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Chapter 1: Problem 36

Write the percentages in decimal form. $$77.7 \%$$

Short Answer

Expert verified
77.7% is 0.777 in decimal form.

Step by step solution

01

Understand the Percentage

A percentage is a way to express a number as a fraction of 100. The symbol '%' stands for 'per cent', which means 'per hundred'.
02

Convert Percentage to Fraction

To convert a percentage to a fraction, you remove the percent sign and divide the number by 100. For instance, 77.7% is written as \( \frac{77.7}{100} \).
03

Convert Fraction to Decimal

Divide 77.7 by 100 to convert the fraction into a decimal: \( 77.7 \div 100 = 0.777 \). This tells us that 77.7% is 0.777 as a decimal.

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Key Concepts

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

Percentage Concepts
Percentage is a versatile way to express numbers, focusing on parts per hundred. It is symbolized by the '%' sign, originating from the Latin phrase 'per centum,' meaning 'by the hundred.' This representation is used widely in various day-to-day contexts like calculating discounts, understanding interest rates, or even examining statistical data such as test scores. Percentages make it easier to compare and understand proportions in data.
  • When you see a percentage, you're seeing how much of something you've got out of 100 total parts.
  • Think of percentages as a 'part-whole' relationship where the whole is always 100.
Grasping the basic concept of percentages helps in effectively converting them into other numerical forms like fractions and decimals. This understanding is crucial in mathematical calculations as well as real-world applications.
Decimal Conversion
Converting a percentage into a decimal is a simple yet essential skill in mathematics. It requires understanding the relationship between percentages and decimals, which are closely intertwined.
  • Start by considering any percentage as a fraction over 100.
  • Once expressed as a fraction, converting to a decimal involves basic division.
For example, to convert 77.7% into a decimal, you follow these steps: 1. **Remove the percent sign**: Interpret 77.7% as 77.7/100. 2. **Perform the division**: Calculate 77.7 divided by 100, which equals 0.777.
This process simplifies the percentage into a decimal form, allowing for easier computation and analysis in diverse mathematical contexts.
Mathematics Education
In mathematics education, understanding how to convert percentages to decimals is an important topic that builds foundational numeracy skills. This conversion enhances a student's ability to handle real-world situations where interpreting numbers accurately is vital.
  • Cross-disciplinary linkage: This conversion skill is vital in subjects like science, economics, and statistics.
  • Analytical thinking: Promotes analytical skills by requiring students to interpret and manipulate numbers thoughtfully.
Teaching this concept effectively involves using practical examples that students can relate to, such as calculating sales tax or determining discounts during shopping. These real-life applications illustrate the utility of converting percentages to decimals, making the learning process engaging and meaningful for students.

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