RD Sharma Solutions for Class 9 Maths Chapter 1 Number Systems

The solutions for RD Sharma Class 9 Maths, Chapter 1, Number System, are provided to help students get high marks in their exams. This chapter mainly covers rational and irrational numbers, natural numbers, whole numbers, and how to show real numbers on a number line. To build a strong foundation in the number system, students should practice these solutions regularly. You can access RD Sharma Class 9 Solutions online or offline.

The RD Sharma Class 9 textbook follows the latest CBSE syllabus. Each chapter ends with an exercise full of multiple-choice questions and a summary for quick revision of key concepts and formulas. To do well in the annual exams, it’s recommended to use RD Sharma Solutions while working through textbook problems.

RD Sharma Class 9 PDF Book With Solutions

Access Answers to RD Sharma Solutions for Class 9 Maths Chapter 1 Number System

Question: What is the definition of a rational number?

Answer: A rational number is any number that can be expressed in the form of pq\frac{p}{q}qp, where ppp and qqq are integers and q≠0q \neq 0q=0.

Question: How do you represent a repeating decimal as a fraction?

Answer: To represent a repeating decimal as a fraction, follow these steps:

1. Let xxx be the repeating decimal.
2. Multiply xxx by a power of 10 such that the repeating part aligns after the decimal.
3. Subtract the original decimal from this new number.
4. Solve for xxx to find the fraction form.

For example, for x=0.3‾x = 0.\overline{3}x=0.3:

1. Let x=0.333…x = 0.333…x=0.333…
2. Multiply by 10: 10x=3.333…10x = 3.333…10x=3.333…
3. Subtract: 10x−x=3.333…−0.333…10x – x = 3.333… – 0.333…10x−x=3.333…−0.333…
4. This simplifies to 9x=39x = 39x=3, so x=39=13x = \frac{3}{9} = \frac{1}{3}x=93=31.

Question: What are irrational numbers? Give an example.

Answer: Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They have non-terminating and non-repeating decimal expansions. An example of an irrational number is 2\sqrt{2}2 or π\piπ.

Question: How do you find the decimal expansion of a rational number?

Answer: To find the decimal expansion of a rational number pq\frac{p}{q}qp:

1. Divide ppp by qqq using long division.
2. If the division terminates, the decimal expansion is terminating.
3. If the division repeats, the decimal expansion is repeating.

For example, 14\frac{1}{4}41:

1. Divide 1 by 4.
2. 1÷4=0.251 \div 4 = 0.251÷4=0.25, so the decimal expansion is 0.25 (terminating).

Question: What is the difference between terminating and non-terminating repeating decimals?

Answer: Terminating decimals are decimals that end after a finite number of digits. Non-terminating repeating decimals are decimals that have a sequence of digits that repeat infinitely.

For example:

• Terminating decimal: 0.750.750.75
• Non-terminating repeating decimal: 0.666…0.666…0.666… (which can be written as 0.6‾0.\overline{6}0.6)

Question: Convert the repeating decimal 0.7‾0.\overline{7}0.7 into a fraction.

Answer: To convert 0.7‾0.\overline{7}0.7 into a fraction:

1. Let x=0.777…x = 0.777…x=0.777…
2. Multiply by 10: 10x=7.777…10x = 7.777…10x=7.777…
3. Subtract: 10x−x=7.777…−0.777…10x – x = 7.777… – 0.777…10x−x=7.777…−0.777…
4. This simplifies to 9x=79x = 79x=7, so x=79x = \frac{7}{9}x=97.

Question: Explain the density property of rational numbers.

Answer: The density property of rational numbers states that between any two rational numbers, there is always another rational number. This means that rational numbers are densely packed on the number line, with no gaps between them.

Question: Determine whether the following number is rational or irrational: 0.101001000100001…0.101001000100001…0.101001000100001…

Answer: The number 0.101001000100001…0.101001000100001…0.101001000100001… is an irrational number because its decimal expansion is non-terminating and non-repeating.

Question: Simplify the expression 50\sqrt{50}50.

Answer: To simplify 50\sqrt{50}50:

1. Factorize 50: 50=25×250 = 25 \times 250=25×2
2. 50=25×2=25×2=52\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}50=25×2=25×2=52

Question: What is the product of a rational number and an irrational number?

Answer: The product of a rational number and an irrational number is generally an irrational number. For example, 2×3=232 \times \sqrt{3} = 2\sqrt{3}2×3=23, which is irrational.

These questions and answers cover the basic concepts and operations related to number systems as found in RD Sharma’s Class 9 Chapter 1.