Question

0.92675 in p/q form if 675 is repeating

Answer 1

I have done in pic. check ones

Answer 2

Answer:

3429/3700

(Proof in the attachment ^_^")

Note:

★ Rational number : The number which can be written in the form of p/q where p and q are integers and q ≠ 0 , is called rational number .

★ Rational numbers are characterized as ;

1). Terminating

2). Non-terminating but repeating

( Non-terminating but recurring )

★ Every terminating decimal and Non-terminating but repeating decimal can be represented in the form of p/q .

Solution:

Let the given number be x .

Thus,

x = 0.92675675.... ---------(1)

Now,

Multiplying eq-(1) by 100 , we get ;

=> 100x = 100 × 0.92675675...

=> 100x = 92.675675... --------(2)

Now,

Multiplying eq-(2) by 100 , we get ;

=> 1000 × 100x = 1000 × 92.675675...

=> 100000x = 92675.675675... -------(3)

Now,

Subtracting eq-(2) from eq-(3) , we get ;

=> 100000x - 100x = 92675.675675...

– 92.675675....

=> 99900x = 92583

=> x = 92583/99900

=> x = 3429/3700

=> 0.92675675.... = 3429/3700

Hence,

The required answer is : 3429/3700