Question

I found somewhere written that, “Maximum number of different decimal digits in p/q is equal to q, i.e. 11/9 will have maximum of 9 different decimal digits.” I don't know whether it is correct or wrong, please tell me if it is correct or wrong with appropriate reason also give examples to support your answer.

*Source of reading is attached in the questions as image.

Answer 1

Answer:

• Wrong statement.

Step-by-step explanation:

We have,

=> p/q = 11/9

We know,

=> Terminating decimal:

• a decimal which can be expressed in a finite number of decimals.
• Ex: 1/2 = 0.5.

=> Non-terminating decimal:

• a decimal which can be expressed in a infinite number of decimals.
• Ex: √2 = 1.41421..

Now, p/q = 11/9,

=> 11/9:

• 1.22222222222.

We see that, it recurs till 11 decimals places and not 9 places.

So, the statement is a wrong statement.