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Yes, as long as the two nonzero numbers are themselves rational. (Since a rational number is any number that can be expressed as the quotient of two rational numbers, or any number that can be written as a fraction using only rational numbers.) If one of the nonzero numbers is not rational, the quotient will most likely be irrational.

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โˆ™ 2011-08-23 01:34:20
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Q: Is the quotient of two nonzero numbers always a rational number?
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Related questions

Should the quotient of an integer and a nonzero integer always be rational?

No.


Is the quotient of an integer divided by a nonzero integer always be a rational number Why?

Yes, always. That is the definition of a rational number.


Is the quotient of an integer divided by a nonzero integer always a rational number?

Yes.


Can the quotient of an integer be divided by a nonzero integer a rational number always?

Yes, it is.


Why is the quotient of an integer divided by a nonzero integer always a rational number?

Because that is how a rational number is defined!


Should the quotient of an integer divided by nonzero integer always be a rational number?

Yes, by definition.


Is the quotient of two rational number always rational numbers?

yes


Should the quotient of an integer divided by a nonzero integer always be a rational number?

I had this name question for homework :| no


Is the quotient of two integers always a rational numbers?

Yes


What if two rational numbers are divided is the quotient always going to be a rational number?

Not if the second rational number is 0: in that case the quotient is not defined. Otherwise the answer is yes.


The quotient of two rational numbers is always a rational number?

Yes, that's true. * * * * * Unless the second number is 0, in which case the quotient is not defined!


Why the product of nonzero rational number and a rational number is an irrational?

Actually the product of a nonzero rational number and another rational number will always be rational.The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)


Is the quotient of two irrational numbers rational?

In general, no. It is possible though. (2pi)/pi is rational. pi2/pi is irrational. The ratio of two rationals numbers is always rational and the ratio of a rational and an irrational is always irrational.


Is a nonzero integer always be a rational number?

Yes.


What is always the result of dividing an integer when the divisor is nonzero?

A rational number is always the result of dividing an integer when the divisor is nonzero.


Is the product of a nonzero rational number and an irrational number rational or irrational?

It is always irrational.


Is a rational number divided by an irrational number always irrational?

No. If we let x be irrational, then 0/x = 0 is a counterexample. However, if we consider nonzero rational numbers, then our conjecture is true. We shall prove this by contradiction. Suppose we have nonzero rational numbers x and y, and an irrational number z, such that x/z = y. Since z is not equal to 0, x = yz. Since y is not equal to 0, x/y = z. Since x/y is a quotient of rational numbers, x/y is rational. Therefore, z is rational, contradicting our assumption that z was irrational. QED.


Is the product of a nonzero rational and a irrational number irrational?

Yes, always.


Is the quotient of a rational number and an irrational number rational?

No. It's always irrational.


Is a rational number a real number?

Yes, a rational number is a real number. A rational number is a number that can be written as the quotient of two integers, a/b, where b does not equal 0. Integers are real numbers. The quotient of two real numbers is always a real number. The terms "rational" and "irrational" apply to the real numbers. There is no corresponding concept for any other types of numbers.


Will repeating decimals always or never be rational numbers?

They will always be rational numbers.


Is the product of a nonzero rational number and an irrational number irrational?

Yes, always.


The quotient of two integers is always a rational number?

Yes. All numbers are rational numbers except repeating decimals like 1.3(repeating). * * * * * Repeating decimals are also rationals. However, the quotient is not defined if the second number is the integer zero!


What is a quotient of two integers that is always a rational number?

It is an incomplete definition of a rational number.


What type of numbers are always significant?

All nonzero numbers are significant.