Question

Express 0.0 overline 90 in p/q form , Where p and q are integers, q≠0​

Answer 1

Answer:

Solution: (i) 

Let x = 0.666…

Multiply by 10 we get

10x = 6.666…

x = 0.666…

subtract them we get

9x  = 6 + x

9x = 6

Divide by 9

x=6/9

simplify it by divide 3 we get

x = 2/3 Answer

(ii) 

Let x = 0.4777…

Multiply by 10 we get

10x = 4.7777…

x    = 0.4777…

subtract x we get

9x  = 4.3

Divide by 9

X = 4.3/9

To remove decimal add zero in denominator we get

x = 43/90

 

(iii) 

Let x = 0.001001…

There are 3 repeating digits so multiply by 10*10*10 = 1000 

1000x = 1.001001…

X         = 0.001001…

subtract x there we get

999 x   = 1

Divide by 999 we get

X = 1/999