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Q1. Express each of the following decimals in the form of rational number.
(i) 0.39
(ii) 0.750
(iii) 2.15
(iv) 7.010
(v) 9.90
(vi) 1.0001
Solution:
(i) Given,
0.39 = 39/100
(ii) Given,
0.750 = 750/1000
(iii) Given,
2.15 = 215/100
(iv) Given,9.101
(iv) Given,
7.010 = 7010/1000
(v) Given,
9.90 = 990/100
(vi) Given,
1.0001 = 10001/10000
Q2. Express each of the following decimals in the form of rational number (p/q)
(i) 
(ii) 
Solution:
(i) Let x = 
Then, x = 
= 0.444… ___ (a)
Multiplying both sides of equation (a) by 10, we get,
10x = 4.44.... ___ (b)
Subtracting equation (1) by (2)
9x = 4
x = 4/9
Hence, = x = 4/9
(ii) Let x =
Then, x = = 0.3737… ___ (a)
Multiplying both sides of equation (a) by 100, we get,
100 x = 37.37.... ___ (b)
Subtracting equation (1) by (2)
99 x = 37
x = 37/99
Hence, = x = 37/99
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FAQs on RD Sharma Solutions Ex-1.3, Number System, Class 9, Maths - RD Sharma Solutions for Class 9 Mathematics
| 1. What is the importance of learning number systems in mathematics? |  |
| 2. What are the different types of numbers in the number system? | |
Ans. The number system consists of various types of numbers, including natural numbers (1, 2, 3, ...), whole numbers (0, 1, 2, ...), integers (-3, -2, -1, 0, 1, 2, ...), rational numbers (fractions and terminating or repeating decimals), and irrational numbers (non-terminating and non-repeating decimals, such as √2 or π). These different types of numbers have specific properties and relationships within the number system.
| 3. How can number systems be applied in real-life situations? | |
Ans. Number systems are widely used in various real-life situations. For example, when measuring distances, time, or money, we use the decimal system. In computer science, the binary number system is used to represent and process information. The concept of negative numbers is applied in situations involving debts or temperatures below zero. Understanding number systems helps in solving practical problems and making sense of numerical information in everyday life.
| 4. What is the relationship between different types of numbers in the number system? | |
Ans. The different types of numbers in the number system are interconnected. Natural numbers are a subset of whole numbers, which are a subset of integers. Integers include both positive and negative numbers, while rational numbers encompass integers and fractions. Irrational numbers are those that cannot be expressed as fractions and have non-terminating and non-repeating decimal expansions. The set of rational and irrational numbers together forms the set of real numbers.
| 5. How can understanding the number system help in solving mathematical problems? | |
Ans. Understanding the number system is essential for solving mathematical problems as it provides a framework for performing various operations. It helps in simplifying expressions, solving equations, and working with fractions and decimals. The properties and relationships within the number system guide the application of mathematical operations. By understanding number systems, students can develop a strong foundation in mathematics and apply their knowledge to solve complex problems efficiently.
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