What you’ll learn
Distinguish rational and irrational numbers.
Key idea
A ratio of integers with a nonzero denominator is rational; roots of perfect integer squares evaluate to integers.
Notation alone does not determine rationality; integer shifts preserve the original type.
Worked example
Classify examples and non-examples for the concept 'Distinguish rational and irrational numbers'.
Classify -8.04 as rational or irrational with evidence.
- The terminating decimal -8.04 equals -804/100.
- Reducing gives -201/25, a ratio of integers, hence rational.
Answer: Rational — -8.04=-201/25, a ratio of integers.
Quick Check
Classify examples and non-examples for the concept 'Distinguish rational and irrational numbers'.
Classify -4.79 as rational or irrational with evidence.