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Chapter 7: Problem 65

Solve. Round to the nearest tenth, if necessary. What number is \(22.3 \%\) of \(53,862 ?\)

Short Answer

Expert verified
The number is 12,014.2.

Step by step solution

01

Convert Percentage to Decimal

To find what number 22.3% of 53,862 is, first convert the percentage into a decimal. To do this, divide 22.3 by 100.\[ 22.3\% = \frac{22.3}{100} = 0.223 \]
02

Multiply Decimal by Total

Next, multiply the decimal found in Step 1 by the total number, 53,862. This will give the number that is 22.3% of 53,862.\[ 0.223 \times 53862 = 12014.226 \]
03

Round to the Nearest Tenth

Since the problem asks us to round to the nearest tenth, look at the number in the hundredths place in 12014.226. It's a 2, which means we round down. Therefore, the rounded number is 12014.2.

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Key Concepts

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

Decimal Conversion
Understanding decimal conversion is essential when working with percentages. Percentages represent a number out of 100, and converting them into decimal form makes calculations easier. To convert a percentage to a decimal:
  • Remove the percentage sign (%).
  • Divide the number by 100.
For instance, to convert \(22.3\%\) into a decimal, you perform the calculation \(\frac{22.3}{100}\), which results in 0.223. This decimal can now be used in further calculations. By understanding this simple step, you can easily handle percentage problems involving real situations.
Rounding Numbers
Rounding numbers is about deciding which digit is most significant given the precision required. It simplifies numbers to make them easier to work with. For rounding to the nearest tenth:
  • Identify the tenths digit first. In the number 12014.226, this is the first digit after the decimal, which is 2.
  • Next, look at the number in the hundredths place, the second digit after the decimal. For 12014.226, it's a 2.
  • If the hundredths digit is 5 or more, you round up the tenths place. If it's less than 5, like in this case, you round down.
So, 12014.226 rounded to the nearest tenth is 12014.2. This simple rule helps with rounding any decimal number effectively, improving accuracy in reporting results.
Multiplication with Decimals
Multiplying decimals involves the same process as multiplying whole numbers, with some attention to where the decimal point should be in the result.Here's a simple way to multiply decimals:
  • First, perform the multiplication ignoring the decimal points. For example, multiply 223 by 53862.
  • Count the total number of digits to the right of the decimals in the original numbers. Here, 0.223 has three decimal places.
  • After multiplying, place the decimal in the result so that it has the same number of decimal places as the total from before. So, the full multiplication \(0.223 \times 53862\) gives 12014.226.
This technique ensures accurate results when working with decimal numbers. Mastering it can be particularly useful for dealing with percentages in calculations.

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Most popular questions from this chapter

A diamond necklace sells for \(\$ 24,966 .\) If the tax rate is \(7.5 \%,\) find the total price.

Write a percent statement that translates to \(\frac{16}{80}=\frac{20}{100}\)

If a number is increased by \(100 \%,\) how does the increased number compare with the original number? Explain your answer.

Perform each indicated operation. See Sections 4.3 through \(4.5,4.7,\) and 5.2 through \(5.4 .\) $$2 \frac{4}{5} \div 3 \frac{9}{10}$$

Given the percent \(52.8647 \%,\) round as indicated. a. Round to the nearest tenth percent. b. Round to the nearest hundredth percent.
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