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Rational numbers - can be expressed as a fraction, and can be terminating and repeating decimals. Irrational Numbers - can't be turned into fractions, and are non-repeating and non-terminating. (like pi)

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Q: What are two characteristics of a rational and irrational number?

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The sum of two irrational numbers may be rational, or irrational.

A rational number is a number that can be expressed as a ratio of two integers in the form A/B where B>0. An irrational number is a real number that is not rational.

The question is nonsense because the product of two rational numbers is never irrational.

No, they are two separate groups of numbers. A number is either rational or irrational, never both.

Yes Yes, the sum of two irrational numbers can be rational. A simple example is adding sqrt{2} and -sqrt{2}, both of which are irrational and sum to give the rational number 0. In fact, any rational number can be written as the sum of two irrational numbers in an infinite number of ways. Another example would be the sum of the following irrational quantities [2 + sqrt(2)] and [2 - sqrt(2)]. Both quantities are positive and irrational and yield a rational sum. (Four in this case.) The statement that there are an infinite number of ways of writing any rational number as the sum of two irrational numbers is true. The reason is as follows: If two numbers sum to a rational number then either both numbers are rational or both numbers are irrational. (The proof of this by contradiction is trivial.) Thus, given a rational number, r, then for ANY irrational number, i, the irrational pair (i, r-i) sum to r. So, the statement can actually be strengthened to say that there are an infinite number of ways of writing a rational number as the sum of two irrational numbers.

Related questions

Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).

yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.

Since the sum of two rational numbers is rational, the answer will be the same as for the sum of an irrational and a single rational number. It is always irrational.

Yes it will be. The set of real numbers can be divided into two distinct sets: rational and irrational. So if it is not rational, then it is irrational.

There is no number which can be rational and irrational so there is no point in asking "how".

It is always rational.

The sum of two irrational numbers may be rational, or irrational.

In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.

In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.

It may be a rational or an irrational number.

An irrational number is a real number that is not rational. A rational number is one that can be expressed as a ratio of two integers. An irrational number cannot be expressed in this way.

The product of two rational number is always rational.

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