Classify: Rational or Irrational

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction or quotient of two integers. Its decimal representation is non-repeating and non-terminating.

Front

Give an example of a rational number.

Back

An example of a rational number is 1/2, 3, or -4.

Front

Give an example of an irrational number.

Back

An example of an irrational number is √2, π (pi), or e (Euler's number).

Front

What is the decimal representation of a rational number like?

Back

The decimal representation of a rational number either terminates (e.g., 0.75) or repeats (e.g., 0.333...).

Front

What is the decimal representation of an irrational number like?

Back

The decimal representation of an irrational number is non-terminating and non-repeating (e.g., 3.14159... for π).

Front

Can the sum of two rational numbers be irrational?

Back

No, the sum of two rational numbers is always rational.

Front

Can the sum of a rational number and an irrational number be rational?

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No, the sum of a rational number and an irrational number is always irrational.

Front

Can the product of two irrational numbers be rational?

Back

Yes, the product of two irrational numbers can be rational (e.g., √2 * √2 = 2).

Front

What is the difference between rational and irrational numbers in terms of their representation on the number line?

Back

Rational numbers can be precisely located on the number line, while irrational numbers cannot be expressed as exact points.