## Chapter 1 Number Systems Exercise 1.1

Question 1: Is zero a rational number? Can we write in the form p/q, where p and q are integers and q ≠ 0?

Answer: Yes, zero is a rational number. We can write 0 in the form of p/q where p and q are integers and q ≠ 0 like 0/1, 0/2 etc.

Question 2: Find six rational numbers between 3 and 4.

Answer:

3 = 3/1

4 = 4/1

3/1 × 10/10 = 30/10

4/1 × 10/10 = 40/10

So, the 6 rational numbers between 3 and 4 are 31/10 < 32/10 < 33/10 < 34/10 < 35/10 < 36/10.

Question 3: Find five rational numbers between 3/5 and 4/5.

Answer:

3/5 × 10/10 = 30/50

4/5 × 10/10 = 40/50

So, the 5 rational numbers between 3/5 and 4/5 are 31/50 < 32/50 < 33/50 < 34/50 < 35/50.

Question 4: State whether the following statements are true or false. Give reasons for your answers.

i) Every natural number is a whole number.

ii) Every integer is a whole number.

iii) Every rational number is a whole number.

Answer:

i) True; Every natural number is a whole number because whole number are a set of numbers that contain all the natural numbers (1, 2, 3, 4, 5, 6….) along with zero.

ii) False; Every integer is not a whole number because integers are a set of numbers which contain all the whole numbers (0, 1, 2, 3, 4, 5, 6….) along with negative numbers (…. -5, -4, -3, -2, -1).

iii) False; Every rational number is not a whole number because these numbers are written in the form of p/q where p and q are integers and q ≠ 0.

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