Unit 3 Rational 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. Examples include 1/2, -3, and 0.75.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction. It cannot be written as a ratio of two integers. Examples include √2, π, and e.

Front

How can you identify if a number is rational or irrational?

Back

A number is rational if it can be written as a fraction a/b, where a and b are integers and b ≠ 0. If it cannot be expressed in this form, it is irrational.

Front

What is the decimal representation of a rational number?

Back

The decimal representation of a rational number either terminates (e.g., 0.5) or repeats (e.g., 0.333...).

Front

What is the decimal representation of an irrational number?

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

Front

Give an example of a rational number and explain why it is rational.

Back

Example: 1/4. It is rational because it can be expressed as a fraction of two integers (1 and 4).

Front

Give an example of an irrational number and explain why it is irrational.

Back

Example: √3. It is irrational because it cannot be expressed as a fraction of two integers.

Front

What is the sum of a rational number and an irrational number?

Back

The sum of a rational number and an irrational number is always irrational.

Front

What is the product of a non-zero rational number and an irrational number?

Back

The product of a non-zero rational number and an irrational number is always irrational.

Front

Can the square root of a non-perfect square be rational?

Back

No, the square root of a non-perfect square is always irrational.