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Q: Does a real number contain the set of rational numbers?

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Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All rational numbers are real.

No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.

Real number, Rational 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.

No, not all real numbers. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

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Not necessarily. All rational numbers are real, not all real numbers are rational.

Rational numbers form a proper subset of real numbers. So all rational numbers are real numbers but all real numbers are not rational.

Rational numbers are a proper subset of real numbers so all rational numbers are real numbers.

Yes. -3 is both rational and real. -3 is an integer. All integers are rational numbers. All rational numbers are real numbers. Thus -3 is a rational number and a real number.

No. All rational numbers are real. Rational numbers are numbers that can be written as a fraction.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. Not all real numbers are rational.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. Not all real numbers are rational.

Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. All rational numbers are real.

No. Every real number is not a natural number. Real numbers are a collection of rational and irrational numbers.

Infinitely rarely, a real number is also a rational number. (There are an infinite number of rational numbers, but there are a "much bigger infinity" of real numbers.)

Not all real numbers are rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

The set of rational numbers is a subset of the set of real numbers. That means that every rational number is a real number, but not every real number is rational. The square root of 2 is an example of a real number that isn't rational; that is, it can't be expressed as the quotient of two integers.

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