Practice Problems: Number System- 1 Video Lecture | UPSC CSAT: Crash Course (English)

Ans. The number system is a way of representing and manipulating numbers. It includes different types of numbers such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers. The number system is important as it forms the foundation for various mathematical operations and calculations. It helps in solving problems related to arithmetic, algebra, geometry, and other branches of mathematics.

Ans. There are different types of numbers in the number system. These include: - Natural numbers: Numbers used for counting and denoted by positive integers starting from 1. - Whole numbers: Natural numbers along with zero. - Integers: Whole numbers along with their negatives. - Rational numbers: Numbers that can be expressed as a fraction or ratio of two integers. - Irrational numbers: Numbers that cannot be expressed as a fraction and have non-repeating, non-terminating decimal representations. - Real numbers: The combination of rational and irrational numbers. - Complex numbers: Numbers that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Ans. To convert a decimal number to a fraction, follow these steps: 1. Let the decimal number be represented by x. 2. Count the number of decimal places in x and multiply both the numerator and denominator of the fraction by 10 raised to the power of the number of decimal places. 3. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor. 4. The resulting fraction is the conversion of the decimal number.

Ans. The base in the number system determines the number of unique digits used to represent numbers. For example, in the decimal system (base 10), there are 10 unique digits (0-9). In the binary system (base 2), there are only 2 unique digits (0 and 1). The base also determines the place value of each digit in a number. The significance of the base lies in its ability to represent numbers efficiently and accurately, allowing for various arithmetic operations and calculations.

Ans. To convert a number from one base to another, follow these steps: 1. Start with the given number in the original base. 2. Divide the number by the new base repeatedly, noting down the remainders at each step. 3. The remainders, read from bottom to top, form the digits of the number in the new base. 4. If there is a quotient in any step, repeat the division process until the quotient becomes zero. 5. The resulting digits in the new base form the conversion of the number from the original base.