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Chapter 11: Problem 68

Find percent notation. $$ \frac{19}{25} $$

Short Answer

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Step by step solution

01

Understand the Problem

The goal is to convert the fraction \(\frac{19}{25}\) into a percentage. Percentages represent parts per hundred.
02

Convert Fraction to Decimal

Divide the numerator by the denominator: \ \ \( \frac{19}{25} = 0.76 \)
03

Convert Decimal to Percentage

Multiply the decimal by 100 to convert it to a percentage: \ \ \( 0.76 \times 100 = 76 \)
04

Write the Result

Express the final result in percentage notation: \ \ \( 76\text{%} \)

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Key Concepts

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

Fraction to Decimal Conversion
When we need to convert a fraction to a decimal, we perform division of the fraction's numerator (top number) by its denominator (bottom number). In this case, we start with the fraction \( \frac{19}{25} \). To convert it into a decimal, we divide 19 by 25. When you do this division, you get 0.76. This decimal value represents the same quantity as the original fraction.
For example: \( \frac{19}{25} = 0.76 \). Division in fractions is one of the basic operations in mathematics which helps in comparing and scaling values easily.
Remember, converting fractions into decimals is a vital skill that simplifies the numbers, making them easier to work with in various applications.
Decimal to Percentage Conversion
Once we have a number in decimal form, converting it into a percentage is straightforward. Percent means 'per hundred', so to turn any decimal into a percentage, we just multiply it by 100.
For instance, take the decimal 0.76, when we multiply it by 100, we get 76. Therefore, 0.76 becomes 76% when converted into a percentage. This step translates the decimal into a more relatable and common format used in everyday life.
For example: \( 0.76 \times 100 = 76\text{%} \).
This method helps understand how much of the whole (100%) the decimal represents, which makes interpreting data more intuitive.
Basic Mathematics
Basic mathematics forms the foundation of all aspects of math. It includes understanding numbers, operations (like addition, subtraction, multiplication, and division), and how they interact with each other. In this particular exercise, several basic math concepts are applied:
  • Division to convert fractions to decimals.
  • Multiplication to convert decimals to percentages.
  • Understanding percent notation as parts per hundred.

Being comfortable with these basic operations is crucial because they are not just academic skills but also everyday tools. Whether working on budgets, cooking recipes, or interpreting data, these fundamental skills come in handy. Math proficiency starts with mastering these core concepts and applying them in different contexts efficiently.

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