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Chapter 4: Problem 15

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$2.7$$

Short Answer

Expert verified
270.0%

Step by step solution

01

Convert the decimal to a fraction

First, recognize that the decimal 2.7 can be written as a fraction. Since there is one digit after the decimal point, write it as \( \frac{27}{10} \).
02

Multiply by 100 to convert to a percent

To convert this fraction to a percent, multiply it by 100: \((2.7) \times 100 = 270\).
03

Simplify and round if necessary

After multiplying, the result is already a whole number, which is 270.0%. Since it's a whole number, there's no need to round further.

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Key Concepts

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

Percent Conversion
Percent conversion is a method used to express a number as a percent. A percent is simply a fraction with a denominator of 100. To convert a number to a percent, you multiply it by 100. For example, if you have a decimal like 2.7, you multiply it by 100 to get 270%.Doing this helps to visualize the number in terms of parts per hundred, which can be easier to understand and compare. Percentages are commonly used in everyday contexts such as calculating discounts, interest rates, and statistics.
Decimal to Fraction
Converting a decimal to a fraction involves recognizing the place value of the digits in the decimal. For example, the decimal 2.7 has one digit after the decimal point. This is in the tenths place, so you can write 2.7 as \(\frac{27}{10}\). Here are a few steps to use:
- Write down the decimal divided by 1 (e.g., \(\frac{2.7}{1}\)).
- Multiply the numerator and the denominator by 10 (or a power of 10 that matches the number of decimal places).
- Simplify the fraction if possible.Converting to a fraction can sometimes make further calculations, like percent conversion, simpler and more straightforward.
Rounding Numbers
Rounding numbers is a technique used to simplify numbers, making them easier to work with. When rounding to a specific place value, look at the digit to the right of the desired place:
- If it's 5 or higher, round up.
- If it's lower than 5, round down.For example, if you convert a fraction to a decimal and get a repeating or long decimal, rounding can make your result more manageable. In our example, where we got 270.0% after converting 2.7 to a percent, there was no need to round further because it's already an exact number. However, for more complex decimals, rounding to the nearest tenth or hundredth can make your results more practical for everyday use.

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Most popular questions from this chapter

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

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. About \(\frac{2}{3}\) of U.S. households with televisions subscribe to a cabletelevision service.

Find the least common multiple of each pair of numbers. 21 and 35

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$\frac{19}{20}$$
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