Table of Contents

Decimal & Percent Level 6

Introduction

Have you ever wondered how to calculate a discount when shopping or convert a fraction into a decimal? Understanding decimals and percents is essential for making sense of numbers in everyday life. This article will guide you through the concepts of decimals and percents, how they relate to each other, and how to solve problems involving them.

Definition and Concept

A decimal is a way of expressing numbers that are not whole, using a dot (called a decimal point) to separate the whole number part from the fractional part. For example, 0.75 is a decimal that represents three-quarters. A percent means ‘per hundred’ and is a way to express a number as a fraction of 100. For instance, 25% means 25 out of 100, or 0.25 in decimal form.

Relevance:

  • Mathematics: Decimals and percents are foundational concepts in math that help with understanding ratios and proportions.
  • Real-world applications: Used in finance, statistics, and everyday calculations like shopping and budgeting.

Historical Context or Origin​

The concept of decimals dates back to ancient civilizations, including the Babylonians. However, the decimal point we use today was popularized in Europe during the 16th century by mathematicians like Simon Stevin. The term ‘percent’ comes from the Latin phrase ‘per centum,’ meaning ‘by the hundred,’ and has been used since the 15th century to describe ratios and proportions.

Understanding the Problem

To solve problems involving decimals and percents, we often need to convert between the two forms. Let’s break down the steps using an example:
Example Problem: What is 20% of 150?

  • Convert the percent to a decimal: 20% = 0.20.
  • Multiply the decimal by the total: 0.20 × 150.

Methods to Solve the Problem with different types of problems​

Method 1: Direct Calculation
To find a percentage of a number, convert the percentage to a decimal and multiply.
Example:
Find 30% of 200.

  • Convert 30% to decimal: 0.30.
  • Multiply: 0.30 × 200 = 60.

    • Method 2: Using Fractions
    You can also express a percent as a fraction and then multiply.
    Example:
    Find 25% of 80.

  • Convert 25% to a fraction: 25/100 = 1/4.
  • Multiply: (1/4) × 80 = 20.

    • Method 3: Finding the Percent
    To find what percent one number is of another, use the formula: (part/whole) × 100.
    Example:
    What percent is 30 of 150?

  • Use the formula: (30/150) × 100 = 20%.

    • Exceptions and Special Cases​

  • More than 100%: Sometimes, the result can exceed 100%. For example, if you calculate 150% of a number, it means you have the whole number plus half of it again.
  • Zero Percent: If something is 0%, it means there is none of it. For example, 0% of 100 is 0.

    • Step-by-Step Practice​

    Problem 1: Find 15% of 60.
    Solution:

  • Convert 15% to decimal: 0.15.
  • Multiply: 0.15 × 60 = 9.

    • Problem 2: What is 50% of 120?
    Solution:

  • Convert 50% to decimal: 0.50.
  • Multiply: 0.50 × 120 = 60.

    • Problem 3: What percent is 45 of 90?
    Solution:

  • Use the formula: (45/90) × 100 = 50%.

    • Examples and Variations

    Easy Example:

    • Problem: Find 10% of 50.
    • Solution:
      • Convert 10% to decimal: 0.10.
      • Multiply: 0.10 × 50 = 5.

    Moderate Example:

    • Problem: Find 75% of 200.
    • Solution:
      • Convert 75% to decimal: 0.75.
      • Multiply: 0.75 × 200 = 150.

    Advanced Example:

    • Problem: What percent is 36 of 90?
    • Solution:
      • Use the formula: (36/90) × 100 = 40%.

    Interactive Quiz with Feedback System​

    You do not have access to this page.

    If you are not a subscriber, please click here to subscribe.
    OR

    Common Mistakes and Pitfalls

    • Forgetting to convert the percent to a decimal before multiplying.
    • Misplacing the decimal point when working with decimals.
    • Confusing the terms ‘percent’ and ‘decimal’.

    Tips and Tricks for Efficiency

    • Always double-check your conversions between decimals and percents.
    • Practice mental math for common percentages (like 10%, 25%, 50%).
    • Use estimation to quickly check if your answer makes sense.

    Real life application

    • Shopping: Calculating discounts during sales.
    • Finance: Understanding interest rates on loans or savings.
    • Statistics: Interpreting data and survey results.

    FAQ's

    To convert a decimal to a percent, multiply it by 100 and add a percent sign. For example, 0.75 × 100 = 75%.
    Convert the fraction to a decimal by dividing the top number (numerator) by the bottom number (denominator), then follow the conversion steps.
    Yes, you can calculate percentages of negative numbers, but the results will also be negative.
    You can still use the same methods; just ensure you are careful with your calculations, especially with larger numbers.
    These concepts help you make informed decisions in daily life, from budgeting to understanding statistics.

    Conclusion

    Mastering decimals and percents is a vital skill that enables you to navigate everyday situations with confidence. By practicing these concepts and applying them to real-world scenarios, you’ll find that they become second nature.

    References and Further Exploration

    • Khan Academy: Interactive lessons on decimals and percents.
    • Book: Math Skills for Everyday Life by Mary Jane Sterling.

    Like? Share it with your friends

    Facebook
    Twitter
    LinkedIn

    Filter

    • Category

    • Levels

    • Subject