Question

What can you say about the prime factorization of denominator of 10.3bar

Answer 1

The given real number is :

x = 10.333333.........   ----------(1)

As it is non terminating repeating Rational number.

Multiplying both sides by 10,we get

1 0 x = 103.333333......   --------(2)

(2) - (1)

1 0 x - x = 103.333333...   - 10.3333333.....

9 x = 93

x= $\frac{93}{9}=\frac{31}{3}$

As, denominator of 10.33333.... is 3, which itself is a prime number.

So Prime factors of 3 are 1 and itself that is 3.

Answer 2

Answer:

The given real number is :

x = 10.333333......... ----------(1)

As it is non terminating repeating Rational number.

Multiplying both sides by 10,we get

1 0 x = 103.333333...... --------(2)

(2) - (1)

1 0 x - x = 103.333333... - 10.3333333.....

9 x = 93

x= 93/9

x=31/3

As, denominator of 10.33333.... is 3, which itself is a prime number.

So Prime factors of 3 are 1 and itself that is 3.