Q.13. Convert into rational number
(i) 0.66666.........
(ii) 0.4747474747.....
(iii) 0.001001001001001.......
(iv) 0.15151515151515........
(v) 15.71212121212121212..
Answers
Answer:
Q.13. Convert into rational number.
(i) 0.66666.......
Let X = 0.6666....
Since, one digit is repeating
Therefore, Multiplying both the sides by 10
10X = 6.6666.......
10X = 6 + 0.6666.......
10X = 6 + X [ X = 0.6666.....]
10X - X = 6
9X = 6
X = 6
9
X = 2
3
(ii)0.474747....
Let X = 0.474747.....
Since, two digit are repeating
Therefore, Multiplying both the sides by 100
100X = 47.474747....
100X = 47 + 0.474747.....
100X = 47 + X [X = 0.474747.....]
100X - X = 47
X = 47
99
(iii) 0.001001001.....
Let X = 0.001001......
Since three digits are repeating
Therefore, Multiplying both the sides by 100
1000X = 1. 001001001......
1000X = 1 + 0.001001001.....
1000X = 1 + X [ X = 0.001001001...]
999X = 1
X = 1
999
(iv) 0.151515......
Let X = 0.151515....
Since two digits are repeating
Therefore, Multiplying both the the sides by 100
100X = 15.151515....
100X = 15 + 0.151515......
100X = 15 + X [X = 0.1515...]
99X = 15
X = 15
99
(v) 15.7121212......
Let X = 15.7121212.....
Since two digits are repeating
Therefore, Multiplying both the sides by 100
100X = 1571.212121.....
100X = 1555.5 + 15.71212...
100X = 1555.5 + X
99X = 1555.5
X = 15555
990