Show the number 7 on the number line.

Steps of construction: Draw a number line. Let O be the origin on the number line l . Let A be on the line such that OA = 1 unit. Draw AB perpendicular to OA at A such that AB = 1 unit. Then OB 2 = OA 2 + AB 2 = 1 2 + 1 2 = 2 . Thus OB = 2 units. With O as centre and OB as radius drawn an arc cutting the line at C . Then OC = OB = 2 units Again draw CD perpendicular to l such that CD = 1 unit. Then OD 2 = OC 2 + CD 2 = 2 + 1 = 3 . Thus OD = 3 units. Draw an arc with O as centre and OD as radius to cut l in E . Then OE = OD = 3 units. Draw EF perpendicular to l at E such that EF = 2 units and join OF . Now OF 2 = OE 2 + EF 2 = 3 + 4 = 7 . Hence, OF = 7 units. With O as centre and OF as radius, cut l at G . Then OG = OF = 7 units. Thus OG represents 7 on number line.

Show the number 7 on the number line.

Steps of construction: Draw a number line. Let O be the origin on the number line l . Let A be on the line such that OA = 1 unit. Draw AB perpendicular to OA at A such that AB = 1 unit. Then OB 2 = OA 2 + AB 2 = 1 2 + 1 2 = 2 . Thus OB = 2 units. With O as centre and OB as radius drawn an arc cutting the line at C . Then OC = OB = 2 units Again draw CD perpendicular to l such that CD = 1 unit. Then OD 2 = OC 2 + CD 2 = 2 + 1 = 3 . Thus OD = 3 units. Draw an arc with O as centre and OD as radius to cut l in E . Then OE = OD = 3 units. Draw EF perpendicular to l at E such that EF = 2 units and join OF . Now OF 2 = OE 2 + EF 2 = 3 + 4 = 7 . Hence, OF = 7 units. With O as centre and OF as radius, cut l at G . Then OG = OF = 7 units. Thus OG represents 7 on number line.

Show the following numbers on a number line. 3 2 , 5 2 , - 3 2

Let us see how to show 3 2 , 5 2 , - 3 2 on the number line. Here 3 2 = 3 × 1 2 , therefore each unit on right side of zero is divided into two equal parts. Third point from zero shows 3 2 or 3 2 = 1 + 1 2 . So the point at 1 2 distance of unit after 1 unit shows 3 2 . Fifth point from zero shows 5 2 or 5 2 = 2 + 1 2 . So the point at 1 2 distance of unit after 2 unit shows 5 2 . To show - 3 2 on the number line, the number is located to the left of zero at the same distance of 3 2 will show the number - 3 2 .

Show the following numbers on a number line. 7 5 , - 2 5 , - 4 5

Let us see how to show 7 5 , - 2 5 , - 4 5 on the number line. Here 7 5 = 7 × 1 5 , therefore each unit on right side of zero is divided into five equal parts. Seventh point from zero shows 7 5 or 7 5 = 1 + 2 5 . So the point at 2 5 distance of unit after 1 unit shows 7 5 Second point from zero shows 2 5 . To show - 2 5 on the number line, the number is located to the left of zero at the same distance of 2 5 will show the number - 2 5 Fourth point from zero shows 4 5 . To show - 4 5 on the number line, the number is located to the left of zero at the same distance of 4 5 will show the number - 4 5 Hence, the representation of numbers 7 5 , - 2 5 , - 4 5 are shown below:

Show the following numbers on a number line. - 5 8 , 11 8

Let us see how to show - 5 8 , 11 8 on the number line. Here 11 8 = 11 × 1 8 , therefore each unit on right side of zero is divided into eight equal parts. Eleventh point from zero shows 11 8 or 11 8 = 1 + 3 8 . So the point at 3 8 distance of unit after 1 unit shows 11 8 Fifth point from zero shows 5 8 . To show - 5 8 on the number line, the number is located to the left of zero at the same distance of 5 8 will show the number - 5 8 So, the number line is represented as:

Show the following numbers on a number line. 13 10 , - 17 10

Let us see how to show 13 10 , - 17 10 on the number line. Here 13 10 = 13 × 1 10 , therefore each unit on right side of zero is divided into ten equal parts. Thirteenth point from zero shows 13 10 or 1 + 3 10 . So, the point at 3 10 distance of unit after 1 unit shows 13 10 Seventeenth point from zero shows 17 10 or 1 + 7 10 . So, the point at 7 10 distance of unit after 1 unit shows 17 10 To show - 17 10 on the number line, the number is located to the left of zero at the same distance of 17 10 will show the number - 17 10

Show the number 5 on the number line.

Represent a point A such that O A = 2 units on the number line. Draw a line X perpendicular to the number line through the point A Take a point B on the line A X such that it is at unit distance from A . Draw a segment O B such that a right angled triangle ∆ O A B is formed. Now, using Pythagoras theorem, O B 2 = O A 2 + A B 2 O B 2 = 2 2 + 1 2 O B 2 = 5 or O B = 5 Draw an arc with centre O and radius O B . Mark the point of intersection of the line and the arc as C . The point C shows the number 5