Represent 9 . 7 on the number line.

To represent 9 . 7 on the number line, we proceed as under: (i) Draw a line and mark a point A on it. Take a point O on this line such that the length of segment AO = 9 . 7 units . (ii) From O , mark a point B on the line such that OB = 1 unit . (iii) Find the mid-point, say M , of the segment AB . With M as centre and radius = AM , draw a semicircle. (iv) At O , draw a perpendicular to AB meeting the semicircle at C , then OC = 9 . 7 units . (v) Treat the line AB as the number line with O representing 0 and B represent 1 and so on. Draw an arc with O as centre and radius = OC to meet the number line AB at P , then the point P represents the number 9 . 7 . Hence, the required answer is as shown above.

Represent 9 . 7 on the number line.

To represent 9 . 7 on the number line, we proceed as under: (i) Draw a line and mark a point A on it. Take a point O on this line such that the length of segment AO = 9 . 7 units . (ii) From O , mark a point B on the line such that OB = 1 unit . (iii) Find the mid-point, say M , of the segment AB . With M as centre and radius = AM , draw a semicircle. (iv) At O , draw a perpendicular to AB meeting the semicircle at C , then OC = 9 . 7 units . (v) Treat the line AB as the number line with O representing 0 and B represent 1 and so on. Draw an arc with O as centre and radius = OC to meet the number line AB at P , then the point P represents the number 9 . 7 . Hence, the required answer is as shown above.

Represent 5 . 6 on the number line.

To represent 5 . 6 on the number line, we proceed as under: (i) Draw a line and mark a point A on it. Take a point O on this line such that the length of segment AO = 5 . 6 units . (ii) From O , mark a point B on the line such that OB = 1 unit . (iii) Find the mid-point, say M , of the segment AB . With M as centre and radius = AM , draw a semicircle. (iv) At O , draw a perpendicular to AB meeting the semicircle at C , then OC = 5 . 6 units . (v) Treat the line AB as the number line with O representing 0 and B represent 1 and so on. Draw an arc with O as centre and radius = OC to meet the number line AB at P , then the point P represents the number 5 . 6 . Hence, the required answer is as shown above.

Rationalise the denominator of the following: 1 2 + 3

From the given, 1 2 + 3 Multiplying the numerator and denominator by 2 - 3 . 1 2 + 3 = 1 2 + 3 × 2 - 3 2 - 3 = 2 - 3 2 2 - 3 2 = 2 - 3 4 - 3 = 2 - 3 So, 1 2 + 3 = 2 - 3 Hence, the required answer is as shown above.

Rationalise the denominator of the following: 1 7 - 2

From the given, 1 7 - 2 Multiplying the numerator and denominator by 7 + 2 . 1 7 - 2 = 1 7 - 2 × 7 + 2 7 + 2 = 7 + 2 7 2 - 2 2 = 7 + 2 7 - 4 So, 1 7 - 2 = 7 + 2 3 Hence, the required answer is as shown above.

Rationalise the denominator of the following: 16 41 - 5

From the given, 16 41 - 5 Multiplying the numerator and denominator by 41 + 5 . 16 41 - 5 = 16 41 - 5 × 41 + 5 41 + 5 = 16 41 + 5 41 - 5 41 + 5 = 16 41 + 5 41 2 - 5 2 = 16 41 + 5 41 - 25 = 16 41 + 5 16 Hence, 16 41 - 5 = 41 + 5