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Chapter 1: Problem 54

What is \(50 \%\) of one hundred?

Short Answer

Expert verified
50

Step by step solution

01

Understanding Percentages

A percentage expresses a number as a fraction of 100. Hence, 50% means 50 out of 100 or 50/100.
02

Converting Percentage to Decimal

To find 50% of a number, convert the percentage to a decimal by dividing by 100: \(50\% = \frac{50}{100} = 0.5\).
03

Calculating the Value

Multiply the decimal by the number to find 50% of it. So, multiply 0.5 by 100: \(0.5 \times 100 = 50\).

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Key Concepts

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

Decimal Conversion
When working with percentages, it's often helpful to convert the percentage into a decimal to simplify calculations. Converting a percentage to a decimal involves a straightforward process: divide the percentage by 100. This step is crucial because percentages are essentially fractions of 100.
For example, to convert 50% into a decimal, you conduct the following calculation:
  • Take the percentage, which is 50.
  • Divide by 100: \( \frac{50}{100} = 0.5\)
Now, you have 0.5 as a decimal, which you can use for further calculations. Decimal conversion transforms the problematic nature of percentages into a simple number that's easier to multiply, aiding in clearer and faster mathematical operations.
Fraction
Understanding fractions is fundamental when dealing with percentages. A percentage is actually a special type of fraction where the denominator is always 100. This means 50% is the same as saying 50 over 100 or \( \frac{50}{100} \).
Fractions show the relationship between parts and a whole. In the context of the example, the fraction 50/100 easily translates to one half (\( \frac{1}{2} \)), simplifying the visualization of percentages.
Comprehending this relationship allows students to transition between percentages, fractions, and decimals seamlessly. Seeing percentages as fractions helps demystify them and offers another perspective for problem-solving.
Calculation Steps
After converting the percentage into a decimal or a fraction, the final step in most problems is finding the percentage of a number. It's about applying this decimal or fraction to a specific quantity.
In our example, the task is to find 50% of 100. Here's how you proceed:
  • First, convert 50% to its decimal form, which is 0.5.
  • Then, multiply the decimal by the number: \( 0.5 \times 100 \).
  • The result of this multiplication gives the answer: 50.
Multiplication here essentially scales the number down to what the percentage represents.
This logical sequence of steps allows for clarity and accuracy in solving various percentage-related problems.

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