Ex-1.1 Number System, Class 9, Maths RD Sharma Solutions | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q: 1. What is the importance of studying the number system in class 9 mathematics?

Ans. The number system is the foundation of mathematics and understanding its concepts is crucial for higher-level math topics. Studying the number system in class 9 helps students grasp the fundamental concepts of numbers, their properties, operations, and conversions. It provides a strong base for solving complex mathematical problems and is essential for future mathematical and scientific studies.

Q: 2. How can I identify whether a given number is rational or irrational?

Ans. To determine whether a number is rational or irrational, we need to check if it can be expressed as a fraction of two integers (p/q), where q is not equal to zero. If the number can be written in this form, it is rational. Otherwise, if the number cannot be expressed as a fraction, it is irrational. For example, √2 is irrational because it cannot be written as a fraction, while 5/7 is rational as it can be expressed as a fraction.

Q: 3. How do I convert a recurring decimal into a fraction?

Ans. To convert a recurring decimal into a fraction, we follow the following steps:1. Let x be the recurring decimal.2. Multiply x by 10 raised to the power of the number of digits in the repeating part.3. Subtract the original x from the new value obtained in step 2.4. Solve the resulting equation to find the value of x.5. Express the obtained x as a fraction.For example, to convert the recurring decimal 0.333... into a fraction:Let x = 0.333...Multiplying both sides by 10 gives:10x = 3.333...Subtracting the original equation from the new equation gives:10x - x = 3.333... - 0.333...Simplifying, we get:9x = 3Dividing both sides by 9, we find:x = 1/3Therefore, the recurring decimal 0.333... is equal to the fraction 1/3.

Q: 4. How do I determine the HCF and LCM of two or more numbers?

Ans. To determine the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of two or more numbers, you can follow these steps:For HCF:1. Find the prime factors of each number.2. Identify the common prime factors and multiply them to obtain the HCF.For example, let's find the HCF of 12 and 18:The prime factors of 12 are 2, 2, and 3.The prime factors of 18 are 2, 3, and 3.The common prime factors are 2 and 3.Multiplying the common prime factors, we get: HCF = 2 * 3 = 6.For LCM:1. Find the prime factors of each number.2. Identify the highest power of each prime factor occurring in any of the numbers and multiply them to obtain the LCM.Continuing with the previous example, let's find the LCM of 12 and 18:The prime factors of 12 are 2, 2, and 3.The prime factors of 18 are 2, 3, and 3.The highest power of 2 is 2^2 = 4.The highest power of 3 is 3^2 = 9.Multiplying the highest powers of the prime factors, we get: LCM = 4 * 9 = 36.

Q: 5. How do I determine the square root of a given number?

Ans. To determine the square root of a given number, you can use the following methods:1. Prime Factorization Method: - Find the prime factors of the given number. - Pair the prime factors in pairs. - Take one factor from each pair and multiply them to obtain the square root.2. Long Division Method: - Write the given number as a dividend under the root symbol. - Group the digits of the dividend in pairs starting from the right. - Find the largest number whose square is less than or equal to the leftmost group. - Write this number as the divisor and divide it into the leftmost group. - Bring down the next pair of digits and continue the process until all the digits are exhausted. - The quotient obtained is the square root of the given number.These methods can be used to find the square root of any non-perfect square number.

Q1. Is 0 a rational number? Can you write it in the form P/Q , where P and Q are integers and Q ≠ 0?

Solution:

Yes, 0 is a rational number and it can be written in P÷Q form provided that Q ≠ 0

0 is an integer and it can be written various forms, for example

0÷2,0÷100,0÷95 etc.

Q2. Find five rational numbers between 1 and 2

Solution:

Given that to find out 5 rational numbers between 1 and 2

Rational number lying between 1 and 2
Rational number lying between 1 and 3/2
Rational number lying between 1 and 5/4
Rational number lying between 3/2 and 2
= 9/2
= 1 < 9/8 < 5/4
Rational number lying between 3/2 and 2
Rational number lying between 7/4 and 2

Therefore,

Q3. Find out 6 rational numbers between 3 and 4

Solution:

Given that to find out 6 rational numbers between 3 and 4

We have,