Unit 3: Rational/Irrational Numbers Review

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 \( \pi \) and \( \sqrt{2} \).

Front

Is \( 1.5 \) a rational number?

Back

Yes, \( 1.5 \) is a rational number because it can be expressed as \( \frac{3}{2} \).

Front

Is \( \sqrt{2} \) a rational number?

Back

No, \( \sqrt{2} \) is an irrational number because it cannot be expressed as a fraction of two integers.

Front

What is the decimal representation of a rational number?

Back

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

Front

What is the decimal representation of an irrational number?

Back

The decimal representation of an irrational number is non-terminating and non-repeating (like 0.14159265... for \( \pi \)).

Front

Is \( \frac{8}{4} \) a rational number?

Back

Yes, \( \frac{8}{4} = 2 \) is a rational number.

Front

Is \( 0.3003033... \) a rational number?

Back

Yes, \( 0.3003033... \) is a rational number because it can be expressed as \( \frac{3003}{10000} \).

Front

What is the value of \( \sqrt{9} \)?

Back

The value of \( \sqrt{9} \) is 3, which is a rational number.

Front

Is \( -\frac{\pi}{2} \) a rational number?

Back

No, \( -\frac{\pi}{2} \) is an irrational number because \( \pi \) is irrational.