Classifying 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 of two integers, where the denominator is not zero.

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.

Front

Is 0.141414141414... rational or irrational?

Back

Rational - it can be expressed as the fraction \( \frac{14}{99} \).

Front

Is \( \sqrt{7} \) rational or irrational?

Back

Irrational - it cannot be expressed as a fraction.

Front

Is \( \sqrt{\frac{4}{25}} \) rational or irrational?

Back

Rational - it simplifies to \( \frac{2}{5} \).

Front

Is \( \sqrt{2} \) rational or irrational?

Back

Irrational - it cannot be expressed as a fraction.

Front

Which of these is an example of an irrational number: \( \sqrt{2} \), \( \sqrt{1} \), \( \sqrt{9} \), \( \sqrt{25} \)?

Back

\( \sqrt{2} \) is irrational.

Front

What is the decimal representation of a rational number?

Back

A rational number can have a terminating or repeating decimal representation.

Front

What is the decimal representation of an irrational number?

Back

An irrational number has a non-terminating, non-repeating decimal representation.

Front

Give an example of a rational number.

Back

An example of a rational number is \( \frac{3}{4} \) or 0.75.