Study guides

☆☆

Q: Is a number either rational or irrational but not both?

Write your answer...

Submit

Still have questions?

Related questions

Integers are rational. In the set of real numbers, every number is either rational or irrational; a number can't be both or neither.

There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.

No. Irrational means "not rational". A number either is rational, or it is not rational - tercium non datur.

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

No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.

A real number can be either rational or irrational. It can't be both at the same time.

No, no number can be both rational and irrational.

It will be irrational.

True.

It is rational.A number cannot be both rational and irrational.

If it can't be expressed as a fraction then it is an irrational number

The number 3 is a rational number (as is any integer).

No. A rational number is a number that either terminates or repeats. An irrational number neither terminates nor repeats. Therefore, it cannot be both.

The product of an irrational number and a rational number, both nonzero, is always irrational

-34 is a rational number

No.A number can fall into only one of those categories ... it can be either rational or irrational, but not both.If you pick a number that is irrational, then I know immediately that it can't be rational, since no number can be both, and you've already told me which one it is.

Integers and fractions that have integers in the numerator and denominator are rational. A number can't be rational and irrational at the same time - irrational means "not rational".

By definition, an irrational number is a number that is not rational, or in other words a number that cannot be expressed as an integer divided by another integer. A number cannot be both "rational" and "not rational."

Real numbers can be rational or irrational because they both form the number line.

A whole number k can be written in the form k/1 where k and 1 are both integers. It can, thus, be expressed in the form of a ratio and so is rational. Since it is rational it cannot be irrational. Simple!

They are both rational.

No.The definition of a rational number is a number that can be written as the quotient of two integers (and the divisor is not zero).The definition of an irrational number is a real number that cannot be written as the quotient of two integers (and the divisor is not zero).A number can either be written as the quotient of two integers or it can't. One or the other.A number cannot be both rational and irrational.

0.727272 is the ratio of 727,272 and 1,000,000. So it's nice and rational.

they are both numbers

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.