Classifying Real Numbers

Front

What is a rational number?

Back

A rational number can be expressed as a ratio of two integers, where the denominator is not zero. Examples include 1/2, -3, and 0.75.

Front

What is an irrational number?

Back

An irrational number cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating. Examples include π and √2.

Front

Which type of decimals are considered irrational?

Back

Decimals that never end and have no repeating pattern.

Front

Is the number 4.89125... rational or irrational?

Back

Irrational.

Front

Identify the only rational number from the following: π, π/4, √2, √49.

Back

√49 (which equals 7) is rational.

Front

What is the definition of a terminating decimal?

Back

A terminating decimal is a decimal that has a finite number of digits after the decimal point, such as 0.5 or 2.75.

Front

What is the definition of a repeating decimal?

Back

A repeating decimal is a decimal that has one or more digits that repeat infinitely, such as 0.333... or 1.666... .

Front

What is the sum of two rational numbers?

Back

The sum of two rational numbers is always a rational number.

Front

What is the product of a rational number and an irrational number?

Back

The product of a rational number (other than zero) and an irrational number is always an irrational number.

Front

Can a rational number be negative?

Back

Yes, rational numbers can be positive, negative, or zero.