Respuesta :
The decimal number 0.142857 is a rational .
A rational number is defined as a number which can be written in the form p/q such that p and q are co-prime.
- Co-prime numbers do not have any common factors between them other than 1.
- Rational numbers are a subset of real numbers.
- Irrational numbers are numbers which can not be written in the form p/q where p and q are both integers. Examples of irrational numbers are √2 or any non-terminating non repeating decimals.
The decimal number given is 0.142857 . This number can be written in the form of a fraction of 142857/1000000 .
Now the prime factorization of 142857 gives 3³ x 11 x 13 x 37 and the Prime factorization of 1000000 is given by 2⁶ × 5⁶
So we can see that there are no common factors between the two numbers. Hence they are co-prime.
∴ 0.142857 is a rational number as it can be written in the form p/q.
To learn more about rational numbers visit:
https://brainly.com/question/24398433
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