Rational vs Irrational Numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

Front

What is an irrational number?

Back

An irrational number cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating.

Front

Is \( \sqrt{16} \) a rational or irrational number?

Back

Rational (because \( \sqrt{16} = 4 \)).

Front

Is \( \pi \) a rational or irrational number?

Back

Irrational (it cannot be expressed as a fraction).

Front

What is an example of a rational number?

Back

\( 0.75 \) (which can be expressed as \( \frac{3}{4} \)).

Front

What is an example of an irrational number?

Back

\( \sqrt{2} \) (its decimal representation is approximately 1.41421356... and does not repeat).

Front

Can a repeating decimal be a rational number?

Back

Yes, a repeating decimal can be expressed as a fraction, making it a rational number.

Front

What is the sum of \( \sqrt{4} + \sqrt{4} \)?

Back

\( 4 \) (which is rational).

Front

What is the product of two rational numbers?

Back

The product of two rational numbers is always a rational number.

Front

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

Back

The sum is always an irrational number.