Decimals

The topic of Decimals is a crucial component of the Quantitative Aptitude section in the Common Law Admission Test (CLAT). This area evaluates your ability to work with decimal numbers, understand their properties and perform various arithmetic operations involving decimals. As a student preparing for the CLAT, mastering the concept of decimals is essential to enhance your mathematical and analytical skills. In this detailed article, we will explore the fundamental concepts of decimals, provide illustrative examples and share effective strategies to solve decimal-related problems.

Understanding Decimal Basics

Before delving into solving decimal problems, it’s essential to establish a clear understanding of the fundamental concepts:

• Decimal Numbers: Decimal numbers are numbers that include a decimal point, which separates the whole part from the fractional part.
• Place Value: Each digit in a decimal number holds a specific place value, determined by its position relative to the decimal point.
• Decimal Point: The decimal point separates the whole number part from the fractional part in a decimal number.
• Decimal Fraction: A decimal fraction is a fraction where the denominator is a power of 10, such as 10, 100, 1000 and so on.
• Rounding Decimals: Rounding decimals involves approximating a decimal number to a specified number of decimal places.

Solving Decimal Problems: Concepts and Examples

Example 1: Addition of Decimals

Question: Calculate the sum of 3.45 and 2.18.

Solution:

1. Line up the decimal points of both numbers.

2. Add the digits in the same columns: 5 + 8 = 13, 4 + 1 = 5 and 3 + 2 = 5.

3. Write down the result, maintaining the decimal point alignment: 3.45 + 2.18 = 5.63.

Example 2: Multiplication of Decimals

Question: Find the product of 0.6 and 0.25.

Solution:

1. Multiply the numbers as if they were whole numbers: 6 * 25 = 150.

2. Count the total decimal places in the original numbers: 1 + 2 = 3 decimal places.

3. Place the decimal point in the result, counting 3 places from the right: 0.6 * 0.25 = 0.150.

Example 3: Division of Decimals

Question: Divide 2.7 by 0.9.

Solution:

1. Multiply both the dividend (2.7) and the divisor (0.9) by 10 to eliminate the decimal in the divisor.

2. Perform the division: 27 ÷ 9 = 3.

3. Since we multiplied the numbers by 10, divide the result by 10: 3 ÷ 10 = 0.3.

Strategies for Solving Decimal Problems

Solving decimal problems requires precision and attention to detail. Here are some strategies to approach decimal-related problems effectively:

1. Alignment: When performing arithmetic operations involving decimals, ensure that the decimal points are aligned correctly.

2. Rounding: Pay attention to the required level of precision. Sometimes, you may need to round decimals to a specific number of decimal places.

3. Conversion: If necessary, convert fractions to decimals and decimals to fractions to simplify calculations.

4. Lining Up: When adding or subtracting decimals, line up the digits vertically to avoid errors.

5. Practice: Regular practice is essential to familiarise yourself with the various types of decimal problems and improve your calculation speed.

Conclusion

Decimals form a fundamental aspect of quantitative aptitude and a solid understanding of decimal concepts is essential for success in the CLAT. By grasping the basics of decimals, practicing calculations accurately and applying strategies like alignment and rounding, you can tackle decimal problems with confidence. As you prepare for the CLAT, mastering decimals not only enhances your mathematical skills but also boosts your overall problem-solving abilities. So, roll up your sleeves, sharpen your pencil and dive into decimal problems with determination and skill!