Mathematics Solutions Solutions for Class 8 Maths Chapter 1 Rational And Irrational Numbers are provided here with simple step-by-step explanations. These solutions for Rational And Irrational Numbers are extremely popular among class 8 students for Maths Rational And Irrational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of class 8 Maths Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class 8 Maths are prepared by experts and are 100% accurate.
Page No 2:
Question 1:
Show the following numbers on a number line. Draw a separate number line for each example.
(1)
(2)
(3)
(4)
Answer:
can be represented on the number line as follows.
![](/img/site_content/ask-answer/loader.gif)
can be represented on the number line as follows.
![](/img/site_content/ask-answer/loader.gif)
can be represented on the number line as follows.
![](/img/site_content/ask-answer/loader.gif)
can be represented on the number line as follows.
![](/img/site_content/ask-answer/loader.gif)
Page No 2:
Question 2:
Observe the number line and answer the questions.
(1) Which number is indicated by point B?
(2) Which point indicates the number ?
(3) State whether the statement, 'the point D denotes the number , is true of false.
Answer:
(1) We observe that each unit on the number line is divided into 4 equal parts.
Now, B is the tenth point on the left of 0.
So, B indicates on the number line .
So, the seventh point on the right of 0 is C that indicates on the number line.
(3) The point D is the tenth point on the right of 0. So, D indicates on the number line.
Now,
So, D denotes on the number line. Hence, the given statement is true.
Page No 3:
Question 1:
Compare the following numbers.
(1) −7, −2
(2) 0,
(3) , 0
(4) ,
(5) ,
(6) −,
(7) ,
(8) ,
(9) ,
(10) ,
Answer:
(1) We know that, 7 > 2
∴ −7 < −2.
(2) We know that, a negative number is always less than 0.
∴ .
(3) We know that, a positive number is always greater than 0.
∴
(4) We know that, −5 < 1.
∴ .
(5) We know that, 40 < 141.
∴ .
(6) We know that, −17 < −13.
∴.
Now,
∴ .
(8) Let us first compare and .
Now,
∴
∴ .
Now,
∴ .
(10) Let us first compare and .
Now,
∴
∴ .
Page No 4:
Question 1:
Write the following rational numbers in decimal form.
(1)
(2)
(3)
(4)
(5) −
Answer:
(1) The given number is .
∴ = 0.243243.... =
The decimal form of is .
(2) The given number is .
∴ = 0.428571428571.... =
The decimal form of is .
(3) The given number is .
∴ = 0.6428571428571.... =
The decimal form of is .
(4) The given number is .
∴ = 20.6
The decimal form of is −20.6.
(5) The given number is .
∴ = 0.846153846153.... =
The decimal form of is .
Page No 5:
Question 1:
The number is shown on a number line. Steps are given to show on the number line using . Fill in the boxes properly and complete the activity.
Activity:
â The point Q on the number line shows the number ........
â A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.
â Right angled â ORQ is obtained by drawing seg OR.
â l(OQ) = , l(QR) = 1
[l(OR)]2 = [l(OQ)]2 + [l(QR)]2
∴ l(OR) =
Answer:
![](/img/site_content/ask-answer/loader.gif)
â The point Q on the number line shows the number .
â A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.
â Right angled â ORQ is obtained by drawing seg OR.
â l(OQ) = , l(QR) = 1
∴ by Pythagoras theorem,
[l(OR)]2 = [l(OQ)]2 + [l(QR)]2
=
= 3
∴ l(OR) =
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 line .
Page No 6:
Question 2:
Show the number on the number line.
Answer:
![](/img/site_content/ask-answer/loader.gif)
Draw a number line as shown in the figure. Let the point O represent 0 and point Q represent 2. Draw a perpendicular QR at Q on the number line such that QR = 1 unit. Join OR. Now, âOQR is a right angled triangle.
By Pythagoras theorem, we have
OR2 = OQ2 + QR2
= (2)2 + (1)2
= 4 + 1
= 5
∴ OR =
Taking O as the centre and radius OR = , draw an arc cutting the number line at C.
Clearly, OC = OR = .
Hence, C represents on the number line.
Page No 6:
Question 3:
Show the number on the number line.
Answer:
Draw a number line as shown in the figure and mark the points O, A and B on it such that OA = AB = 1 unit. The point O represents 0 and B represents 2. At B, draw CB perpendicular on the number line such that BC = 1 unit. Join OC. Now, âOBC is a right angled triangle.
In âOBC, by Pythagoras theorem
(OC)2 = (OB)2 + (BC)2
= (2)2 + (1)2
= 4 + 1
= 5
∴ OC =
Taking O as centre and radius OC = , draw an arc cutting the number line at D.
Clearly, OC = OD =
At D, draw ED perpendicular on the number line such that ED = 1 unit. Join OE. Now, âODE is a right angled triangle.
In âODE, by Pythagoras theorem
(OE)2 = (OD)2 + (DE)2
= ()2 + (1)2
= 5 + 1
= 6
∴ OE =
Taking O as centre and radius OE = , draw an arc cutting the number line at F.
Clearly, OE = OF =
At F, draw GF perpendicular on the number line such that GF = 1 unit. Join OG. Now, âOFG is a right angled triangle.
In âOFG, by Pythagoras theorem
(OG)2 = (OF)2 + (FG)2
= ()2 + (1)2
= 6 + 1
= 7
∴ OG =
Taking O as centre and radius OG = , draw an arc cutting the number line at H.
Clearly, OG = OH =
Hence, H represents on the number line.
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