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Question
Observe the number line and answer the questions.
- Which number is indicated by point B?
- Which point indicates the number `1 3/4`?
- State whether the statement ‘the point D denotes the number `5/2`’ is true or false.
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Solution
Here, each unit is divided into 4 parts.
∴ the denominator will be 4.
(1) Point B is on the 10th equal part on the left side of point O.
∴ B is `(-10)/4`.
(2) `1 3/4 = (4 xx 1 + 3)/4 = (4 + 3)/4 = 7/4`
Here, Point C is marked on the 7th equal part on the right side of point O.
∴ Point C indicates `1 3/4`.
(3) `5/2 = (5 xx 2)/(2 xx 2) = 10/4` True
Point D is marked on the 10th equal part on the right side of O.
∴ D denotes the number `10/4 = 5/2`
RELATED QUESTIONS
The number `sqrt2` is shown on a number line. Steps are given to show `sqrt3` on the number line using `sqrt2`. Fill in the boxes properly and complete the activity.
Activity :
- The point Q on the number line shows the number ______.
- A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.
- Right angled ∆ORQ is obtained by drawing seg OR.
`l ("OQ") = sqrt2` , `l("QR") = 1`
`therefore` by Pythagoras theorem,
`[l("OR")]^2 = [l("OQ")]^2 + [l("QR")]^2 `
= `square^2`+ `square^2` = `square` + `square`
= `square`
∴ l(OR) = `square`
Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number `sqrt3`.
Evaluate:
`0 + (-2)/7`
Find the rational numbers represented by the question marks marked on the following number line
Draw a number line and represent the following rational numbers on it
`(-17)/(-5)`
Draw a number line and represent the following rational numbers on it
`15/(-4)`
The rational number `57/23` lies to the left of zero on the number line.
The rational number `7/(-4)` lies to the right of zero on the number line.
The rational numbers `1/2` and `- 5/2` are on the opposite sides of 0 on the number line.
The rational number `(-3)/4` lies to the right of zero on the number line.
Find a rational number exactly halfway between:
`1/15` and `1/12`
