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Chapter 13: Problem 50

Express each percent as a decimal. $$3.56 \%$$

Short Answer

Expert verified
3.56% as a decimal is 0.0356.

Step by step solution

01

Understanding the Concept of Percent

Percent means per hundred, or out of 100. So, to convert a percent to a decimal, we need to express it as a fraction of 100.
02

Dividing by 100

To convert from percent to decimal, divide the percent value by 100. For example, divide 3.56 by 100.
03

Calculation

Perform the division: \( 3.56 \div 100 = 0.0356 \).
04

Result Interpretation

The decimal representation of 3.56% is 0.0356.

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Key Concepts

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

Understanding Percent
Percentages represent a fundamental way of expressing ratios or fractions. The term "percent" comes from the Latin phrase "per centum," which means "by the hundred." Essentially, when we state a value as a percent, we describe how many parts out of a hundred something is.
For example, saying "50%" is just another way of saying "50 out of 100" or "half." Every percentage is just a number divided by 100. Whenever you see a percentage, remember it's representing a portion of a whole that is standardized to 100 parts.
In the exercise, we're starting with 3.56%, so we're dealing with a measurement of 3.56 out of 100.
Dividing by 100
To convert a percentage to a decimal, you divide the percentage number by 100. Why do we do this? It's all about shifting from a fraction of 100 to the actual number. By dividing the percentage value by 100, we transform the ratio (where the whole is 100) into its decimal form.
Think of it as scaling down the number by moving the decimal point two places to the left. For instance, in the example with 3.56%, dividing by 100 (or moving the decimal to the left) gives us the decimal representation.
  • Take the percentage, like 3.56%
  • Move the decimal two places left: 3.56 becomes 0.0356.
This step essentially converts percent into a fraction and then a decimal, making it easier to understand in standard mathematical operations.
Decimal Representation
Once you've divided the percentage by 100, you're left with the decimal representation. This form is incredibly useful for calculations and comparisons since decimals are often more intuitive and simpler to work with in mathematics.
In scientific calculations, financial computations, and statistics, decimals give us precision and clarity.
For instance, with a percentage like 3.56%, converting it to the decimal 0.0356 allows you to apply it directly in equations or financial formulas specified in decimal form without additional conversions.
  • Think of decimals as the 'true' number form of percentages.
  • They provide a direct, clear visual representation of what proportion the percentage exhibits relative to a whole.
Hence, knowing how to convert percents to decimals ensures accurate math results and better comprehension of numerical data.

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