Approximate Irrational Numbers

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a fraction of two integers. Its decimal representation is non-repeating and non-terminating.

Front

Give an example of an irrational number.

Back

Examples of irrational numbers include √2, π, and e.

Front

What is the approximate value of √40?

Back

The approximate value of √40 is between 6 and 7.

Front

Which two integers is √77 between?

Back

√77 is between 8 and 9.

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b is not zero.

Front

Identify a rational number from the following: √20, √64, 6π, √7.

Back

√64 is a rational number because it equals 8.

Front

What is the decimal representation of the rational number -4/5?

Back

The decimal representation of -4/5 is -0.8.

Front

Is the number 0.444444444 rational or irrational?

Back

0.444444444 is a rational number because it can be expressed as 4/9.

Front

What is the significance of the number π in mathematics?

Back

π (pi) is an irrational number that represents the ratio of a circle's circumference to its diameter.

Front

How can you determine if a square root is rational or irrational?

Back

A square root is rational if the number under the root is a perfect square; otherwise, it is irrational.