Class 9 Exam  >  Class 9 Notes  >  Extra Documents & Tests for Class 9  >  RS Aggarwal Solutions: Exercise 1F - Number System

RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 PDF Download

Q.1. Write the rationalising factor of the denominator in RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Here, the denominator i.e. 1 is a rational number. Thus, the rationalising factor of the denominator in RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.2. Rationalise the denominator of each of the following.
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iv)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(v)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(vi)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(vii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(viii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ix)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
On multiplying the numerator and denominator of the given number by √7, we get:
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
On multiplying the numerator and denominator of the given number by √3, we get:
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
On multiplying the numerator and denominator of the given number by 2 - √3, we get:
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iv)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
On multiplying the numerator and denominator of the given number by √5 +2, we get:

RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(v)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

On multiplying the numerator and denominator of the given number by 5-3√2, we get:
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(vi)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Multiplying the numerator and denominator by √7+√6, we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(vii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Multiplying the numerator and denominator by √11+√7, we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(viii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Multiplying the numerator and denominator by 2+√2, we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ix)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Multiplying the numerator and denominator by 3-2√2, we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.3. It being given that √2 = 1.414, √3 = 1.732, √5 = 2.236 and √10 = 3.162, find the value of three places of decimals, of each of the following.
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Ans.
(i)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

(iii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.4. Find rational numbers a and b such that

(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iv)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Ans.

(i)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iv)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.5. It being given  that √3 = 1.732, √5 = 2.236, √6 = 2.449  and √10 = 3.162, find to three places of decimal, the value of each of the following.

(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iv)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(v)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(vi)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
(i)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
= 0.213
(ii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
=3 × (2.236 − 1.732)
= 1.512
(iii)

RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iv)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(v)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
= 16.660
(vi)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
= 4.441

Q.6. Simplify by rationalising the denominator.
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
(i)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.7. Simplify
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iv)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
(i)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
= 0
(iii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
= 16 − √3
(iv)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
= 0

Q.8. Prove that
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
(i)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
= 2/2
= 1
(ii)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.9. Find the values of a and b if
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Comparing with the given expression, we get
a = 0 and b = 1
Thus, the values of a and b are 0 and 1, respectively.

Q.10. Simplify
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.11. If x = 3 + 2√2, check whether RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9is rational or irrational.
Ans.

x = 3 + 2√2    .....(1)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Adding (1) and (2), we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9which is a rational number
Thus, RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9is rational.

Q.12.
If x = 2 − √3, find value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
x = 2 − √3    .....(1)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Subtracting (2) from (1), we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Thus, the value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.13. If x = 9 − 4√5, find the value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
x = 9 − 4√5    .....(1)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Adding (1) and (2), we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Squaring on both sides, we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Thus, the value of x2 + RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 is 322.

Q.14. If x = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 find the value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.

RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Adding (1) and (2), we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Thus, the value of x +RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9is 5.

Q.15. If a = 3 − 2√2, find the value of a- RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
a = 3−2√2
⇒ a2 = (3−2√2)2
⇒ a2 = 9 + 8 − 12√2
⇒ a= 17 − 12√2    .....(1)
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Subtracting (2) from (1), we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Thus, the value of a2 - RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.16. If x = √13 + 2√3, find the value of x − RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Subtracting (2) from (1), we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Thus, the value of x RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.17.

If x = 2 + √3, find the value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 
Adding (1) and (2), we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Cubing both sides, we get
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Thus, the value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.18. If RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9andRS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9show that RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
Disclaimer: The question is incorrect.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
The question is incorrect. Kindly check the question.
The question should have been to show that x − y = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.19. If a = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9and b = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9show that 3a+ 4ab − 3b= RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
According to question,
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Now,
3a+ 4ab − 3b2
= 3(a− b2) + 4ab
= 3 (a + b)(a − b) + 4ab
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, 3a+ 4ab − 3b= RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.20.
If a = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9and b =RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9find the value of a2 + b2 – 5ab.
Ans.
According to question,
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Now,
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, the value of a2 + b2 – 5ab is 93.

Q.21.
If p = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9and q = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9find the value of p2 + q2.

Ans.
According to question,
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Now,
p2 + q2 = (p+q)− 2pq
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, the value of p2 + q2 is 47.

Q.22. Rationalise the denominator of each of the following.
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 
(ii) RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
(i)RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, the rationalised form is RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(ii) RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, the rationalised form is RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
(iii) RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, the rationalised form is RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

Q.23. Given, √2 = 1.414 and √6 = 2.449, find the value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9correct to 3 places of decimal.
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, the value of RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9correct to 3 places of decimal is −1.465.

Q.24. If x = RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9find the value of x3 – 2x2 – 7x + 5.
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Now,
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Also,
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Now,
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence, the value of x– 2x2 – 7x + 5 is 3.

Q.25. Evaluate RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 it being given that √5 = 2.236 and √10 = 3.162.
Hint

RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Ans.
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9
Hence,RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9

The document RS Aggarwal Solutions: Exercise 1F - Number System | Extra Documents & Tests for Class 9 is a part of the Class 9 Course Extra Documents & Tests for Class 9.
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FAQs on RS Aggarwal Solutions: Exercise 1F - Number System - Extra Documents & Tests for Class 9

1. What are the different types of number systems?
Ans. The different types of number systems are: 1. Decimal number system: It is the most commonly used number system, which uses the base 10 and consists of digits from 0 to 9. 2. Binary number system: It is a base 2 number system, which uses only two digits, 0 and 1. It is widely used in computer systems. 3. Octal number system: It is a base 8 number system, which uses digits from 0 to 7. 4. Hexadecimal number system: It is a base 16 number system, which uses digits from 0 to 9 and alphabets A to F. It is often used in computer programming and digital electronics. 5. Roman numeral system: It is an ancient number system, which uses combinations of letters from the Latin alphabet to represent numbers.
2. How to convert a decimal number to a binary number?
Ans. To convert a decimal number to a binary number, follow these steps: 1. Divide the decimal number by 2 and note down the remainder. 2. Divide the quotient obtained in step 1 by 2 again and note down the remainder. 3. Repeat step 2 until the quotient becomes 0. 4. The binary number is obtained by writing down the remainders in reverse order, starting from the last remainder obtained. For example, to convert decimal number 25 to binary: 25 ÷ 2 = 12 remainder 1 12 ÷ 2 = 6 remainder 0 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Therefore, the binary representation of 25 is 11001.
3. What is the significance of the base in number systems?
Ans. The base of a number system determines the number of digits used in that system and the value each digit can take. It is also known as the radix. In the decimal number system, the base is 10, which means it has 10 digits from 0 to 9. Each digit's value is multiplied by powers of 10 based on its position in the number. In binary system, the base is 2, which means it has only two digits, 0 and 1. Each digit's value is multiplied by powers of 2 based on its position. The significance of the base is that it determines the counting system and the range of numbers that can be represented in that number system. Different bases are used in different applications, such as binary in computers and decimal in everyday life.
4. How is the octal number system used in computer programming?
Ans. The octal number system is used in computer programming for several purposes, including: 1. Representation of file permissions: In Unix-like operating systems, file permissions are represented using octal digits. Each digit represents the permission for a specific user group, such as owner, group, and others. 2. Bitwise operations: Octal numbers are often used in bitwise operations, where each octal digit represents three binary digits. This makes it easier to perform operations on groups of bits. 3. Conversion between binary and hexadecimal: Octal numbers can be used as an intermediate step when converting between binary and hexadecimal numbers. Binary numbers can be grouped into groups of three bits, and each group can be represented by a single octal digit. 4. Addressing modes: In computer architecture, addressing modes are often represented using octal numbers. These modes define how data is accessed or stored in memory or registers.
5. How is the Roman numeral system used in modern times?
Ans. Although the Roman numeral system is no longer widely used in everyday life, it still has some applications in modern times, such as: 1. Clock faces: Roman numerals are commonly used on clock faces to represent the hours. For example, the number 4 is represented as IV, and 9 is represented as IX. 2. Numbering of monarchs and popes: Roman numerals are often used to number monarchs and popes. For example, Queen Elizabeth II is the second monarch with that name. 3. Copyright dates: Roman numerals are sometimes used in copyright dates to give a traditional and timeless feel. For example, a book published in 2021 may have the copyright date MMXXI. 4. Book chapters and sections: Roman numerals are occasionally used to number chapters and sections in books or legal documents for a hierarchical structure. 5. Decorative purposes: Roman numerals are often used in decorative purposes, such as on buildings, statues, or awards, to give a classic and elegant appearance.
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