Question

express each of the following decimals in the rational numbers form p/q 0.9bar and 0.57bar

Answer 1

I hope it helps you

Answer 2

Answer:

$0.\overline{9}=\frac{1}{1}$

$0.\overline{57}=\frac{19}{33}$

Step-by-step explanation:

Given Numbers $0.\overline{9}\;\:and\:\:0.\overline{57}$

To Do: Express given number in p\q form

Consider,

1st number,

$x=0.\overline{9}$

x = 0.999 ...     ..........................(1)

multiply both sides by 10

10x = 9.999...    .............................(2)

Subtract (1) from (2),

10x - x = 9.999... - 0.999...

9x = 9

x = 1/1

Therefore, $0.\overline{9}=\frac{1}{1}$

2nd number,

$x=0.\overline{57}$

x = 0.5757 ...     ..........................(3)

multiply both sides by 100

100x = 57.5757...    .............................(4)

Subtract (4) from (3),

100x - x = 57.5757... - 0.5757...

99x = 57

x = 57/99

x = 19/33

Therefore, $0.\overline{57}=\frac{19}{33}$