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Chapter 6: Problem 2

Write \(22.2 \%\) as a decimal. A. 0.0222 B. 2.22 C. 0.222 D. 22.2

Short Answer

Expert verified
22.2% as a decimal is 0.222, which corresponds to option C.

Step by step solution

01

Understand Percentages

To convert a percentage to a decimal, you need to recognize that the '%' symbol means 'per 100'. This means that any percentage is a fraction out of 100.
02

Set up the Fraction

Convert the percentage to a fraction by dividing the percentage number by 100. For 22.2%, this is written as \( \frac{22.2}{100} \).
03

Perform the Division

Perform the division \( 22.2 \div 100 \). When you divide 22.2 by 100, you move the decimal point two places to the left, resulting in 0.222.
04

Match with Choices

Now find the decimal equivalent from the given choices. The correct decimal form of 22.2% is 0.222, which matches choice C.

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Key Concepts

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

Understanding Percentages
Percentages are a common way to express how much out of 100 a certain value represents. For instance, when something is expressed as 50%, it means 50 out of 100, which is the same as half. Knowing this is crucial for converting percentages to other numerical forms, like decimals or fractions.
  • The symbol '%' represents 'per 100'.
  • This can easily be thought of as telling us how many parts of a hundred something is equivalent to.
When we convert percentages to decimals, we rely on this basic understanding of them as being inherently connected to the number 100.
Linking Percentages and Fractions
Converting percentages to fractions is usually the first step before changing them into decimals. This process helps reinforce that percentages are closely related to fractions, providing an intermediate step that simplifies further conversion.
  • To change a percentage to a fraction, you divide the percentage by 100.
  • In mathematical terms, this is represented as \( \frac{percentage}{100} \).
  • For instance, 22.2% becomes \( \frac{22.2}{100} \).
Once you express the percentage as a fraction, it becomes much easier to manipulate or convert into other formats, such as decimals.
Mastering Decimal Division
Decimal division is an essential skill when converting percentages to decimals. This process involves moving the decimal point, which is often much simpler than it sounds. For the fraction \( \frac{22.2}{100} \), you need to divide 22.2 by 100.
  • When dividing by 100, you move the decimal two places to the left.
  • This will transform 22.2 into 0.222.
This intuitive method serves two purposes: it shows the direct relationship between percentages and decimals, and it reinforces the easy movement of decimal points in division.
The Role of Place Value in Conversions
Understanding place value is key to properly converting and interpreting decimals. Place value tells us the value of each digit in a number depending on its position.
  • In 0.222, the digit '2' in the tenth place has a different value than the '2' in the hundredths place.
  • This stepwise difference emphasizes the importance of each digit's position.
Once you grasp how place value works, you can better understand why shifting decimals during division relates directly to converting percentage values to decimal forms.

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Most popular questions from this chapter

Write 0.27 as a percent. A. \(0.27 \%\) B. \(0.0027 \%\) C. \(2700 \%\) D. \(27 \%\)

Write \(9 \%\) as a decimal. A. 0.009 B. 0.09 C. 0.9 D. 9.0

Write \(6 \frac{3}{4}\) as a percent. A. \(6.75 \%\) B. \(67.5 \%\) C. \(675 \%\) D. \(0.675 \%\)

Write \(145 \%\) as a decimal. A. 1.45 B. 0.145 C. 0.00145 D. 145

A person bought a motorcycle for \(\$ 8,000\) and made a \(25 \%\) down payment. How much was the down payment? A. \(\$ 320\) B. \(\$ 200\) C. \(\$ 3,200\) D. \(\$ 2,000\)
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