Question

Look at several examples of rational numbers in the form p/q(q isn't equal to 0) where p and q are integres with no common factors other than 1 and having terminating decimal representations(expansions). Can you guess what property q must satisfy?

Answer 1

Answer:

Rational Numbers :Any number which can be represented in the form of p/q where q is greater than 0 is called a rational number.

Irrational Numbers : The real numbers which cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0 are known as irrational numbers.

If we observe some examples of Rational numbers in the form of p/q where q is greater than 0, having no factors in common rather than 1.

For example,

•1/2 , q = 2^ 1

•4/5, q = 5^1

•7/8, q = 2^3

We conclude that,

The property that q must satisfy in order that the rational numbers in the from p/q, where p and q are integers with no common factor other than 1, have maintaining decimal representation is prime factorization of q has only powers of 2 or power of 5 or both .

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Answer 2

Step-by-step explanation:

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