Representation of Rational and Irrational Numbers on Number Line | Number Systems | Assessment | English | Grade 9

Which of the following representations of 2.44 is correct?

• 
• 
• 
• 

Answer explanation

Here, we have asked correct representation of 2.44. we will divide place between 2 and 3 into 10 equal parts. We can see 2.4 here but we have to find 2.44 which will be between 2.4 and 2.5. So again we will divide place present between 2.4 and 2.5 into 10 equal part.

Which of the following statements is true?

• -1.56 lies to the right of the zero on the number line.

• 2.4222 lies to the left of the zero on the number line.

• -6 and 2.9 both lie to the right of the zero on number line.

• -2 lies to the left of the zero and 7 lies to the right on the number line.

Answer explanation

Negative number lies to the left of the zero and positive numbers lies to the right of the zero on number line.

Which of the following representations of -1.4 is correct?

• 
• 
• 
• 

Answer explanation

Here, we have asked correct representation of -1.4. We will divide the region between -1 and -2 into 10 equal parts. On moving 4 steps to the left of -1, we reach at -1.4.

Which of the following statements is true?

• 9.2 and 9.22 lie on the same point.

• We can represent only rational numbers on the number line.

• We can represent only those numbers on the number line whose decimal expansion is non-terminating and non-recurring.

• We can represent every real number on the number line

Answer explanation

We can represent every real number on the number line.

You can locate √n for any positive integer n, after ______ has been located on the number line

• 
• 
• 
• 

Answer explanation

Which of the following options is correct?

• √6.5 comes between 2 and 3 on the number line

• √6.5 comes between -2 and -3 on the number line

• √6.5 comes between 1 and 2 on the number line

• √6.5 comes between 3 and 4 on the number line

Answer explanation

To represent √6.5 on the number line, we will take a line segment AB such that AB = 6.5 cm From B, take a distance of 1 unit and mark the new point as C. Consider the point B as 0 and mark points on number line at unit distance from each other. Now we will take the midpoint of AC (AB + BC) / 2 = (6.5 + 1) / 2 = 7.5 / 2 = 3.75 From point C move towards left and take a distance of 3.75 and name that point as O. Now we will draw semicircle with centre O and radius OC = 3.75cm. Draw a perpendicular at B that intersects the semicircle at D. Join OD. Now, AB = 6.5 units AO = OC = 3.75 units OB = AB - AO = 6.5 - 3.75 = 2.75 units By pythagoras theorem BD² = OD² - OB² = (3.75)² - (2.75)² = 14.0625 - 7.5625 BD² = 6.5 BD = √6.5 Now we will draw an arc by taking BD as the radius which will intersect the number line between 2 and 3.