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 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 12 a rational number?

Back

Yes, 12 is a rational number because it can be expressed as 12/1.

Front

Is 5/2 a rational number?

Back

Yes, 5/2 is a rational number because it is the quotient of two integers.

Front

Which of the following is rational: π, √25, √12?

Back

√25 is rational because it equals 5, which is an integer.

Front

Which of the following is irrational: 9.6, √45, 3/8?

Back

√45 is irrational because it cannot be expressed as a fraction of two integers.

Front

Is √64 a rational number?

Back

Yes, √64 is rational because it equals 8, which is an integer.

Front

What is an example of an irrational number?

Back

An example of an irrational number is π (pi), which cannot be expressed as a fraction.

Front

What is the decimal representation of a rational number?

Back

The decimal representation of a rational number either terminates (e.g., 0.5) or repeats (e.g., 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 (e.g., 0.14159... for π).