Rational vs Irrational

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Examples include \( \frac{1}{2}, 3, -4.5 \).

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 \( \frac{a}{b} \) where \( a \) and \( b \) are integers. Examples include \( \sqrt{2}, \pi, e \).

Front

Is \( \sqrt{4} \) rational or irrational?

Back

Rational. \( \sqrt{4} = 2 \), which can be expressed as \( \frac{2}{1} \).

Front

Is \( \sqrt{5} \) rational or irrational?

Back

Irrational. \( \sqrt{5} \) cannot be expressed as a fraction of two integers.

Front

What is the decimal representation of \( \frac{1}{3} \)?

Back

The decimal representation of \( \frac{1}{3} \) is 0.333..., which is a repeating decimal.

Front

What is the decimal representation of \( \sqrt{3} \)?

Back

The decimal representation of \( \sqrt{3} \) is approximately 1.73205..., which is non-repeating and non-terminating.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. Examples include 1, 4, 9, 16, etc.

Front

What is a perfect cube?

Back

A perfect cube is a number that can be expressed as the cube of an integer. Examples include 1, 8, 27, 64, etc.

Front

Is \( 0.75 \) rational or irrational?

Back

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

Front

Is \( \pi \) rational or irrational?

Back

Irrational. \( \pi \) cannot be expressed as a fraction of two integers.