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; it cannot be written as a ratio of two integers.

Front

Give an example of a rational number.

Back

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

Front

Give an example of an irrational number.

Back

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

Front

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

Back

The sum of a rational number and an irrational number is always irrational.

Front

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

Back

The product is always irrational.

Front

Is the number 0.333... rational or irrational?

Back

Rational, because it can be expressed as 1/3.

Front

Is the number √3 rational or irrational?

Back

Irrational, because it cannot be expressed as a fraction.

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation.

Front

What is scientific notation?

Back

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, typically in the form a × 10^n.