# Class 8 Maths Chapter 1 Question Answers - Number System

Q1. Find a rational number between 1 and 2.

Let x = 1 and y = 2, then

Thus,  3/2 is a rational number between 1 and 2.

Q2. Write a rational number equivalent to 5/9 such that its numerator is 25.

∵ 25/5 = 5

Thus, 25/45 is the required rational number whose numerator is 25.

Q3. Find two rational numbers between 0.1 and 0.3.

Let x = 0.1, y = 0.3 and n = 2

∴ Two rational numbers between 0.1 and 0.3 are: x + d and x + 2d

Q4. Express  in the form of a decimal.

We have,
Now, dividing 25 by 8,

Since, the remainder is 0.
∴ The process of division terminates.

Q5. Express  as a rational number.

Multiplying (1) by 100, we have 100x = 100 x 0.3333…
⇒ 100x = 33.3333              …(2)
Subtracting (2) from (1), we have
100x – x = 33.3333… – 0.3333…
⇒ 99x = 33

Q6. Simplify: (4+ √3) (4 −3)

∵ (a + b)(a – b) = a2 – b2
(4 +√3) (4 −√3) = (4)2 – ( √3)2 = 16 – 3 = 13
Thus, (4 +√3) (4 −√3) = 13

Q7. Simplify: (√3 +√2)2

∵ (a + b)2 = a+ 2ab + b2
(√3 +√2)2 = (√3)2 + √2 ( √3 ×2) + (√2)2 = 3 + 2 √6 + 2 = 5 + 2 √6
Thus, (√3 +(√2)2 = 5 + 2√6

Q8. Rationalise the denominator of

Since RF of (√x - √y ) is (√x +√y )
∴ RF of (√3 - √2 ) is (√3 +√2 )
Now, we have

Thus,

Q9. Find

As, 64 = 4 x 4 x 4 = 43

Q10. Define a non-terminating decimal and repeating decimals.

The decimal expansion of some rational numbers do not have a finite number of decimal places in their decimal parts, rather they have a repeating block of digits in decimal parts. Such decimal expansion is called non-terminating and repeating decimal.
Example:

Q11. What is the difference between "pure recurring decimals" and "mixed-recurring decimals"?

A decimal in which all the digits after the decimal point are repeated is called a pure recurring decimal. A decimal in which at least one of the digits after the decimal point is not repeated and then some digit(s) repeated is called a mixed recurring decimal.
Example:  are pure recurring decimals.
are mixed recurring decimals.

Q12. What type of decimal expansion does an irrational number have?

The decimal expansion of an irrational number is "non-terminating and non-recurring."

Q13. Find a rational number lying between

Rational numbers between 1/2 and 1/5 are infinite. Some of them are 3/10 , 4/10 , 45/100 , 35/100. Step-by-step explanation: As per the question, We need to find drational numbers lying between 1/5 and 1/2 As we know,
• Rational Numbers are numbers that can be expressed in the form of p/q where q is not equal to zero.
• Now, we know that  1/5 = 0.2 and 1/2 = 0.5
• So, numbers between 0.2 and 0.5 are infinite. Some of them are 0.3,0.4,0.45,,0.35 etc.
• And these may be written as 3/10,4/10,45/100,35/100 tec.
Hence, Rational numbers between 1/2 and 1/5 are infinite. Some of them are 3/10 , 4/10 , 45/100 , 35/100.

Q14. Express  as a fraction in the simplest form.

Let X =  = 0.24545     ... (1)
Then, multiplying (1) by 10,
We have 10X = 10 x 0.24545...
⇒ 10x = 2.4545                      ... (2)
Again multiplying (1) by 1000,
we get 1000 x X = 0.24545... x 1000
⇒ 1000X = 245.4545                ... (3)
Subtracting (2) from (3),
1000X – 10X = 245.4545... – 2.4545...

Thus

Q15. If x = (2 +√5) , find the value of

We have x = 2 + √5

Now

The document Class 8 Maths Chapter 1 Question Answers - Number System is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9

## Mathematics (Maths) Class 9

48 videos|378 docs|65 tests

## FAQs on Class 8 Maths Chapter 1 Question Answers - Number System

 1. What is the number system?
Ans. A number system is a set of symbols used to represent quantities. It includes a base or radix that determines the number of digits used in the system, and each digit position represents a power of the base. The most commonly used number systems are decimal, binary, octal, and hexadecimal.
 2. What is the significance of the base or radix in a number system?
Ans. The base or radix in a number system determines the number of digits used in the system. For example, the decimal system has ten digits (0-9), while the binary system has two digits (0 and 1). The base also determines the value of each digit position, with each position representing a power of the base.
 3. What is the difference between a decimal and a binary number system?
Ans. The decimal system is a base-10 number system that uses ten digits (0-9) to represent quantities, while the binary system is a base-2 number system that uses two digits (0 and 1). In the decimal system, each digit position represents a power of 10, while in the binary system, each digit position represents a power of 2.
Ans. The hexadecimal system is a base-16 number system that uses 16 digits (0-9 and A-F) to represent quantities. It is commonly used in computer programming because it can represent large numbers in a compact form. Each hexadecimal digit represents four binary digits, making it easier to convert between binary and hexadecimal values.
 5. How do you convert a decimal number to a binary number?
Ans. To convert a decimal number to a binary number, you can use the division-by-2 method. Divide the decimal number by 2 and write down the remainder. Divide the quotient by 2 and write down the remainder again. Repeat this process until the quotient is 0, and write down the remainders in reverse order to get the binary equivalent. For example, to convert the decimal number 13 to binary, the remainders are 1, 0, 1, and the binary equivalent is 1101.

## Mathematics (Maths) Class 9

48 videos|378 docs|65 tests

### Up next

 Explore Courses for Class 9 exam

### Top Courses for Class 9

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Track your progress, build streaks, highlight & save important lessons and more!
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;