Advertisements
Advertisements
Question
Find three rational numbers between –1 and –2
Solution 1
Let y = –1 and x = –2
Here, x > y and we have to find three rational numbers, so n = 3
∵ `d = (y - x)/(n + 1)`
= `(-1 + 2)/(3 + 1)`
= `1/4`
Since, the three rational numbers between x and y are x + d, x + 2d and x + 3d.
Now, `x + d = -2 + 1/4`
= `(-8 + 1)/4`
= `(-7)/4`
`x + 2d = -2 + 2/4`
= `(-8 + 2)/4`
= `(-6)/4`
= `(-3)/2`
And `x + 3d = - 2 + 3/4`
= `(-8 + 3)/4`
= `(-5)/4`
Hence, three rational numbers between –1 and –2 are `(-7)/4, (-3)/2` and `(-5)/4`
Solution 2
Let x = –1 and y = –2
We know, a rational number between x and y = `(x + y)/2`
A rational number between –1 and –2
= `(-1 - 2)/2`
= `-3/2`
And a rational number between –1 and `-3/2`
= `(-1 - 3/2)/2`
= `(-2 - 3)/4`
= `-5/4`
Similarly, `-7/4` is a rational number between –1 and –2.
Hence, required solution = `-3/2, -5/4, -7/4`
APPEARS IN
RELATED QUESTIONS
Examine, whether the following number are rational or irrational:
`sqrt5-2`
Give an example of two irrational numbers whose:
sum is an irrational number.
Explain why 0.15015001500015……. is an irrational form.
Which of the following is rational?
Which of the following is irrational?
State, whether the following numbers is rational or not : ( 3 - √3 )2
Insert two irrational numbers between 5 and 6.
Classify the following number as rational or irrational with justification:
`sqrt(9/27)`
Classify the following number as rational or irrational with justification:
1.010010001...
Classroom activity (Constructing the ‘square root spiral’): Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1 P2 perpendicular to OP1 of unit length. Now draw a line segment P2 P3 perpendicular to OP2. Then draw a line segment P3 P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn–1Pn by drawing a line segment of unit length perpendicular to OPn–1. In this manner, you will have created the points P2, P3,...., Pn,.... ., and joined them to create a beautiful spiral depicting `sqrt2, sqrt3, sqrt4,` ...
