- Chapter No.1 Introduction to Biology
- Chapter No. 2 Solving a Biological Problem
- Chapter No.3 Biodiversity
- Chapter No.4 Cells and Tissues
- Chapter No.5 Cell Cycle
Q1. Identify which of the following are rational and irrational numbers.
(i) sqrt(3) (ii) 1/6 (iii) pi (iv) 15/2 (v)7.25 (vi) sqrt(29)
Solution:
To identify which of the numbers are rational or irrational, let’s review the definitions:
Rational Numbers: Rational numbers are numbers that can be expressed as a fraction of two integers (a/b), where “a” is the numerator and “b” is the non-zero denominator.
Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They cannot be represented by terminating or repeating decimals.
Now, let’s determine the nature of each number:
(i) √3: This is an irrational number because the square root of a non-perfect square is irrational.
(ii) 1/6: This is a rational number since it can be expressed as a fraction of two integers (1 and 6).
(iii) π (pi): This is an irrational number. Pi is a transcendental number, meaning it is not the root of any non-zero polynomial equation with rational coefficients.
(iv) 15/2: This is a rational number since it can be expressed as a fraction of two integers (15 and 2).
(v) 7.25: This is a rational number since it can be expressed as a fraction in decimal form (7.25 = 725/100).
(vi) √29: This is an irrational number because the square root of 29 is not a perfect square.
Q.2 Convert the following fractions into decimal fractions.
(i) 17/25
(ii) 19/4
(iii) 57/8
(iv) 205/18
(v)5/8
(vi)25/38
Solution:
To convert the given fractions into decimal fractions, we’ll perform the division. Keep in mind that some fractions might result in terminating decimals, while others could result in repeating decimals.
(i) 17/25:
17 ÷ 25 ≈ 0.68
(ii) 19/4:
19 ÷ 4 = 4.75
(iii) 57/8:
57 ÷ 8 = 7.125
(iv) 205/18:
205 ÷ 18 ≈ 11.388888…
(v) 5/8:
5 ÷ 8 = 0.625
(vi) 25/38:
25 ÷ 38 ≈ 0.657894736…
So, the decimal representations of the fractions are:
(i) 17/25 ≈ 0.68
(ii) 19/4 = 4.75
(iii) 57/8 = 7.125
(iv) 205/18 ≈ 11.39 (rounded to two decimal places)
(v) 5/8 = 0.625
(vi) 25/38 ≈ 0.658 (rounded to three decimal places)
Q.3 Which of the following statements are true and which are false?
(i) 2/3 is an irrational number.
(ii) pi is an irrational number.
(iii) 1/9 a terminating fraction
(iv) 3/4 is a terminating fraction.
(v) 4/5 a recurring fraction.
Solution:
Let’s evaluate each statement:
(i) 2/3 is an irrational number. – False
Explanation: 2/3 is a rational number because it can be expressed as a fraction of two integers.
(ii) π (pi) is an irrational number. – True
Explanation: Pi (π) is an irrational number. It cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal representation.
(iii) 1/9 is a terminating fraction. – False
Explanation: 1/9 is not a terminating fraction. When you divide 1 by 9, you get 0.111… with the digit 1 repeating infinitely.
(iv) 3/4 is a terminating fraction. – True
Explanation: 3/4 is a terminating fraction. When you divide 3 by 4, you get 0.75, which terminates.
(v) 4/5 is a recurring fraction. – False
Explanation: 4/5 is not a recurring fraction. When you divide 4 by 5, you get 0.8, which terminates.
In summary:
(i) False
(ii) True
(iii) False
(iv) True
(v) False
Q.4 Represent the following numbers on the number line.
(i)2/3 (ii) – 4/5 (iii) 1 3/4 (iv)- 2 5/8 (v) 2 3/4 (vi) sqrt(5)