9 divided by 23.
  • To convert this to a percentage, you aim to find out how many parts this fraction there are in 100 parts.
  • This is done by first dividing 9 by 23 to get a decimal.
Understanding this conversion helps in various real-world applications, such as interpreting statistical data or comparing results in different contexts.
Multiplication by 100
After obtaining the decimal equivalent of a fraction, the next step in percent conversion is multiplying by 100. This multiplication converts the decimal into a percentage by finding out how many parts of the fraction can fit into 100 parts of a whole. The decimal result, in our example \( \frac{9}{23} \approx 0.3913 \), becomes a bit more intuitive when expressed as a percentage.

Here is why and how we multiply by 100:
  • This step scales up the decimal fraction so that it represents its proportion relative to 100, the basis of percentage notation.
  • If you simply move the decimal two places to the right, you effectively multiply by 100, illustrating the fraction out of 100 as 39.13%.
By multiplying by 100, you are essentially answering the question: "What would this fraction be if compared to a full 100 units?" This gives a more relatable sense of proportion.
Rounding Decimals
When dealing with percentages, it's often necessary to round to make numbers easier to interpret and use. Rounding involves adjusting a number to make it simpler, though potentially less precise. To round to the nearest tenth of a percent, focus on the number in the tenths place and the one following it. In our example of 39.13%, this means looking at both the 1 and 3.

Rounding is important for these reasons:
  • It simplifies numerical results, making them easier to understand and communicate.
  • The rounding process involves checking the hundredths place: if the number is 5 or more, increase the tenths place by one; otherwise, leave it.
  • In 39.13%, the hundredths place is 3, which is less than 5, so the tenths place remains 1. Thus, the rounded result is 39.1%.
Rounding can sometimes slightly change the original value, but it helps in providing a clear and concise figure without unnecessary detail.

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