The Difference Between Rational and Irrational Numbers - Lesson Topic Index | Grade 7 Math | Intermediate Test Prep | StudyZone

Rational numbers are numbers that can be expressed as a ratio of two integers.  They can be in fraction, decimal or whole number form.

Irrational numbers are numbers that cannot be expressed as a ratio of two integers.

Go to the lesson on number subsets for further review.

Let's take a look at "pi" (π) for example.  Pi has many different forms and approximations.

 3.14 3.1416 3.14159265... This is an approximation. This is rounded to the hundredths place. This is rounded to the ten- thousandths place (as NYS would like to see it). This is not an approximation.  Pi is an infinite number (does not repeat or end).

The three approximations of pi are rational numbers.

The actual number pi is an irrational number.

Non-perfect square roots are also irrational...

Examples are:, , and

Let's do some practice problems!

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