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Chapter 1: Problem 39

Convert each percent to its decimal equivalent. $$ 12 \% $$

Short Answer

Expert verified
12% as a decimal is 0.12.

Step by step solution

01

Identify the Percent

The first step is to identify the given percentage. In this exercise, you are given 12%.
02

Understand the Percent-to-Decimal Conversion

Know that to convert a percent to a decimal, you divide the percentage number by 100.
03

Perform the Division

Divide 12 by 100. This operation converts the percentage into a decimal: \[ \frac{12}{100} = 0.12 \]
04

Verify the Decimal Result

Ensure that the decimal is correctly placed. Since 12% is equivalent to dividing 12 by 100, the decimal is 0.12.

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Key Concepts

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

Understanding Decimal Conversion
Decimal conversion is a fundamental concept in mathematics that involves transforming a percentage into its decimal form. This process is crucial because it allows us to express percentages as numbers that are easier to work with in calculations.

When converting a percentage to a decimal, you shift its viewpoint from being a part of a hundred to a part of one. This change is achieved by dividing the percentage by 100.
  • Take the example of 12%. Initially, it represents 12 parts out of 100.
  • To convert 12% into a decimal, divide the 12 by 100, resulting in 0.12.
  • Now, the decimal 0.12 signifies the same proportion but in a format suited for various arithmetic operations.
Decimal conversion is not just about changing a number's form, but rather adapting it for broader mathematical use.
Simplifying Division for Decimal Conversion
Division is a key mathematical operation that plays an essential role in converting percentages to decimals. The idea is to distribute a quantity evenly, which when applied to percentages, means evenly dividing by 100.

In our example of 12%:
  • Think of the division as spreading the value of 12 across 100 equal parts.
  • This operation results in forming the number 0.12.
  • The formula is straightforward: \[ \frac{12}{100} = 0.12 \]
Performing this division helps to visualize how a given percent fits into a smaller whole number system. Remember, dividing by 100 is equivalent to moving the decimal point two places to the left.

Thus, division is not just cutting numbers down, but aligning them in a precise way to facilitate easier mathematical handling.
Grasping the Meaning of Percentages
Percentages are everywhere in our daily lives. They represent fractions based on a denominator of 100, portraying the idea of portions out of a whole. Understanding percentages as parts of 100 makes them intuitive and useful for comparison.

Consider 12%:
  • This percentage implies 12 out of every 100 units of a given quantity.
  • Saying something is at 12% allows us to directly think about it in terms of its part of a complete whole.
Converting a percentage to a decimal transforms this broad comparison into a usable number for calculations.

Thus, understanding percentages is about recognizing their universal applicability and their simplification into decimals, enhancing clarity in both everyday contexts and advanced mathematical problems.

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