Year 8: Identify rational and irrational numbers

What are Numbers?

Numbers are used to count, measure, and represent quantities. They can be broadly divided into two main categories: rational and irrational numbers.

Rational Numbers

Definition

Rational numbers can be expressed as a fraction, where both the numerator and denominator are integers (whole numbers). They can also be expressed as terminating decimals or repeating decimals.

Examples:

• Integers: -3, 0, 5
• Fractions: 1/2, 3/4, 7/10
• Terminating Decimals: 0.5, 1.25, 0.75
• Repeating Decimals: 0.333..., 1.111...

Irrational Numbers

Definition

Irrational numbers cannot be expressed as a fraction of two integers. They result in decimal representations that go on forever without repeating.

Examples:

• π (pi): 3.14159...
• √2 (square root of 2): 1.41421...

Key Difference: Rational numbers can be written as fractions, while irrational numbers cannot.