MAP 8th Grade Math

A comprehensive course covering essential 8th grade math concepts to prepare students for high school and real-world problem solving.

Basic Concepts

Rational and Irrational Numbers

Understanding Numbers

Numbers can be sorted into different groups based on their properties. Two important groups you’ll see in 8th grade are rational and irrational numbers.

Rational Numbers

Rational numbers are numbers that can be written as a fraction, where both the numerator and denominator are integers and the denominator isn’t zero. This includes all integers, fractions, and repeating or terminating decimals.

Irrational Numbers

Irrational numbers cannot be written as a simple fraction. Their decimal expansions go on forever without repeating. Famous examples are \( \pi \) and \( \sqrt{2} \).

Why It Matters

Knowing the difference helps you work with all kinds of numbers in algebra, geometry, and beyond!

Spotting the Difference

  • Rational numbers: \( \frac{3}{4}, -2, 0.75, 5 \)
  • Irrational numbers: \( \pi, \sqrt{3}, 0.1010010001\ldots \)

Real-Life Connections

Rational and irrational numbers appear in real measurements, engineering, and science, like measuring areas or calculating distances involving circles.

Examples

  • The number 7.5 is rational because it can be written as \( \frac{15}{2} \).

  • The number \( \sqrt{5} \) is irrational because its decimal never ends or repeats.

In a Nutshell

Rational numbers can be written as fractions; irrational numbers can’t and have endless, non-repeating decimals.

Key Terms

Rational Number
A number that can be written as a fraction of two integers.
Irrational Number
A number that cannot be written as a fraction; its decimal goes on forever without repeating.