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 or quotient of two integers. Its decimal representation is non-repeating and non-terminating.

Front

Is the number √45 rational or irrational?

Back

Irrational, because it cannot be expressed as a fraction of two integers.

Front

Is the number √25 rational or irrational?

Back

Rational, because it equals 5, which can be expressed as 5/1.

Front

Is the number -17.5 rational or irrational?

Back

Rational, because it can be expressed as -35/2.

Front

Is the number 77/3 rational or irrational?

Back

Rational, because it is expressed as a fraction of two integers.

Front

Is the number 0.141414141414... rational or irrational?

Back

Rational, because it can be expressed as the fraction 14/99.

Front

What is an example of a rational number?

Back

Examples include 1/2, -3, 0.75, and 4.

Front

What is an example of an irrational number?

Back

Examples include π (pi), e (Euler's number), and √2.

Front

How can you determine if a number is rational?

Back

A number is rational if it can be written as a fraction a/b, where a and b are integers and b is not zero.