Classifying Real Numbers

Front

What is a rational number?

Back

A rational number is any number that 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 is a number that cannot be expressed as a simple fraction or ratio. Its decimal representation goes on forever without repeating. Examples include √2 and π.

Front

What type of decimals are considered rational?

Back

Rational decimals are those that either terminate (like 0.5) or repeat a pattern (like 0.333...).

Front

What type of decimals are considered irrational?

Back

Irrational decimals are those that never end and have no repeating pattern, such as 0.1010010001... or π.

Front

Can a rational number be negative?

Back

Yes, rational numbers can be positive or negative. For example, -1/3 is a negative rational number.

Front

What is the decimal representation of 1/4?

Back

The decimal representation of 1/4 is 0.25, which is a terminating decimal.

Front

Is 0 a rational number?

Back

Yes, 0 is a rational number because it can be expressed as 0/1.

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 non-zero rational number and an irrational number is always an irrational number.

Front

How can you convert a repeating decimal into a fraction?

Back

To convert a repeating decimal into a fraction, set the decimal equal to a variable, multiply to shift the decimal point, and then solve for the variable.