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Chapter 7: Problem 22

Convert the given percent to a decimal. $$ 0.21 \% $$

Short Answer

Expert verified
0.21% as a decimal is 0.0021.

Step by step solution

01

Understand the Problem

We are given a percentage, which is 0.21%, and we need to convert it to a decimal.
02

Convert Percent to Decimal

To convert a percentage to a decimal, divide it by 100. Hence, we take 0.21 and divide by 100.
03

Calculate the Decimal

Perform the division: \( 0.21 \div 100 = 0.0021 \).
04

Confirm the Calculation

Double-check the division to ensure the decimal conversion is correct. 0.21 divided by 100 results in 0.0021, confirming our solution.

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Key Concepts

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

Decimal Conversion
Converting a percentage to a decimal is a straightforward process that involves a simple division. Understanding decimal conversion requires us to know that the term "percent" means "per hundred." When you see a percentage, think of it as a fraction of 100. For instance, 0.21% can be expressed as:
  • 0.21 per 100
  • 0.21/100
To find the decimal equivalent, we divide the percentage by 100. Doing this shifts the decimal point two places to the left. For example, converting 0.21% involves performing the calculation:
  • \[0.21 \div 100 = 0.0021\]
Hence, the decimal conversion of 0.21% is 0.0021. Always remember, with any percentage, dividing by 100 is the way to turn it into a decimal.
Percentage Calculation
Percentage calculation often involves converting numbers to or from percentages. When dealing with percentages, understanding their fractional nature is key. Here鈥檚 how you can generally work with percentages:
  • To convert a decimal to a percentage, multiply by 100.
  • To convert a percentage to a decimal, divide by 100.
  • To find a percentage of a number, multiply the number by the percentage in decimal form.
Knowing these operations helps not only in converting percentages but also in various mathematical problems. The underlying principle is recognizing that a percentage is always part of a whole, with the whole being 100.
Mathematical Operations
In mathematics, many tasks involve basic operations such as addition, subtraction, multiplication, and division. When dealing with the conversion of percentages to decimals, division is the primary operation. Here鈥檚 a short breakdown of how we use these operations in this context:
  • **Division by 100**: To convert a percentage to a decimal, you divide. This operation is crucial for shifting the decimal point. For example, 0.21% becomes 0.0021 after division.
  • **Checking Work**: It鈥檚 important to verify results. After performing the division, review the calculation to ensure accuracy.
Breaking down these operations into simple steps helps in understanding not just percentage conversion but also in building a solid foundation for more complex mathematical challenges. Mastering these basic operations allows for greater flexibility in problem-solving.

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