Mastering Basic Percentage Conversions for Competitive Exams
Welcome to the foundational module on Basic Percentage Conversions. Understanding how to fluently convert between percentages, fractions, and decimals is a cornerstone of success in quantitative aptitude sections of competitive exams like the CAT. This skill allows for quicker calculations and deeper comprehension of problem statements.
What are Percentages?
The word 'percent' literally means 'per hundred'. A percentage is a way of expressing a number as a fraction of 100. For example, 50% means 50 out of 100, which can be written as the fraction 50/100 or the decimal 0.50.
It signifies 'per hundred', meaning a fraction out of 100.
Converting Percentages to Fractions
To convert a percentage to a fraction, simply divide the percentage value by 100 and simplify the resulting fraction. For instance, to convert 25% to a fraction, you write it as 25/100, which simplifies to 1/4.
Divide 75 by 100 (75/100) and simplify to 3/4.
Converting Percentages to Decimals
Converting a percentage to a decimal is even simpler: just divide the percentage by 100. This is equivalent to moving the decimal point two places to the left. For example, 40% becomes 0.40 or simply 0.4.
1.50 or 1.5
Converting Fractions to Percentages
To convert a fraction to a percentage, first convert the fraction to a decimal by dividing the numerator by the denominator. Then, multiply the decimal by 100 and add the '%' sign. For example, 3/5 = 0.6, and 0.6 * 100 = 60%, so 3/5 is 60%.
1/8 = 0.125. 0.125 * 100 = 12.5%.
Converting Decimals to Percentages
To convert a decimal to a percentage, multiply the decimal by 100 and add the '%' sign. This is the reverse of converting a percentage to a decimal. For example, 0.75 becomes 0.75 * 100 = 75%.
0.05 * 100 = 5%.
Key Percentage Equivalents
Memorizing common percentage-fraction-decimal equivalents can significantly speed up your problem-solving. These are frequently tested in competitive exams.
| Percentage | Fraction | Decimal |
|---|---|---|
| 100% | 1/1 | 1.0 |
| 50% | 1/2 | 0.5 |
| 25% | 1/4 | 0.25 |
| 75% | 3/4 | 0.75 |
| 20% | 1/5 | 0.2 |
| 10% | 1/10 | 0.1 |
| 5% | 1/20 | 0.05 |
| 1% | 1/100 | 0.01 |
Visualizing the conversion process helps solidify understanding. Imagine a pie chart representing 100%. 50% is half the pie, 25% is a quarter, and so on. Similarly, think of a number line from 0 to 1, where 0.5 is exactly in the middle, corresponding to 50%. This visual mapping aids in recalling conversions.
Text-based content
Library pages focus on text content
Practice Makes Perfect
The key to mastering percentage conversions is consistent practice. Work through various problems that require these conversions, and you'll find yourself becoming faster and more accurate. Pay attention to the context of the question to ensure you're applying the correct conversion.
Pro Tip: For percentages like 33.33% (1/3) or 66.67% (2/3), it's crucial to recognize their fractional equivalents as they appear frequently in exam questions.
Learning Resources
A clear video introduction to the concept of percentages and their meaning.
Explains the fundamental conversions with examples and interactive elements.
A comprehensive guide covering the relationships between these three numerical forms.
Offers a variety of practice questions with solutions for percentage conversions.
Focuses on percentage concepts specifically tailored for CAT exam preparation.
A wiki page listing essential equivalents that are frequently used in competitive exams.
Provides a foundational understanding of percentages with a focus on exam strategies.
A visual tutorial that uses graphics to explain percentage concepts and conversions.
A focused guide on the specific process of converting percentages into their fractional forms.
A straightforward explanation of how to convert decimal numbers into percentages.