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Chapter 1: Problem 635

Convert each percent to a decimal. $$ 21.4 \% $$

Short Answer

Expert verified
21.4% = 0.214

Step by step solution

01

Understand the Percent

A percent represents a part out of 100. So, 21.4% means 21.4 out of 100.
02

Divide by 100

To convert a percent to a decimal, divide the percent value by 100. Therefore, compute: \( 21.4\% = \frac{21.4}{100} \)
03

Simplify the Division

Perform the division: \( \frac{21.4}{100} = 0.214 \)

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Key Concepts

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

percent
A percent is a way to express a number as a fraction of 100. It uses the symbol '%' and is fundamental in mathematics for describing proportions. For example, if you score 50 out of 100 on a test, you can say you scored 50%. It brings clarity in expressing how large or small a quantity is relative to 100. Percentages are used widely in various fields like finance, statistics, and everyday shopping. When you see 21.4%, it鈥檚 referring to 21.4 parts out of 100.
The crucial thing to remember about percents is that they simplify parts of a whole into a format that鈥檚 easy to understand and communicate.
decimal conversion
Converting percents to decimals is a straightforward process. Since percent means per 100, you simply divide the percent number by 100 to get the decimal.
For example, let鈥檚 convert 21.4% to a decimal:
  • Start with the percent number: 21.4%
  • Remove the percent sign: 21.4
  • Divide by 100: \( \frac{21.4}{100} = 0.214 \)

So, 21.4% is 0.214 in decimal form. This method applies universally to any percentage. Dividing by 100 shifts the decimal point two places to the left.
basic arithmetic
Understanding basic arithmetic operations is essential for converting percentages to decimals.
These operations include:
  • Addition
  • Subtraction
  • Multiplication
  • Division

In our case, division is the critical operation. Dividing by 100 seems simple, but it鈥檚 handy in many contexts. For instance, moving the decimal point two places to the left:
21.4%: Move the point two places left --> 0.214
This operation aligns with the rule in basic arithmetic where division by powers of ten adjusts the position of the decimal point. Mastering these simple steps can significantly ease your mathematical processes.

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