Question

find three rational numbers between 0.285714bar and 0.428571bar

Answer 1

0.29
0.3
0.4
these are three simple rational numbers

Answer 2

Solution :-

Given two numbers are 0.285714bar and 428571bar.

Let x = 0.285714bar

Then, x = 0.285714285714..........(1)

Since there are six repeating digits,

⇒ we will multiply both the sides of equation (1) by 1000000

⇒ x*1000000 = 0.285714285714*1000000

⇒ 1000000x = 285714.285714 .............(2)

Subtracting (1) from (2), we get.

⇒ 1000000x - x = 285714.285714 - 0.285714

⇒ 999999x = 285714

⇒ x = 285714/999999

⇒ x = 2/7

Let x = 0.428571bar

x = 0.428571428571 .............(1)

Since there are six repeating digits.

⇒ We will multiply both the sides of equation (1) by 1000000

⇒ (x*1000000) = (0.428571428571*1000000)

⇒ 1000000x = 428571.428571 ............(2)

Now, subtracting (1) from (2), we get.

⇒ 1000000x - x = 428571.428571 - 0.428571

⇒ 999999x = 428571

⇒ x = 428571/999999

⇒ x = 3/7


Now, we have to find three rational numbers between 2/7 and 3/7

⇒ Multiplying the denominators and numerators of both the fractions by 20, we get.

⇒ 2/7  =  (2*20)/(7*20) = 40/140

⇒ 3/7  =  (3*20)/(7*20) = 60/140

Three rational numbers between 40/140 and 60/140

= 42/140 ; 49/140 and 56/140

Answer.