Question

express the following recurring decimals as a rational number i) 0.4 ii) 0.21 iii) 0.14 iv)19.45 v) 0.124 ​

Answer 1

Explanation:

1] 0.444444444......... = x .......(1)

multiply both side by 10, we get

4.444444.... = 10x .......(2)

Subtract the equation (2) by (1) we get

4.444444.... - 0.444444 = 10x - x

4 = 9x

x =
`(9)/(4)` (divide both side by 4)

0.444444444......... = 9/4

2] Let 0.212121212121.......= X .....(1)

Multiply both side by 100 we get

21.2121212121..... = 100X ........(2)

Subtract the equation (2) by (1) we get

21.2121212121..... - 0.212121212121....... = 100X - X

21 = 99X

X = 21/99

0.212121212121....... = 21/99