Rational and Irrational Numbers

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 integers, fractions, and terminating or repeating decimals.

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

Which of the following is NOT a rational number: Natural numbers, Integers, Terminating Decimals, or \( \pi \)?

Back

\( \pi \) is NOT a rational number.

Front

What is an example of a repeating decimal?

Back

An example of a repeating decimal is \( 3.33333... \) which can be written as \( 3.3 \) with a repeating 3.

Front

What types of numbers are included in rational numbers?

Back

Rational numbers include integers, fractions, terminating decimals, and repeating decimals.

Front

Which is the greatest rational number among \( \sqrt{81} \), \( \sqrt{1} \), \( \sqrt{9} \), and \( \sqrt{25} \)?

Back

The greatest rational number is \( \sqrt{81} \) which equals 9.

Front

What is a terminating decimal?

Back

A terminating decimal is a decimal number that has a finite number of digits after the decimal point. For example, 0.75 is a terminating decimal.

Front

What is the decimal representation of \( \frac{1}{4} \)?

Back

The decimal representation of \( \frac{1}{4} \) is 0.25, which is a terminating decimal.

Front

Is \( 0.666... \) a rational number?

Back

Yes, \( 0.666... \) is a rational number because it can be expressed as \( \frac{2}{3} \).

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as fractions, while irrational numbers cannot be expressed as fractions.