Question

What can you say about the prime factorization of the denominator of the rational number 27.142857 bar.

Answer 1

3^2 (111111)is factor

Answer 2

$\bold{\frac{27142830}{3^{2}(111111)}}$ is the prime factorization of the denominator of the rational number $\bold{27 . \overline{142857}}$.

Given:

$27 . \overline{142857}$

To find:

Prime factorization of the denominator of the rational number = ?

Solution:

The rational number given in the question is $27 . \overline{142857}$

Now to find the denominator  

Let us shift the decimal back to seven to get the value of  $27142857 . \overline{142857}$

Now subtract the number $27142857 . \overline{142857}$ with $27 . \overline{142857}$

Subtracting  $1000000 x-x$ we get the value of $999999 x$

$1000000 x-x=27142857 . \overline{142857}-27 . \overline{142857}$

After subtracting the value of $27142857 . \overline{142857}-27 . \overline{142857}$ we get the value of $27142830$

$999999 x=27142830$

The value after prime factorization stands for:

$\bold{x=\frac{27142830}{999999}=\frac{27142830}{3^{2}(111111)}}$ .