Number lines: Overview, Questions, Preparation

The number line makes it easy to know which numbers are greater or lesser. It extends on both sides with zero at the middle of the number line. We are aware that the number on the left is always less than the number on the right. The number line is used to add and subtract or perform any arithmetic operations.

The number refers to the visual representation of all the numbers on a line. Zero is the middle point of the number line. The line extends from both sides horizontally and makes the comparison of numbers easier.   

The collection of real numbers is made up of all rational and irrational numbers denoted by ‘R’. A real number can either be rational or irrational. Every real number is represented by a unique point on the number line. 

Operations on a Number Line

• The addition of two positive numbers will be a positive number lying on the number line’s right side.
• The addition of two negative numbers will always be a negative number lying on the left side.
• The subtraction of two positive numbers moves to the left, and two negative numbers move to the right as far as the value of the second number.

Weightage and Importance

Number lines are a part of the number system and have a good weightage for class 10th. Approximately 6 mark questions are asked from the chapter on numbers.

• Write the opposites of the following:

(a) Increase in weight (b) 30km north (c) 326 BC (d) Loss of Rs 700 (e) 100 m above sea level

Solution:

(a) Decrease in weight

(b) 30 km south

(c) 326 A.D.

(d) Gain of Rs 700

(e) 100 m below sea level

• In each of the following pairs, which number is to the other’s right on the number line?

(a) 2, 9 (b) − 3, − 8 (c) 0, − 1 (d) − 11, 10 (e) − 6, 6 (f) 1, − 100

Solution: 

(a) 9 (9 > 2) 

(b) −3 (−3 > −8) 

(c) 0 (0 > −1) 

(d) 10 (10 > −11) 

(e) 6 (6 > −6) 

(f) 1 (1 > −100)

• Write all the integers between the given pairs (write them in the increasing order).

(a) 0 and − 7 (b) − 4 and 4 (c) − 8 and − 15 (d) − 30 and − 23

Solution: 

(a) −6, −5, −4, −3, −2, −1

(b) −3, −2, −1, 0, 1, 2, 3

(c) −14, −13, −12, −11, −10, −9

(d) −29, −28, −27, −26, −25, −24

Q: What is a rational number?

Q: Is every integer a rational number?

Q: What is an irrational number?

Q: What numbers can be represented on the number line?

Q: When and why was the number line invented?

Q: In the number system, on what basis are the numbers classified?