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Chapter 4: Problem 12

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$\frac{3}{71}$$

Short Answer

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Step by step solution

01

Convert Fraction to Decimal

To convert the fraction \(\frac{3}{71}\) to a decimal, divide the numerator by the denominator: \(\frac{3}{71} \approx 0.0422535\).
02

Convert Decimal to Percent

To convert the decimal 0.0422535 to a percent, multiply by 100: \(0.0422535 \times 100 = 4.22535\).
03

Round to the Nearest Tenth

Round 4.22535 to the nearest tenth. Look at the digit in the hundredths place, which is 2. Since it is less than 5, the digit in the tenths place remains 2. Therefore, 4.22535 rounded to the nearest tenth is 4.2.

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Key Concepts

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

Fraction to Decimal
To convert a fraction to a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). In this exercise, we converted the fraction \( \frac{3}{71} \) by dividing 3 by 71. This gives us a decimal value of approximately \( 0.0422535 \).
Using a calculator, you would input 3 梅 71 to get this value.
Understanding this step is crucial, as many math problems involve moving between fractions and decimals.
Decimal to Percent
Once you have a decimal, converting it to a percent is easy. Just multiply the decimal by 100.
For example, to convert \( 0.0422535 \) to a percent, you multiply it by 100: \( 0.0422535 \times 100 = 4.22535 \).
The reason we multiply by 100 is because 'percent' means 'per hundred,' so essentially we're scaling up our decimal to a value out of 100.
This concept is fundamental in various applications, such as statistics and real-world problems involving percentages.
Rounding Decimals
Rounding decimals is an essential skill to make numbers more manageable and easier to understand.
In our example, we had \( 4.22535 \) and needed to round it to the nearest tenth.
To round to the nearest tenth, you look at the hundredths place (the second digit to the right of the decimal point).
If that digit is 5 or greater, you round up. If it's less than 5, you round down.
Here, the hundredths place is 2, which is less than 5, so we leave the tenths place as 2.
Thus, \( 4.22535 \) rounded to the nearest tenth is \( 4.2 \).
Rounding is often used in reporting data to make it more readable and to simplify complex numbers.

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Most popular questions from this chapter

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. The number of students in band is about \(115 \%\) of the number in orchestra and about \(\frac{5}{4}\) of the number in choir.

It is often useful to use benchmark percents to estimate the values of actual percents. Useful benchmarks include multiples of \(10 \%\) ( \(10 \%\), \(20 \%, 30 \%, \text { and so on }),\) as well as \(25 \%\) and \(75 \%\) a. Of the 910 students attending Mill Middle School, 179 walk to school. Use a benchmark to estimate the percent of students who walk to school, and explain how you decided which benchmark to use. b. A human skeleton is made up of 206 bones. There are 54 bones in the hands. Use a benchmark to estimate the percent of a human skeleton's bones found in the hands, and explain how you decided which benchmark to use. c. The girl's softball team won 25 of the 33 games it played last season. Use a benchmark to estimate the percent of games the team won, and explain how you decided which benchmark to use.

Estimate each result using benchmarks. Then find the exact value. \(75 \%\) of 80

Estimate each result using benchmarks. Then find the exact value. \(57 \%\) of 80

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. In \(1820,\) almost \(72 \%\) of U.S. workers were employed in farm occupations. By \(1994,\) only \(\frac{1}{40}\) of U.S. workers were employed in farming.
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