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

Front

Is the number 0.525 rational or irrational?

Back

0.525 is a rational number because it can be expressed as the fraction 525/1000.

Front

Is the number π (pi) rational or irrational?

Back

π (pi) is an irrational number because it cannot be expressed as a fraction of two integers.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer.

Front

Is 125 a perfect square?

Back

No, 125 is not a perfect square because there is no integer that, when squared, equals 125.

Front

Which of the following is not a rational number: √5 or 2.5?

Back

√5 is not a rational number because it cannot be expressed as a fraction of two integers.

Front

Which of the following is a rational number: 2.5 or π?

Back

2.5 is a rational number because it can be expressed as the fraction 25/10.

Front

What is the decimal representation of a rational number like 1/3?

Back

The decimal representation of 1/3 is 0.333..., which is repeating.

Front

What is the decimal representation of an irrational number like √2?

Back

The decimal representation of √2 is approximately 1.41421356..., which is non-repeating and non-terminating.