Exercise 2.1

Exercise 2.1

Fill in the blanks

i) The potable water available at 100m below the ground level is denoted as −100  m.

ii) A swimmer dives to a depth of 7 feet from the ground into the swimming pool. The integer that represents this, is −7 feet.

iii) −46 is to the left of −35 on the number line.

iv) There are 11 integers from −5 to +5 (both inclusive).

v) 0 is an integer which is neither positive nor negative.

2. Say True or False

i) Each of the integers −18, 6, −12, 0 is greater than −20. [True]

ii) −1 is to the right of 0. [ False]

iii) −10 and 10 are at equal distance from 1. [ False]

iv) All negative integers are greater than zero. [ False]

v) All whole numbers are integers. [True]

3. Mark the numbers 4, −3, 6, −1 and −5 on the number line.

4. On the number line, which number is

i) 4 units to the right of −7? 

Answer: −3

 ii) 5 units to the left of 3?

Answer: −2

5. Find the opposite of the following numbers.

i) 44

ii) −19

iii) 0

iv) −312

v) 789

i) 44 = Opposite of 44 is −44

ii) −19 = Opposite of −19 is +19

iii) 0 = It has no sign

iv) − 312 = Opposite of −312 is + 312

v) 789 = Opposite of 789 is −789

6. If 15 km east of a place is denoted as + 15 km, what is the integer that represents 15 km west of it?

Answer: −15

7. From the following number lines, identify the correct and the wrong representations with reason.

i) Wrong Integers are not continuously marked.

ii) Correct Integers are correctly marked.

iii) Wrong Integer − 2 is marked wrongly.

iv) Correct Integers are marked at equal distance.

v) Wrong negative integers marked wrongly.

8. Write all the integers between the given numbers.

i) 7 and 10

ii) −5 and 4

iii) −3 and 3

iv) −5 and 0

i) 7 and 10 = 8, 9

ii) −5 and 4 = −4, −3, −2, −1, 0, 1, 2, 3

iii) −3 and 3 = −2, −1, 0, 1, 2

iv) −5 and 0 = −4, −3, −2, −1

9. Put the appropriate signs as <, > or = in the box.

i) −7  8

ii) −8  −7

iii) −999  −1000

iv) −111  −111

 v) 0  −200

Answer:

i) −7 < 8

ii) −8 <  −7

iii) −999 > −1000

iv) −111 = − 111

v) 0 > − 200

10. Arrange the following integers in ascending order.

i) −11, 12, −13, 14, −15, 16, −17, 18, −19, −20

−20, −19, −17, −15, −13, −11, 12, 14, 16, 18

ii) −28, 6, −5, −40, 8, 0, 12, −1, 4, 22

−40, −28, −5, −1, 0, 4, 6, 8, 12, 22

iii) −100, 10, −1000, 100, 0, −1, 1000, 1, −10

−1000, −100, −10, −1, 0, 1, 10, 100, 1000

11. Arrange the following integers in descending order.

i) 14, 27, 15, −14, −9, 0, 11, −17

 27, 15, 14, 11, 0, −9, −14, −17

ii) −99, −120, 65, −46, 78, 400, −600

 400, 78, 65, −46, −99, −120, −600

iii) 111, −222, 333, −444, 555, −666, 7777, −888

 777, 555, 333, 111, −222, −444, −666, −888

Objective Type Questions

12. There are __________ positive integers from −5 to 6.

 a) 5

b) 6

c) 7

d) 11

Answer: c) 7

13. The opposite of 20 units to the left of 0 is

a) 20

b) 0

c) −20

d) 40

Answer: a) 20

14. One unit to the right of −7 is...........

a) +1

b) −8

c) −7

d) −6

Answer: d) −6

15. 3 units to the left of 1 is

a) −4

b) –3

c) −2

d) 3

Answer: c) −2

16. The number which determines marking the position of any number to its opposite on a number line is

a) −1

b) 0

c) 1

d) 10

Answer: b) 0

ANSWERS:

Exercise 2.1

1. i) –100 ii) −7 iii) left iv) 11 v) 0

2. i) True ii) False iii) False iv) False v) True

3. 

4. i) −3 ii) −2

5. i) −44 ii) +19 or 19 iii) 0 iv) 312 v) −789

6. i) −15 km

7. i) Wrong, Integers are not continuously marked

ii) Correct, Integers are correctly marked.

iii) Wrong, Integer −2 is marked wrongly.

iv) Correct, Integers are marked at equal distance.

v) Wrong, negative integers marked wrongly.

8. i) 8, 9 ii) −4, −3, −2, −1, 0, 1, 2, 3 iii) −2, −1, 0, 1, 2 iv) −4, −3, −2, −1

9. i) −7 < 8 ii) −8 < −7 iii) −999 >−1000 iv) −111 = −111 v) 0 > −200

10. i) −20, −19,−17, −15, −13, −11, 12, 14, 16, 18

ii) −40, −28, −5, −1, 0, 4, 6, 8, 12, 22

iii) −1000, −100, −10, −1,0, 1, 10, 100, 1000

11. i) 27, 15, 14, 11, 0, −9, −14, −17

ii) 400, 78, 65, −46, −99, −120, −600

iii) 777, 555, 333, 111, −222, −444, −666, −888

12. c) 7

13) a) 20

14) d) −6

15) c) −2

16) b) 0