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Number System is an important chapter of mathematics. A student needs to be strong in the fundamentals of the number system to solve other problems related to maths. Some students face difficulty in solving sums of the number system. So, here in this article, we have provided some crucial sums relating to the number system. A student can practice these questions, and it would be easy for him/her to understand the chapter. In this article, we have provided various questions based on number systems such as number system questions and answers, number system practice questions, MCQs on number systems and many other important questions.

Q1. Determine whether the numbers are rational or irrational.

√2

1.5

√100

3.14

Ans. A rational number is a number which can be represented in the form of p/q, whereas an irrational number cannot be represented in the form of p/q. So,

√2 is Irrational.

1.5 is Rational.

√100 is Rational.

3.14 is Irrational.

Q2. Without Actual Division, state which of the following is a terminating decimal.

\[\frac{9}{25}\]

\[\frac{37}{78}\]

Ans. In \[\frac{9}{25}\], the prime factors of denominator 25 are 5,5. Thus, it is a terminating decimal. In \[\frac{37}{78}\], the prime factors of denominator 78 are 2, 3, and 13. Thus, it is a non-terminating decimal.

Q3. Express each of the following as a rational number in the form of p/q, where q ≠ 0.

\[0.\overline{6}\]

\[0.\overline{43}\]

Ans. 1. Let x = 0.6666 …..(i)

Multiplying both side of eqn (i) by 10 we get,

10x = 6.6666…..(ii)

Now, subtracting eqn (i) from eqn (ii) we get,

10x = 6.6666

x = 0.6666

9x = 6.

⇒ x = 6/9 which is equal to ⅔, So required fraction is ⅔.

2. Let x = 0.43434343….(i)

Multiplying both sides of eqn (i) by 100 we get,

100x = 43.43434343…..(ii)

Now, subtracting eqn (i) from eqn (ii) we get,

100x = 43.43434343

x = 0.43434343

99x = 43

⇒ x = 43/99, Hence the fraction is 43/99.

Q4. Find 4 rational numbers between 1 and 2.

Ans. To find 4 rational numbers between 1 and 2, we need to divide and multiply both the numbers by (4 + 1) which is 5. So we get,

1 X 5/5 = 5/5 and 2 X 5/5 = 10/5, Therefore the rational numbers are:

5/5, 6/5, 7/5, 8/5, 9/5, 10/5.

Q5. Compare the following numbers.

(i) 0 and -9/5.

(ii) -17/20 and -13/20.

(iii) 40/29 and 141/29.

Ans. (i) We know that a negative number is always less than 0. Therefore,

0 > - 9/5.

(ii) Here the denominator is the same and we know that -17 < -13. Therefore,

-17/20 < -13/20.

(iii) Here the denominator is the same and we know that 40 < 141. Therefore,

40/29 < 141/29.

Q6. Write the following in decimal numbers and state what expansion it is.

(i) 40/100 (ii) 9/10 (iii) 9/37 (iv) 103/5

Ans. (i) 40/100 is 0.40, and it is terminating.

(ii) 9/10 is 0.9, and it is terminating.

(iii) 9/37 is 0.243243… it is non-terminating.

(iv) 103/5 is 20.6, and it is terminating.

Q7. Insert one rational number between ⅗ and 7/9.

Ans. If a and b are two rational numbers, then one rational number between these two will be

\[\frac{a + b}{2}\]. Hence the required rational number will be

\[\frac{1}{2} (\frac{3}{5} + \frac{7}{9}) = \frac{1}{2} (\frac{27 + 35}{45}) = \frac{1}{2} \times \frac{62}{45} = \frac{31}{45}\]

So, the rational number is 31/45.

Here, we have provided some number system math questions which are based on number system conversion.

Q1. Convert each of the following into a decimal number.

(i) \[\frac{4}{15}\]

(ii) \[2\frac{5}{12}\]

(iii) \[\frac{9}{27}\]

(iv) \[5\frac{31}{55}\]

Q2. Convert the following into a rational number.

(i) \[0.\overline{227}\]

(ii) \[0.\overline{2104}\]

As we know, practice makes everyone perfect, so for the better understanding of students, we have provided some number system important questions for practice.

Q1. Show the number √5 on the number line.

Q2. Insert three rational numbers between 4 and 5.

Q3. Represent the following rational numbers in decimal form

(i) 18/42 (ii) -11/13

Q4. Rationalise the denominator of \[\frac{1}{3 - \sqrt{5}}\].

Q5. Simplify the following expression (2^{4} - 3^{2}) . ( 5 + 2^{3})

FAQ (Frequently Asked Questions)

Q1. Give Some MCQs on the Number System.

Answer. Some important MCQs on Number System are:

1. From the following choose Co-prime numbers.

(a) 2, 3 (b) 2, 4 (c) 2, 6 (d) 2, 110

2. On adding 2√3 and 3√2 we get:

(a) 5√5 (b) 5(√3 + √2) (c) 2√3 + 3√2 (d) None of these

3. A rational number between √2 and √3.

(a) 1.9 (b) (√2.√3)/2 (c)1.5 (b) 1.8

4. Which of the following is irrational?

(a) √4/9 (b)√12/√3 (c) √5 (d) √81

5. The Value of (16)^{3/4} is equal to:

(a) 2 (b) 4 (c) 8 (d) 16

Q2. What do You Mean by Number System? What are its Types?

Answer. The number system can be defined as the expression of numbers in a written format. These are a set of symbols and rules used to denote numbers. The number system is used to state how many objects are there in a given set. There are different types of number systems, and here we have mentioned some of the types of number systems for better knowledge of students. The following are the types of number system:

Real Numbers.

Natural Numbers.

Whole Numbers.

Rational Number system.

Irrational Number system.

Complex Number system.

Binary Number system.

Decimal Number System.

Hexa-Decimal Number System.

Octal-Decimal Number System.